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The Kalman filter is an iterative state estimation algorithm employed extensively, including in electricity generation, aerospace, robotics, etc. Inputting noisy measurements on a dynamical system, it outputs a state estimate and associated covariance. This work focuses on the time evolution of the covariance matrix given regular, uniform measurements. Prior work has derived important results for the covariance at $t\rightarrow \infty $ , but has inadequately described the approach to that fixed point. That behavior is determined by the Jacobian of the Kalman iteration, evaluated at the fixed point. I show that the Jacobian factors into the Kronecker product of a “square root” matrix times itself, resulting in special convergence properties for the Kalman filter. When the leading eigenvalues of the square-root are a complex conjugate pair, the Jacobian matrix has 3 leading eigenvalues of equal magnitude, producing a triplet of modes all decaying at the same exponential rate. One has simple exponential decay and the other two oscillate sinusoidally with exponentially decaying amplitude. I demonstrate the process using two example kinematic systems, with Gaussian white noise in acceleration or jerk, respectively. The examples parameterize the trade-off between the sensor’s measurement rate versus its spatial precision. Interestingly, the first example toggles from triplet-dominated to singlet-dominated by increasing the process noise. In sum, this work provides needed analytical insight into the behavior of Kalman filters and algebraic Riccati equations in general.

This paper investigates the adaptive control for a class of uncertain nonlinear systems under denial-of-service (DoS) attacks. We analyze the closed-loop system stability under DoS attacks in terms of attack duration, attack frequency and resting time duration respectively. Three scenarios of DoS attacks against the system stability are considered. Firstly, it is shown that if the duration of each attack is less than a given constant, asymptotical convergence of system output is still preserved. Secondly, if the bounds on the frequency and duration of attacks with respect to overall intervals meet certain conditions, the proposed event-triggered control scheme guarantees that all the closed-loop signals are globally bounded and the stabilization error converges to a ball with a radius arbitrarily small. Thirdly, if resting time duration meets certain conditions after an arbitrarily long attack, closed-loop boundedness is still preserved. Simulation results are shown to illustrate the effectiveness of the proposed control schemes. [ABSTRACT FROM AUTHOR]

Typical communication and detection issues in a nonideal information environment, such as sensing failure, communication and sensing delay, and packet loss, further aggravate the adverse impacts of human-driven vehicle (HV) uncertainty on a mixed vehicle platoon. To guarantee the performance of the mixed vehicle platoon featuring HVs and connected and automated vehicles under the nonideal information environment, this article proposes a platoon control strategy integrating a combined longitudinal and lateral control and message recovery. Specifically, by building the dataset associated with HV behaviors, a long short-term memory (LSTM) predictor is established to recover the problematic HV messages (i.e., position, velocity, and heading) caused by the nonideal information environment. Furthermore, based on the boundary of the HV states, an evaluation and correction (EC) method is presented to suppress the adverse impacts of prediction failures. Then, a combined longitudinal and lateral controller cooperating with the LSTM predictor and EC method is developed to enhance the stability and safety of the mixed vehicle platoon under the nonideal information environment. In a theoretical analysis, the relatedness between the asymptotic stability and string stability of the platoon and predictor accuracy is strictly proved. Finally, comparative experiments verify the effectiveness of the proposed control strategy by employing driver-in-the-loop simulations. [ABSTRACT FROM AUTHOR]

This paper investigates the stability problem of fractional-order periodic piecewise nonlinear systems. As a preparation, the existence and uniqueness of solutions of the system are derived under the Lipschitz condition and expressed in an equivalent integral expression based on the memorability of fractional derivative. We further propose an upper bound of the system states by using the Laplace transform technique. With the help of piecewise Lyapunov functions and class- $\mathcal {K}$ functions, some sufficient conditions are given to verify the Mittag-Leffler and asymptotic stability of the investigated system mixed with stable and unstable subsystems. Furthermore, asymptotic stability criteria are proposed for a general case, i.e., all subsystems are unstable. Three numerical simulation examples are finally provided to illustrate the effectiveness of the proposed results.

Modular multilevel converter (MMC) has achieved its popularity in wide range of voltage applications over other multilevel topologies due to its modularity, scalability, and ease of design. A typical MMC is composed of many capacitors and the voltages across them are required to be measured for the control of system variables like the circulating current and for capacitor voltage balancing. The number of capacitors and their associated measurement devices increase with higher voltage levels. Hence, to reduce the economical and design burden, several techniques for the observation of capacitor voltages have been presented till date. In this article, capacitor voltages of the submodules are observed using a simple Lyapunov-based observer (LBO) and the convergence proof of the observation error is established mathematically. The performance of the proposed LBO is studied in simulation using MATLAB/Simulink and also experimentally validated. The proposed observer is also compared in simulation with two other existing observation techniques from literature. [ABSTRACT FROM AUTHOR]

This article addresses a fundamental issue in power converter control. Namely, the direct output-voltage control of power converters with higher order dynamics. We argue that despite of the burst in the development of new topologies, legacy control design principles—inherited from second-order converter analysis— have been unduly adopted as de facto rules of procedure. In particular, we refer to the minimum-phase requirement on the feedback variable, as the underlying stabilizing mechanism. In this article, we demonstrate that the requirement of minimum-phaseness for higher order converters and the legacy ad hoc solution via ancillary current control, can be bypassed without compromising closed-loop performance. To prove this, we unveil important differences between stability properties of second-order and higher order converters. Then, we introduce new linear and nonlinear control design strategies that permit direct output-voltage control. Experimental results are provided to validate the theory. [ABSTRACT FROM AUTHOR]

In this article, we propose a backstepping (BS)-based direct power control (DPC) strategy for the dual-cage rotor brushless doubly fed induction generator (DCR-BDFIG). The relationship between the power winding (PW) output power and the control winding (CW) voltage is derived according to the complete mathematical model of DCR-BDFIG. Based on that, a BS-based DPC controller, also known as a nonlinear controller, is designed with the global asymptotic stability analyzed for the grid-connected DCR-BDFIG. Compared with the dual-closed-loop control in the advanced vector control method, only single-closed-loop is required for the PW power in the proposed BS-based control scheme, and thus it has more simple structure and faster responses. The global stability of the proposed control scheme can be easily guaranteed with a Lyapunov function properly selected. In addition, in order to improve the performance of the proposed BS-based DPC strategy under unbalanced network, the resonant controller is introduced to suppress the oscillating components in the PW power, PW current, and CW current, whose harmonic order is twice of the grid frequency referring to the synchronous reference frame. Finally, the detailed experimental results demonstrate the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

To cope with future goal of efficiency, next generation of more electrical aircraft is likely to embed reconfigurable microgrid for the primary electrical distribution. The stability analysis of such time-varying structure is challenging. Conventional linear and nonlinear approaches failed to produce proper answers from a practical point of view. Under conditions, passivity property of each equipment is sufficient to ensure stability of the overall microgrid. But with improper passivity-based control (PBC) design, the passivity property may not be propagated. The main contribution of this article is to propose a modified IDA-PBC procedure that will ensure the passivity properties of the system regarding its electrical inputs and outputs involved in the interconnection. Thus, for electrical microgrids resulting from the interconnection of controllable equipment, input/output filters, and electrical lines, if all the equipment embed the proposed control, the whole microgrid have passive properties and the global stability of the system is ensured. Moreover, this article will also present how to achieve the proposed control with high transient and robust performances thanks to nonlinear parameters’ estimator preserving the passivity proper. Experimental validation of the proposed control in representative electrical conditions is provided. [ABSTRACT FROM AUTHOR]

The asymptotic stability and extended dissipativity performance of T-S fuzzy generalized neural networks (GNNs) with mixed interval time-varying delays are investigated in this paper. It is noted that this is the first time that extended dissipativity performance in the T-S fuzzy GNNs has been studied. To obtain the improved results, we construct the Lyapunov-Krasovskii functional (LKF), which consists of single, double, triple, and quadruple integral terms containing full information of the delays and a state variable. Moreover, an improved Wirtinger inequality, a new triple integral inequality, and zero equation, along with a convex combination approach, are used to deal with the derivative of the LKF. By using Matlab’s LMI toolbox and the above methods, the new asymptotic stability and extended dissipativity conditions are gained in the form of linear matrix inequalities (LMIs), which include passivity, $L_{2}-L_{\infty }$ , $H_{\infty }$ , and dissipativity performance. Finally, numerical examples that are less conservative than previous results are presented. Furthermore, we give numerical examples to demonstrate the correctness and efficacy of the proposed method for asymptotic stability and extended dissipativity performance of the T-S fuzzy GNNs, including a particular case of the T-S fuzzy GNNs.

This paper is concerned with the stability analysis of fixed-point state-space digital filters with generalized overflow arithmetic and a time-varying delay. This paper aims to derive a delay and nonlinear function bound dependent asymptotical stability criterion with less conservatism. Firstly, a new Lyapunov functional with several augmented terms, including extra free matrices and overflow nonlinear function, is constructed such that it has a relaxed positive condition. Then, for bounding the summation term arising in the forward difference of Lyapunov functional, a new lemma is developed to introduce the terms for linking the delayed states and the overflow nonlinear function, the Wirtinger-based summation inequality and several zero-value terms are applied to add more cross terms. As a result, a stability criterion with less conservatism is established and its conservatism. Finally, several numerical examples are given to illustrate the advantages of the proposed method.

This article presents an effective method to address the tracking control problem arising in uncertain switched high-order nonlinear system in strict-feedback form. The system under consideration contains unknown functions, which causally make the asymptotic tracking performance difficult to be achieved. By adopting the adding a power integrator approach in the framework of backstepping, a novel tracking controller is developed to guarantee an asymptotic tracking performance in the presence of the approximation error cased by neural networks (NNs) under arbitrary switching. The main contributions lie in: 1) the article for the first time embeds the backstepping technique in designing a kind of discontinuous controller with proportional integral (PI) compensation and 2) with the help of Filippov’s theory, a new defined system described by differential inclusions can be first obtained by taking some transformations, and then a novel nonsmooth Lyapunov function approach along with its upper right Dini derivative technique is applied to complete the construction of the discontinuous controller. Finally, two simulation examples are exhibited to verify the validity of the proposed design techniques. [ABSTRACT FROM AUTHOR]

In this article, a passivity-based virtual oscillator control strategy with enhanced synchronization stability for grid-forming inverters (GFMs) is proposed. By adopting the port-controlled Hamiltonian system theory for orbital stabilization problems, an energy pumping-and-damping block is proposed to render GFMs globally asymptotically stable with respect to the prespecified solutions of the power-flow equations from any initial condition. This allows for stable integrations of GFMs to any other globally asymptotically stable systems without their explicit knowledge, e.g., helping maintain synchronism with the bulk power system in a wide range of short-circuit-ratio conditions or under large disturbances and keeping synchronism among multiple GFMs in power systems. Both simulations and experiments are presented to demonstrate the proposed control approach. [ABSTRACT FROM AUTHOR]

This article presents a novel Lyapunov-based model predictive control strategy for squirrel-cage induction motor fed by a voltage source inverter. The model predictive control method has received enormous attention thanks to its rapid response to load perturbations. However, the traditional model predictive control method may suffer from instability due to the poor choice of the objective function, weighting factors, or other design parameters. In particular, the selection of the objective function may not be sufficient to ensure global stability. Since the performance of the model predictive control method highly relies on the explicit model of the system, a simple penalization term in the objective function can lead to system instability. As a result, the transient and steady-state performances are negatively affected. The objective function is reformulated as the Lyapunov energy function to deal with this ambiguous situation in this article. The control input constraints are defined in the formulated optimal control problem, and the optimal solution is explored by assessing the Lyapunov stability criterion. The proposed method ensures asymptotic stability since the control action that satisfies the Lyapunov stability condition is selected. The experimental work proves the theoretical concepts. Moreover, the proposed method does not require the weighting factors to control the multiple control goals. The experimental results demonstrate that the proposed control strategy improves the steady-state performance. The machine torque and speed are well regulated, and the quality of the stator current is improved. [ABSTRACT FROM AUTHOR]

This article is concerned with the stochastic stability and $l_{1}$ -gain control of two-dimensional (2-D) positive Markov jump systems (PMJSs) with directional delays based on the Roesser model. First, necessary and sufficient conditions (NSCs) for the stochastic stability of the addressed system are established by constructing a deterministic “equivalent” system and applying a stochastic copositive Lyapunov function. This reveals that the stochastic stability of 2-D PMJSs with delays is affected by the size of directional delays, the transition matrix, and system matrices. Second, the exact $l_{1}$ -gain index is calculated and NSCs in the form of linear programming (LP) are established for the addressed system. Systematic methods for the $l_{1}$ -gain controller design are proposed so that the closed-loop system (CLS) is positive and stochastically stable and has an optimal $l_{1}$ -gain performance, which is achieved using an iterative algorithm and an analytical calculation method for a single-input case. Finally, the potency and accuracy of the theoretical results are verified using two examples. [ABSTRACT FROM AUTHOR]

For output-constrained switched systems, uniformly local stabilization problem via state feedback is addressed. A unified tool, a common tangent-type barrier Lyapunov function (Tan-BLF), is developed to deal with the stabilization problem of switched systems and to cope with constraints imposed on system output with or without. Then, combining adding a power integrator technique (APIT) and the developed common barrier Lyapunov function, state-feedback stabilizing laws are designed systematically to make the resultant closed-loop switched systems asymptotically stable while preventing the violation of output constraints. The efficiency of the proposed method is illustrated by numerical results. [ABSTRACT FROM AUTHOR]

In this article, the problem of stability is investigated for a class of hybrid time-delay systems with double degrees. The systems consist of both discrete and continuous subsystems that have homogeneity and nonzero degrees. Conditions are derived to guarantee the preasymptotic stability of the systems. The relationships of solutions are established between the systems with different sizes using homogeneous properties. Then, equivalent conditions are presented for the analysis of preasymptotic stability. Furthermore, necessary and sufficient delay-independent conditions are developed to analyze the stability of the systems. Finally, two examples are provided to illustrate the effectiveness of the proposed new stability analysis methods. [ABSTRACT FROM AUTHOR]

This article investigates the fixed-time adaptive fuzzy containment control problem for nonlinear multiagent systems under the directed communication topologies. The controlled systems have the unknown internal dynamics and mismatched disturbances, and fuzzy logic systems are utilized to identify the unknown internal dynamics. The mismatched disturbances and approximate errors are reconstructed via a disturbance observer. Then, by introducing an adding power integral method, a fixed-time adaptive fuzzy containment DSC scheme is developed to deal with the problem of “computation complexity.” The presented containment control method can not only guarantee that the controlled system is semiglobal practical fixed-time stable, but also avoid the “singular problem” in fixed-time backstepping recursive control technology. Finally, an application of marine surface vehicle is provided to verify the effectiveness of the presented fixed-time fuzzy containment control method. [ABSTRACT FROM AUTHOR]

This article discusses the prescribed performance control problem for multiagent systems involving the state triggering and the controller output triggering simultaneously. To successfully apply the backstepping technique in the event-triggered control design, the virtual control signal is constructed by the original system state. Compared with the existing results on the prescribed performance, a new barrier Lyapunov function is developed with considering the characteristics of multiagent systems, and a fuzzy adaptive event-triggered control protocol is proposed by the backstepping procedure. It guarantees that the consensus tracking error converges to a predefined region of the origin in a preset finite time. At the same time, all other closed-loop signals remain bounded without the Zeno behavior. Finally, a simulation example confirms the availability of the developed control scheme with a comparison. [ABSTRACT FROM AUTHOR]

This article addresses the delay-dependent Takagi–Sugeno (T–S) fuzzy state feedback control and exponential admissibility analysis for a class of T–S fuzzy singular uncertain systems. First, the T–S fuzzy model is employed to approximate the singular uncertain system with time-varying delay, saturation input, and unmatched disturbance. Second, the delay-dependent T–S fuzzy state feedback controller is designed by employing the T–S fuzzy model. Third, the free-weighting matrices and delay-dependent Lyapunov–Krasovskii functional with multiple integral terms are employed to derive the delay-dependent exponential admissibility conditions and prescribed H-infinity performance is guaranteed. Compared with previous works, the delay-dependent T–S fuzzy state feedback controller is designed for the T–S fuzzy singular uncertain system to relax system design conditions. The convex hull lemma is employed to convert the closed-loop system with saturation input into the closed-loop system without saturation input to enhance controller design flexibility. The Schur complement lemma and Gronwall Bellman lemma are employed to derive the less conservative delay-dependent stability conditions for determining controller gain matrices. The exact invariant set with less conservativeness is employed to convert the controller design problem into linear matrix inequalities (LMIs) optimization constraints to reduce computation complexity of solving LMIs. Finally, simulation examples are presented to show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this brief, emphasis is placed on the global uniform asymptotic stability analysis of a switched system formulated by cyclic or periodic switching laws. First, several concepts and properties of cyclic or periodically switched systems are defined. Next, by using the cycle dwell time or cyclic period time switching method, new stability criteria for cyclic or periodically switched systems with all Hurwitz stable sub-systems are obtained in the context of general solutions. Moreover, new stability conditions for cyclic or periodically switched systems with partially unstable sub-modes are derived in the framework of general solutions. Finally, two examples are provided to demonstrate the feasibility of the developed criteria. [ABSTRACT FROM AUTHOR]

This brief addresses the problem of global asymptotic stability for impulsive switched nonlinear systems (ISNSs) with double state-dependent delays (DSDDs), where the state-dependent delays exist in both subsystem functions and impulsive functions. The innovations of our results are that: 1) Due to the ubiquitous asynchronous phenomenon between the switches and impulses in many practical systems, we investigate the asynchronous phenomenon for ISNSs with DSDDs. 2) Meanwhile, the stabilizing and destabilizing effects of state-dependent delays impulses are fully considered. 3) By utilizing multiple Lyapunov functions, the switching strategy and the impulsive strategy, based on the asynchronous phenomenon, some stability criteria on global asymptotic stability are presented for ISNSs with DSDDs. As a result, the existing results are improved and can be regarded as a special case of the stability criteria in this brief. A simulation example is provided to verify the effectiveness of the developed methods. [ABSTRACT FROM AUTHOR]

In this brief, a new criterion to determine whether the roots of a polynomial $p(z^{-1})$ with real coefficients are strictly inside the unit circle is presented. It is based on representing the polynomial in a form corresponding to the characteristic polynomial of a closed-loop systems in which all-pass transfer functions are included in both direct chain and feedback loop. The novel and simple criterion for assessing the asymptotic stability of linear discrete-time systems is proved applying the small-gain theorem in the discrete-time domain. [ABSTRACT FROM AUTHOR]

This article is concerned with the stability of the closed-loop system using various control policies generated by value iteration. Some stability properties involving admissibility criteria, the attraction domain, and so forth, are investigated. An offline integrated value iteration (VI) scheme with a stability guarantee is developed by combining the advantages of VI and policy iteration, which is convenient to obtain admissible control policies. Also, based on the concept of attraction domain, an online adaptive dynamic programming algorithm using immature control policies is developed. Remarkably, it is ensured that the state trajectory under the online algorithm converges to the origin. Particularly, for linear systems, the online ADP algorithm with a general scheme possesses more enhanced stability property. The theoretical results reveal that the stability of the linear system can be guaranteed even if the control policy sequence includes finite unstable elements. The numerical results verify the effectiveness of the present algorithms. [ABSTRACT FROM AUTHOR]

This article proposes a novel fixed-time converging forward-backward-forward neurodynamic network (FXFNN) to deal with mixed variational inequalities (MVIs). A distinctive feature of the FXFNN is its fast and fixed-time convergence, in contrast to conventional forward-backward-forward neurodynamic network and projected neurodynamic network. It is shown that the solution of the proposed FXFNN exists uniquely and converges to the unique solution of the corresponding MVIs in fixed time under some mild conditions. It is also shown that the fixed-time convergence result obtained for the FXFNN is independent of initial conditions, unlike most of the existing asymptotical and exponential convergence results. Furthermore, the proposed FXFNN is applied in solving sparse recovery problems, variational inequalities, nonlinear complementarity problems, and min–max problems. Finally, numerical and experimental examples are presented to validate the effectiveness of the proposed neurodynamic network. [ABSTRACT FROM AUTHOR]

Underactuated systems are widely applied in industry, construction, manufacturing, etc., and the complex working environment puts forward higher demands for safety and transient performance. Hence, it is necessary to consider how to simultaneously ensure actuated and unactuated motion constraints by fewer control inputs, especially when systems suffer from model uncertainties, unavailable velocities, etc. Unfortunately, it is still a significant challenge to overcome in real applications and theoretical analysis. Additionally, most existing studies merely consider the specific control objects and few general methods are applicable to a class of underactuated systems. To this end, we design a new adaptive output-feedback controller for a class of uncertain underactuated systems. Compared with existing methods only handling actuated constraints, an important merit of this article is that by introducing the elaborately designed coupling term composed of actuated and unactuated constraints together, all state variables are kept within the preset time-variant ranges and converge to their desired values. Furthermore, a new Lyapunov function candidate is utilized to provide a theoretical guarantee. As far as we know, without the need of exact model knowledge and velocity feedback, this article provides the first solution to achieve accurate motion control and state constraints for both actuated and unactuated variables, which is meaningful both theoretically and practically. Meanwhile, the asymptotic stability of the equilibrium point for the closed-loop system is proven by utilizing Lyapunov techniques and Barbalat’s lemma. For verification, the presented controller is applied to underactuated overhead and rotary cranes, respectively, together with detailed theoretical analysis and experimental validations. [ABSTRACT FROM AUTHOR]

Distributed population dynamics offer a game-theoretical framework for distributed decision making. As such, the application of these methods to the control of networked systems has been widely studied in the literature. The theoretical analyses available in the literature have only considered continuous-time formulations of distributed population dynamics. However, given that modern computers can only process information in a discrete-time fashion, the practical implementation of distributed population dynamics-based methods is inevitably discrete. In consequence, it is paramount to extend the available theory to a more implementable discrete-time approach. For that reason, in this article, we provide a discrete-time analysis of a general class of distributed population dynamics, and we derive sufficient conditions on the discretization time to ensure the asymptotic stability of the discretized dynamics. To illustrate the relevance and performance of the proposed methods, we apply the developed theory to distributed optimization and control problems, including a real multirobot platform, which consider noncomplete communication networks and coupled constraints. [ABSTRACT FROM AUTHOR]

In this work, we study a group of $N$ homogeneous vehicles travelling on a ring road by describing the collective vehicle dynamics via the so-called Optimal Velocity Model (OVM). We analyze the stability of the equilibrium motion regime in which all vehicles drive at the same speed and keep the same headway. First, stability is studied through linearization, thereby highlighting the roles of the model parameters. Next, we tackle the full nonlinear model and we determine ellipsoidal estimates of the equilibrium’s region of attraction by defining and solving suitable Linear Matrix Inequalities (LMIs). Finally, safety aspects are discussed, incorporated in our LMI formulation as lower bounds of the inter-vehicle distances, and illustrated via simulations. [ABSTRACT FROM AUTHOR]

Vehicle platoon control based on vehicle-to-vehicle (V2V) communication is one of the promising technologies to improve the performance of transportation systems. This paper presents a distributed controller to optimize a vehicle platoon’s fuel consumption by combining the switching feedback control and economic model predictive control (EMPC) methods. The closed-loop dynamics involving switching feedback gains with the constant time headway (CTH) policy are established firstly, and the multiple-predecessor following (MPF) communication topology is considered. In order to obtain the economy optimal feedback gain, we design a local optimal control problem for each vehicle, based on which the average dwell time is defined and the distributed EMPC algorithm is designed. Based on linear matrix inequalities (LMIs) and the Lyapunov theorem, the feedback gain selection method and the lower bound for average dwell time that guarantees asymptotic stability are analyzed rigorously. Then a modified algorithm that can ensure string stability is designed. Numerical simulations show a maximum of 6.84% fuel benefit compared with pure tracking-oriented methods. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed fault-tolerant control problem for the heterogeneous vehicular platoon system (HVPS) suffering from actuator faults, saturation, and external disturbances. Firstly, an exponential spacing policy is developed to tackle the string stability (SS) and traffic flow stability issues when the actuator faults occur. Then, a nonlinear observer is developed to estimate the saturation approximation error, bias fault, and external disturbances. Moreover, to achieve the SS of the whole system in finite-time and fault tolerance ability, a distributed adaptive fault-tolerant control scheme based on bidirectional-leader information flow topology is proposed. Adaptive estimation laws are also involved to estimate and update the unknown parameters, in which the effect of actuator saturation can be compensated. Finally, the SS in finite-time and traffic flow stability of the closed-loop system are proved, respectively. Experiment results and comparisons demonstrate the feasibly and advantages of the method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the motion control for a quadrotor with a cable-suspended load (QCSL). A fixed-time control strategy is presented to improve the transient response and robustness of the QCSL with external disturbance. The overall control scheme is designed with a cascade structure to better cope with the underactuated property of the QCSL and the indirect effect of the control force on the load’s velocity through the tensile force on the cable. The simulation results are given to demonstrate the performance of the proposed scheme. Furthermore, actual flight tests were performed on a new experimental QCSL to validate the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

This article develops a new platoon control strategy for heterogeneous connected vehicles (CVs) subject to time delays and external disturbances. Specifically, based on the third-order vehicle model, a novel platoon controller is developed by embedding the variable time headway (VTH) spacing policy and the nonlinear motion coupling interactions between CVs. Simultaneously, an integral sliding mode (ISM) controller is developed to resist the disturbances. Then, the condition of asymptotic stability for the CV platoon and the upper bound of communication delay are deduced by using the Lyapunov theorem. Also, the string stability is proved by using the infinity-norm method. Finally, extensive simulations and co-simulations are provided to show the validity of the developed controller. Moreover, experiments with intelligent micro vehicles are conducted further to validate the practical feasibility of the developed controller. [ABSTRACT FROM AUTHOR]

An islanded microgrid (MG) including low-inertia converter-based distributed generations (DGs) is subjected to instability. The virtual inertia concept was proposed to alleviate the stability issues by imitating the synchronous generators behavior. This paper spotlights on the optimization of virtual synchronous generator (VSG) parameters and virtual impedances (VI) in islanded MGs using particle swarm optimization (PSO). A small-signal model for MG is developed at first. The permissible ranges of virtual inertia (J) and virtual damping (D) based on MG small-signal stability are scrutinized afterwards. Moreover, VI are considered to lower the reactive power mismatch between converters. Finally, considering the permitted intervals for these parameters, an optimization method and objective function are defined to calculate VSG parameters and VI in the islanded MG. The proposed optimization method enhances the small-signal stability of the MG, decreases the current overshoot and minimizes reactive power mismatches. Simulation results drawn by the “VSG + VI” control include three scenarios. The effectiveness of the proposed “VSG + VI” control method in comparison with “droop” control, “droop + VI”, “non-optimal VSG + VI”, and “VSG ” is verified through simulation studies. [ABSTRACT FROM AUTHOR]

The power flow equation of the DC micro-grid with distributed generations (DGs) under MPPT control (MPPT-DGs) and constant power loads (CPLs) is a strongly coupled nonlinear equation, which is difficult to solve. Moreover, the negative impedance of CPL tends to make the system unstable. This paper analyzes the existence conditions and stability of the power-flow of DC micro-grids, which contain distributed generations (DGs) under droop control (Droop-DGs), MPPT-DGs, and constant power loads (CPLs). To begin with, the power-flow equation of the DC micro-grid is derived. Next, by constructing a contraction mapping, the analytic solvability condition of the nonlinear power-flow equation is obtained based on Banach’s fixed-point theorem. Under the proposed solvability condition, an equivalent linearized model around the equilibrium is developed to analyze the stability of the DC micro-grid. By analyzing the eigenvalues of the Jacobian matrix, we have obtained a robust stability condition of the equilibrium. Finally, simulation results verify the presented results. [ABSTRACT FROM AUTHOR]

This article is concerned with the stability and stabilization of delayed discrete-time T–S fuzzy systems. The purpose is to develop less conservative stability analysis and state-feedback controller design methods. First, a matrix-separation-based inequality is proposed, which can provide a tighter estimation for the augmented summation term. Then, by constructing a delay-product-type Lyapunov–Krasovskii functional, using the proposed inequality to estimate its forward difference and using a cubic functional negative-determination lemma to handle nonconvex conditions with respect to the delay, a delay and its variation-dependent stability criterion are obtained. Moreover, the corresponding controller design method for closed-loop delayed fuzzy systems is derived via parallel distributed compensation scheme. Finally, two examples are given to demonstrate the effectiveness and merits of the proposed approaches. [ABSTRACT FROM AUTHOR]

This article investigates the admissibility analysis for Takagi–Sugeno fuzzy singular systems (T–S FSSs) with time-varying delays. First, according to the decomposed state vectors, a state decomposition Lyapunov–Krasovskii functional (LKF) is constructed, which possesses fewer decision variables. And, the LKF is augmented by considering more features of the second-order Bessel–Legendre inequality (BLI). Then, the second-order BLI and the generalized reciprocally convex matrix inequality are employed to dispose the derivative of the LKF, where the $d^{2}(t)$ -dependent term exists. Meanwhile, by setting an adjustable parameter, the $d^{2}(t)$ -dependent term of the condition is handled by a relaxed quadratic function negative-determination condition. As a result, a less conservative admissibility criterion for T–S FSSs is obtained. And, the relationship between the conservatism and the numerical burden is better considered. Finally, a numerical example is given to demonstrate the reduced conservatism and computational complexity. [ABSTRACT FROM AUTHOR]

Cooperation among multiple connected vehicles (CVs) brings swarm intelligence to our transportation systems and helps improve their performance. This study proposes a fuel economy optimization approach for a platooning vehicle swarm via distributed economic model predictive control (DEMPC). Within the DEMPC framework, each CV shares its assumed trajectory in the predictive horizon with its neighboring CVs at each control loop. With its neighbors’ and its own assumed trajectories, each CV first solves an open-loop control optimization problem for platoon formation, and then solves an open-loop economic optimization problem for direct fuel economy improvement. In particular, the optimal cost of the former optimization problem is used in the latter one to build an upperbound constraint for stability guarantee. The asymptotic convergence of assumed terminal states is given in the analysis, and the recursive feasibility of the two optimization problems are proved with an explicit constraint on the weight matrices in the open-loop control optimization problem. Based on these analyses, the asymptotic stability of the closed-loop system is finally proved through Lyapunov analysis. Numerical simulation results validate the effectiveness of the proposed approach in terms of closed-loop stability and fuel economy improvement. Note to Practitioners—This work aims to optimize the fuel economy for a swarm of vehicles running in a platoon. Existing approaches on platoon control mainly focus on the accurate tracking of the following vehicles, but this may cause aggressive control and hence lead to poor fuel economy. Therefore, this paper proposes a distributed economic model predictive control approach to explicitly optimize the fuel consumption rate of each vehicle. The proposed method can improve fuel economy and reduce communication requirements and burdens for platooning vehicle swarms. The paper assumes no communication time delay and packet drops, so the impact of unreliable communication will be studied in the future work. [ABSTRACT FROM AUTHOR]

This article researches the control of triangular tethered satellite formation (TTSF) system and nonlinear state observer (NSO) design when velocity vector is unmeasured. First, the stability around the equilibrium of open-loop system is discussed, which is stable around certain equilibrium pairs. To improve the system performance, linear feedback control is designed using Jacobian matrix of original nonlinear system, which is locally stable around linearized point. Besides, nonlinear control is designed subsequently which owns global stability domain. Then in case of the unmeasured velocity states, NSO is designed which contains a nonlinear function of estimation error to regulate the observation bias. With the designed nonlinear control and NSO, the simulation of the deployment of TTSF is made thereafter. Compared with linear feedback control and general observer with linear regulation, the proposed nonlinear control together with NSO has global stability domain and less chattering, which is promising in practical application. [ABSTRACT FROM AUTHOR]

The $\mathcal {L}_{2}-\mathcal {L}_{\infty }$ filter design for linear stochastic time-varying delay systems based on the filter velocity constraint is considered in this dissertation. Different from existing $\mathcal {L}_{2}\,-\,\mathcal {L}_{\infty }$ performance analysis and filter design, a new criterion is proposed to make a more accurate judgment, which can not only guarantee the stability of the filtering error system with $\mathcal {L}_{2}-\mathcal {L}_{\infty }$ performance level but also can estimate the convergence speed of the filter. The ideal filter should has the same convergence speed as the original system, so as to ensure the rapid convergence of the error system, but also not to reduce the anti-interference ability and increase the bandwidth of the filter system. By the new filter design method, an ideal filter can be designed, which can regulate the convergence speed of the filter system to the desired effect. A simulation instance is provided to exhibit the validity of the new approach. [ABSTRACT FROM AUTHOR]

The extensively studied fractional-order dynamical networks only contain a uniform fractional derivative, which restricts the scope of fractional-order investigation. One type of Takagi–Sugeno fuzzy second-fractional-order linear networks is established in this article. First, by defining a novel Lyapunov functional, a sufficient criterion is offered to ensure global asymptotic stability of the addressed networks with time delay. Second, a fuzzy state-feedback control scheme is designed for the Takagi–Sugeno fuzzy second-fractional-order delayed linear networks to achieve global stabilization. Third, considering that only a few scholars have worked on adaptive control of fractional-order networks, an adaptive control method is also designed to realize the global stabilization of the Takagi–Sugeno fuzzy second-fractional-order linear networks, which does not contain the sign function and chattering problem can be averted. All results, given as algebraic criteria, are proved directly from the Takagi–Sugeno fuzzy second-fractional-order networks without utilizing the reduced-order approach. Three simulation examples are conducted to show the validity of the theoretical results at last. [ABSTRACT FROM AUTHOR]

This article investigates the finite-time stability (FTS) of switched nonlinear systems (SNSs) with state jumps. Our main concerns are twofold. One is that the SNS only consists of FTS subsystems. The other is that the SNS has both FTS subsystems and exponentially stable (ES) subsystems. Due to the switches and state jumps, the main challenge of the study comes from the estimation of settling time and the synthesis of different Lyapunov functions for FTS/ES subsystems. Based on the analytical-inductive method and the initial-value-dependent dwell-time approach, several FTS criteria for the SNSs are established. Then, we provide the estimation of settling time which is explicitly dependent on the dwell time and initial value. Our results can be applied to the finite-time control problem of switched systems with/without state jumps, even when some subsystems can only be exponentially stabilized through linear feedback control and others are finite-time stabilized by discontinuous/nonlinear controls. Finally, three examples are given to illustrate the proposed results. The finite-time stabilization of a continuous stirred tank reactor and the finite-time consensus of a multiagent system are both adopted as potential applications. [ABSTRACT FROM AUTHOR]

The stabilization problem for switched linear systems with quantization and event-triggered control is addressed in this article. The state information is quantized and transmitted to the controller. An event-triggered mechanism is presented in terms of the quantizer parameter. The updating law of the dynamic quantizer is suggested for the purpose of guaranteeing the state operating within the quantization range. Meanwhile, the contour line of the Lyapunov function is developed to provide an efficient way for system performance improvement. A co-design strategy is put forward to determine the event-triggered parameter and the quantization scheme simultaneously. The asynchronization issue between the controller and the subsystem is solved by designing a suitable switching signal. The Zeno behavior is eliminated by calculating a lower bound of the event-triggered interval. In the end, a strategy for finding the initial value of the quantization parameter is discussed. Simulations are carried out to demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This paper considers the multi-objective platooning control problem of a group of connected and automated vehicles (CAVs) with bidirectional topologies. A new distributed economic model predictive control (DEMPC) algorithm is presented to reconcile the conflict of the control objectives of tracking, safety, stability and fuel economy of the heterogeneous vehicle platoon with guaranteed string stability. Using transient engine energy efficiency indices and cooperative performance of tracking and string stability, two distributed receding horizon optimal control problems are orderly formulated by a Lyapunov-based coupling constraint. Moreover, a new concept of $\gamma $ -string stability is defined for the platoon with bidirectional topologies. Some distributed terminal conditions are then derived to guarantee the recursive feasibility and asymptotic stability of the DEMPC as well as $\gamma $ -string stability of the platoon in the presence of constraints. Compared to traditional platooning control, the new DEMPC has a 4.2% energy-saving of vehicles while achieving the cooperative tasks of the platoon in several simulation scenarios. [ABSTRACT FROM AUTHOR]

Vehicle platoon, as an important application of connected automated vehicles (CAVs), is a hot topic in the intelligent transportation systems (ITSs). Most existing results on platoon control used the exact feedback linearization method to transform nonlinear vehicle dynamics into linear ones, which required complete prior knowledge of parameters. As the measurement errors and the environment disturbance exist, the accurate parameters are difficult to obtain in real world. This paper considers a nonlinear uncertain vehicle platoon under a network topology (NT) modeled by a spanning tree in a digraph. Radial basis function neural networks (RBFNNs) are used to approximate the uncertain function and an adaptive distributed controller is designed by backstepping control method. To reduce the update rate of the controllers, an event-triggered control scheme is proposed with two different kinds of triggering conditions. It is proven that vehicle platoon practical consensus can be achieved under the Zeno-free adaptive event-triggered control scheme. Moreover, for bidirectional (BD) NT and two predecessor-following (TPF) NT, vehicle platoon reaches the string stability. Finally, a vehicle platoon under three different kinds of NTs is simulated to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

The work on this paper studies the combined effect of vehicle dynamics, sampling period and the quality of inter-vehicle sensing and communication on the performance of platoon control. First, we induce the sampled control protocol from continuous–time linear consensus protocol by employing zero–order hold circuit and periodic sampling technology, then by virtue of the obtained sampled control protocol, the continuous–time platoon system is equivalently transformed into a discrete–time system. Second, for the inter–vehicle communication with ideal channel and under undirected information flow topology (UIFT), the stability thresholds of control gains are explicitly established by solving a discrete–time simultaneous stabilization problem, bilinear transformation and the Routh-Hurwitz stability criterion. Meanwhile, to ensure the fastest asymptotic stability of the platoon dynamics, we propose an optimal asymptotic convergence factor and a correspondingly optimal sampled control protocol. Third, For the inter–vehicle communication with identical fading networks and under UIFT, through solving a modified Riccati inequality, we provide a sampled control protocol depending not only on information flow topology (IFT) and sampling period, but also on the statistics of the inter–vehicle communication channel. Besides, employing Lyapunov inequality in probability theory, we show a necessary condition for the sampled control protocol ensuring the platoon dynamics mean square stable. Finally, simulations are performed to demonstrate the theory’s discoveries. [ABSTRACT FROM AUTHOR]

This article investigates the predefined-time stabilization problems of Takagi–Sugeno (T–S) fuzzy systems. For addressing the considered problems, a class of novel integral sliding mode surface is first designed based on the time-regulator function, on which the system states are forced to converge to the origin in a predefined time after the sliding mode surface is reached. Further, the proposed sliding surface is employed to construct predefined-time integral sliding mode controller for the time delayed and disturbed T–S fuzzy system. The settling time appears as the sum of two predefined-time parameters in the controller design, which, respectively, adjusts the convergence time for reaching the sliding mode surface and the convergence time for arriving the origin from the sliding mode surface. The sufficient conditions for maintaining the predefined-time stability of the T–S fuzzy systems are obtained through systematic Lyapunov stability analysis. Finally, a numerical simulation example on delayed and disturbed Chua circuit is presented to verify the effectiveness of the proposed predefined-time integral sliding mode controller. [ABSTRACT FROM AUTHOR]

This article aims to propose time-delayed and simplified inequality conditions and establish more novel fixed-time (FXT) stability principles of delayed Filippov systems. First, the sign function is used to unify the orders of the Lyapunov–Krasovskii functional, and the time-delayed term is introduced in the inequality conditions, then some new FXT stability theorems are established and new estimations of the settling time involving delayed parameter are given that are absolutely different from the previous ones. The traditional inequality conditions $\dot{V}(z)\leq -aV^\alpha (z)-bV^\beta (z)$ is optimized and improved. For the purpose of illustrating the applicability, a class of delayed discontinuous fuzzy Cohen–Grossberg neural networks (DDFCGNNs) is studied. Some new criteria are derived, and the FXT stabilization of the addressed DDFCGNNs is achieved. Finally, a representative example and simulations are provided to examine the correctness. [ABSTRACT FROM AUTHOR]

Hierarchical controls, consisting of primary, secondary, and tertiary layers to realize different functionalities at different time scales, have been applied for microgrids to achieve the stable and economic operations. However, in islanded microgrids with pure renewables (i.e., wind, solar, and battery storage systems (BSS) only), the three layers shall interact rather tightly and frequently in order to effectively leverage limited capabilities of available resources against disturbances. To this end, this paper discusses a more responsive control framework, including the distributed schemes for individual primary, secondary, and tertiary control layers as well as the real-time closed-loop scheme for a prompt coordination of the three layers. Thus, the proposed control framework could promote real-time interaction of resources in islanded microgrids with limited communication and computation burdens. Based on this, an enhanced control module design for BSSs of different configurations is further discussed to optimally coordinate their power and energy states with improved operational stability and economics. The steady-state analysis confirms the compatibility of the designed power and energy goals in tracking optimal power and energy equilibria simultaneously, and a customized Lyapunov candidate function is used to prove the asymptotic stability of the overall control framework. The hardware-in-the-loop simulation validates efficacy of the designed control framework in promptly mitigating disturbances and effectively achieving convergence to the optimal economic equilibria. [ABSTRACT FROM AUTHOR]

In this article, we study the finite-time stabilization and the asymptotic stabilization with probability one of Markovian jump Boolean control networks (MJBCNs) by sampled-data state feedback controls (SDSFCs). Based on the semi-tensor product (STP), we introduce an augmented variable multiplied by the vector form of the switching signal and the state of MJBCN. We find that under SDSFC, the sequence of the states of the augmented variable at sampling instants satisfies the Markov property. Based on the convergences of the switching signal and the augmented variable, we obtain the sufficient and necessary criteria for the finite-time stabilization and the asymptotic stabilization of MJBCNs by SDSFCs, respectively. Moreover, for the two kinds of stabilization, the feedback matrices of SDSFCs are constructed, respectively. Finally, the obtained results are applied to an apoptosis network and a model of the lactose operon in the Escherichia Coli. [ABSTRACT FROM AUTHOR]

The nonminimum-phase property of the dc–dc boost converter can create difficulties in designing a stable, robust, and fast control for the output voltage. In this article, these difficulties are reduced by modifying the state model of the boost converter in such a way that it behaves like a minimum-phase system. More specifically, the control input entering the state equation for the output voltage is treated as an unknown disturbance to make the relative degree of the system equal the system’s order. As a result, the modified model does not exhibit zero dynamics, so that it can be treated as a minimum-phase system for the control design. The modified model is, then, used to derive a dynamic compensator for the output voltage regulation. More explicitly, the dynamic compensator is designed based on combining linearizing feedback control with a disturbance observer. The latter is employed to compensate for model uncertainties and unknown load with a view to ensure asymptotic regulation under the composite controller. The asymptotic regulation is achieved due to the integral action property characterizing the disturbance observer. More interestingly, after simple algebraic manipulation, it turns out that the composite controller reduces to a dynamic state feedback control plus an antiwindup scheme to mitigate the effect of control saturation during transients. The performance of the proposed controller is verified by experimental tests. The experimental results demonstrate the ability of the proposed controller to achieve good transient and steady-state performances. [ABSTRACT FROM AUTHOR]

In this article, a composite nonlinear feedback (CNF) controller with anti-windup extended state observer (ESO) is proposed for path-following control of unmanned ground vehicles (UGVs). To describe steering dynamics accurately, a saturation model with bounded disturbances is developed subject to path-following, lateral dynamic, and steering capability. The anti-windup ESO is investigated for real-time disturbance estimation under saturated input. The CNF controller is designed for path-following. In terms of asymptotically null controllability, a practical semiglobal stabilization result is derived for the closed-loop system with saturated input and bounded disturbances. Experimental results show that the proposed strategy is effective for UGVs. [ABSTRACT FROM AUTHOR]