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Since the inherent nature of many applied high-technological systems and networks possesses switching behaviors, modeling, controlling, and stabilizing problems of the switching plants are becoming as the important research scenarios in the current literature. Moreover, consideration of the effects of mismatching uncertainties along with matching uncertain parts as well as unknown dynamics is a significant topic in the control engineering community. As a result, this paper is dedicated to the controlling problem of partially unknown nonlinear switched systems whose dynamics are perturbed by both matched and mismatched uncertainties. In addition, since the existence of gain deviations in real-world implementations of physical actuators can lessen the control act of the switching system, this paper handles the corresponding gain variations in the control inputs via some adaptation variables. In the design procedure, no limiting supposition is made for the switch signal of the switched plant. The proposed control algorithm is based on the variable structure control theory in which the selected sliding surface is able to deal with mismatching uncertainties and the deriving control law is robust against the lumped uncertain components. As a contribution, the Lyapunov functions are built such that not only to provide an asymptotic stable system but also to assure the global (practical) finite-time stability of the equilibrium state of the final closed-loop cascade switched plant. The robust performance of the developed control strategy is confirmed via two illustrative examples. [ABSTRACT FROM AUTHOR]

This paper investigates the robust containment control problem of multiagent systems with heterogeneous uncertainty and nonlinearity while the nonlinear parts have to satisfy the Lipschitz condition. In this paper, both input time-delay and data transmission time-delay between the agents are considered simultaneously and communication topology of the multiagent systems may switch in the steady-state condition. Under the mentioned conditions, the objective of this paper is to make all the followers’ states converge to the convex hull shaped by the leaders’ states with an expected exponential rate. To this end, an appropriate smooth protocol is proposed. Then, a Lyapunov–Krasovskii functional composed of five terms is proposed and the stability condition is denoted by two linear matrix inequalities (LMIs). In addition to the stability assurance, solving the LMIs would obtain the suitable gains for the protocol. Finally, some numerical simulations are given to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we address the adaptive neural tracking control problem for a class of uncertain switched stochastic nonlinear pure-feedback systems with nonlower triangular form. The significant design difficulty is the completely unknown nonlinear functions with all state variables that can neither be directly estimated by radial basis function (RBF) neural networks (NNs) nor be eliminated by the traditional backstepping technique. To achieve the control objective of this paper, a common state-feedback controller for all subsystems is first systematically constructed by using the common coordinate transformation, the variable separation technique, and the universal approximation capability of RBF NNs. Then the stability analysis shows that the semi-global bounded in probability of the whole closed-loop switched system can be obtained and the desired tracking performance can also be insured under a class of switching signals with the average dwell time property. Finally, simulation results are given to demonstrate the effectiveness of the obtained control scheme. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of controller design for normal nonlinear switched systems with unknown dynamics. The situation assumes that the nonlinear component of the system dynamics is unknown and there are extra uncertain terms and external perturbations affecting the system responses. Unlike previous methods that usually apply artificial neural networks to obtain an approximate model for an unknown dynamics, we use simple adaptive laws to surmount such fluctuations as well as to circumvent the steady state errors in the approaches provided by neural networks or fuzzy logics. No information on the bounds and parameters of the uncertain parts is needed. We design a twofold sliding mode control methodology to stabilize the whole switched system with arbitrary switching signals. To handle the consequences of the inherent chattering, a smooth integral type control signal is constructed. It is proved that once the system states attain the developed sliding manifold, the system becomes insensitive to both the lumped uncertainties and the dynamics of the switched system. The common assumption of a known Lyapunov functions for the subsystems is relaxed and the derived adaptive approach provides nonconservative circumstances for guaranteeing the global stability of the equilibrium state. The theoretical results of this paper are generalized for the canonical nonlinear systems with mismatched uncertainties and a novel adaptive sliding manifold is proposed to suppress the effects of the system mismatching uncertain parts. A comparative computer simulation is developed to examine the effective performance of the introduced controllers. [ABSTRACT FROM AUTHOR]

This paper deals with a state-feedback control scheme for nonlinear stochastic systems with Markovian switching. First, we present the results on the practically $ {p}$ -moment exponential stability with respect to an additional disturbance and the practically $ {p}$ -moment asymptotic stability relying on a specific event. However, elements in this event are hard to be observed directly. The main aim of this paper is to develop a self-triggered sampling rule to overcome this difficulty. By applying the improved monotone growth condition, Itô’s formula, Fubini’s theorem, Gronwall inequality, and comparison lemma, we establish a novel lemma to estimate the lower bound and upper bound of second-moment for state and error, respectively. Moreover, we also establish the practically asymptotic stability in mean square with the help of Jensen’s inequality technique, properties of $ {\mathcal {K}}$ -function and result on $ {p}$ -moment input-to-state stability. Furthermore, from Lipschitz continuity and monotonicity of functions, we obtain the value of the maximum triggering interval based on lasted-observed state. Finally, we give some remarks and discussions to show the significance of our results by comparing with those in the previous literature. [ABSTRACT FROM AUTHOR]

This paper considers the global stabilization for a class of uncertain nonlinear systems with unknown powers, unknown control directions, and unknown nonlinearities. Mainly due to the presence of the unknown powers which have not known upper bound, no existing methods are applicable to the control problem to be solved. In this paper, to compensate the serious system uncertainties and particularly to overcome the major obstruction from unknown powers, we appeal to the mechanism of switching adaptive feedback. By flexibly combining the domination and the method of adding a power integrator, we propose a new adaptive controller design, whose design parameters are tuned online based on a switching logic. The designed controller will become operative as long as finite switchings happen and will not lead to Zeno phenomenon, and can guarantee the global boundedness as well as ultimate convergence of the resulting closed-loop system. Two numerical examples are given to demonstrate the effectiveness of the developed design scheme. [ABSTRACT FROM AUTHOR]

In the system and control community, the sliding mode control technology has been known as a tool which is able to handle system uncertainties and external disturbances. Simplicity in implementation and good stability performance are the other interesting features of the sliding modes. However, traditional sliding mode controllers exhibit two weaknesses, as follows: 1) generally, they have asymptotic stability in sliding mode dynamics which results in a slow speed system and 2) the so-called chattering phenomenon exists, which produces undesirable high frequency oscillations in the control signal. In this paper, the former problem is solved using a twofold terminal sliding manifold displaying desired transient and steady state behavior. The latter issue is responded to by a twofold sliding mode technology which leads to a continuous sliding control rule instead of a discontinuous switching control. The effects of uncertain terms as well as external perturbations with unknown bounds are fully compensated using updated parameters. The values of the updated parameters approach fixed values as the system trajectories converge to the equilibrium states. The analytical results of this paper are theoretically proved using the Lyapunov technique and the finite-time control strategy. Comparative computer simulations on a robotic manipulator confirm the fast convergence attribute and robust performance of the introduced adaptive robust nonsingular terminal sliding control algorithm. [ABSTRACT FROM AUTHOR]

We propose, in this paper, an observer-based nonlinear feedback controller for four degrees of freedom (4-DOF) offshore ship-mounted tower cranes, which includes a robust-type term to address the observation uncertainty, and a switching logic tuning mechanism to update the involved unknown parameter. As a typical nonlinear underactuated mechatronic system, unlike the land-fixed tower cranes, an offshore ship-mounted tower crane also suffers from persistent disturbances caused by sea waves or currents, which leads to many difficulties and challenges in the controller design of such systems. Existing offshore crane control methods require either linearizations or approximations when performing analysis; moreover, most of them are only applicable for simplified 2-DOF crane models, and the ranges of system state errors cannot be guaranteed during the overall process. Motivated by these facts, to achieve simultaneous accurate jib/trolley positioning and fast payload swings suppression against complex unknown external disturbances, in particular, a disturbance observer is first designed in this paper, based on which a novel nonlinear switching logic-based control scheme for offshore cranes with jib rotation and horizontal transportation is proposed. As far as we know, the proposed method yields the first observer-based feedback closed-loop control without simplification operations to the original 4-DOF offshore tower crane dynamics and achieves the first asymptotic stability of the closed-loop system’s equilibrium point for offshore cranes. To support the theoretical derivation, the corresponding stability analysis of the closed-loop system’s equilibrium point is implemented by Lyapunov techniques. Numerous simulation and hardware experimental results are presented to demonstrate the superior performance of the proposed method. Note to Practitioners—This paper is motivated by the issue of controlling a four- degree-of-freedom (4-DOF) offshore ship-mounted tower crane system under the effects of unknown external disturbances. In practical applications, the persistent disturbances caused by sea waves or currents can always happen and make the offshore crane operation very challenging. Moreover, it brings more difficulties in the controller design for such a system due to its nonlinear underactuated property. Existing control approaches for offshore cranes are developed based upon linearized or oversimplified crane models or require exact model knowledge, and they may not work well in the presence of harsh sea conditions. Toward this end, this paper suggests a new control approach for 4-DOF offshore tower cranes suffering from sea wave effects to achieve a satisfactory performance. The asymptotic stability of the closed-loop system’s equilibrium point is derived, implying that the accurate jib/trolley positioning and fast payload swings suppression against complex unknown external disturbances are achieved simultaneously. Preliminary physical experiments implemented on a self-built offshore tower crane hardware test bed verify the effectiveness and the robustness of the proposed observer-based control method. In the future research, we will apply the suggested control approach to industrial offshore crane systems to improve their working efficiency. [ABSTRACT FROM AUTHOR]

The availability of reliable analytical models is essential to the optimal design of energy harvesters and for the prediction of the system behavior. In this paper, we consider a low-input nonlinear system based on a flexible buckled beam forced in a bistable configuration. The harvester has been demonstrated to generate power in the excess of $400~\mu \text{W}$ with the optimal resistive load of 15 $\text{k}\Omega $ and a monotonic input with root-mean-square accelerations of 13.35 m/s2. The power generated is suitable for powering low-power measurement systems or sensor nodes. This paper focuses on a methodology for the modeling of the mechanical dynamical behavior of the device subject to a periodic impulsive signal. A measurement protocol for the evaluation of system’s hidden quantities, the beam’s restoring force, and the beam’s displacement between its stable states is introduced. A second-order behavioral model with a nonlinear term representing the beam’s restoring force has been used. In order to model the nonlinearity, two different potential energy functions have been compared by fitting the models to the experimental data with different constrains, through a performance index evaluating the fitting error. [ABSTRACT FROM AUTHOR]

This paper deals with the issue of adaptive observer-based stabilization for a more general class of uncertain switched stochastic nonlower triangular nonlinear systems with average dwell-time (ADT) switching. The completely unknown nonlinear functions possessing the entire states are handled using the neural networks universal approximation property and the variable separation technique. The main novelty of this paper is that it presents a universal formula for constructing an adaptive output-feedback controller of the considered system with only one adaptive parameter by designing a switched state observer. The theoretical analysis shows that the Lyapunov stability of the overall closed-loop system is ensured in the presence of ADT switching. Finally, the effectiveness and practicability of the obtained design scheme are illustrated by two simulation examples. [ABSTRACT FROM AUTHOR]

This paper addresses adaptive neural output feedback control for uncertain nonlinear switched systems. The main difficulty for control design comes from the loss of the precise information on those virtual coefficients of each subsystem. To overcome this difficulty, we give a robust observer design scheme by using convex combination approach. Furthermore, develop an observer-based output feedback control strategy. During the procedure of control design, adaptive neural control approach is used to deal with the unknown nonlinear functions and backstepping technique is employed to construct the ideal control laws. It is shown that the presented control law achieves the control issue of getting small tracking error, meanwhile, ensuring boundedness of all the closed-loop signals. Finally, a simulation example is used to test our results. [ABSTRACT FROM AUTHOR]

The global output feedback stabilization problem is investigated in this paper via sampled-data control for switched nonlinear systems in the $p$ -normal form. First, a reduced-order state observer is designed. Then, an output feedback sampled-data controller is constructed with the relaxation of some restrictions of switched nonlinear systems. The proposed controller can ensure that all states of the corresponding closed-loop system can converge to the origin. Simulation results are given to show the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper concerns with the stability analysis for a class of discrete-time switched Takagi–Sugeno (T–S) fuzzy systems. By establishing a semitime-dependent Lyapunov function and exploring the property of mode-dependent average dwell-time switching, improved stability criteria are provided for switched T–S fuzzy systems containing both stable and unstable modes. Then, slow and fast switching strategies are designed, which are adopted for stable and unstable subsystems, respectively. Especially, we also provide the stability conditions for switched systems with all modes stable and unstable. Finally, the validities and advantages of provided techniques are illustrated by some simulation examples. [ABSTRACT FROM AUTHOR]

This paper addresses the adaptive fault-tolerant control (FTC) problem of uncertain switched nonaffine nonlinear systems with actuator failures and time delays. Unlike the literature employing the FTC methods, the novel nonlinear fault compensate function with adjustable parameter factor, whose norm is used for approximation with fuzzy logic systems, is constructed based on the mean value theorem. Accordingly, a standard transformation scheme from the multi-input and single-output nonaffine nonlinear system to the corresponding affine nonlinear system is first to be given; then, the designed adaptation mechanism with state-dependent switching strategy can effectively eliminate the effects of multiple time delays and actuator faults, including outage and stuck modes. Furthermore, by using the Lyapunov–Krasovskii stability analysis method, it is proved that the proposed adaptive switched controller can guarantee the states of the overall closed-loop systems to asymptotically converge to zero. Finally, the simulation results are displayed to verify the feasibility of the presented approach. [ABSTRACT FROM AUTHOR]

The problem of adaptive decentralized fault-tolerant control is investigated in this paper for the pure-feedback nonlinear switched large-scale systems. The considered systems possess the unknown compounded nonlinearities (unknown nonlinear functions, unknown interconnected terms, unknown nonlinear function faults, and unknown actuator dead-zone nonlinearity). The radial basis function neural networks are utilized for identifying the unknown compounded nonlinear functions so that the problems of unknown nonlinearities can be solved. A switched neural networks ${k}$ -filter observer is constructed to estimate the unmeasurable states, deal with the unknown actuator dead-zone nonlinearity and compensate the nonlinear function faults simultaneously. Then, by combining the average dwell time theory, adaptive decentralized control method, and under the framework of backstepping design, an adaptive output-feedback fault compensation control method is presented. Under the certain assumptions, the stability of the closed-loop system is proved by use of Lyapunov function stability theory. Finally, the applicability of the proposed controller is well carried out by a double-inverted-pendulums simulation example. [ABSTRACT FROM AUTHOR]

This paper investigates the decentralized fault detection (FD) problem within a type of nonlinear large-scale systems under the parameter uncertainties constraints. First of all, a nonlinear system is treated as the T–S fuzzy large-scale model with unknown membership functions. Then, a switching method is employed in the FD filter integration. Combining the local measurements of each subsystem and the lower and upper bounds information collected from the unknown membership functions, a new decentralized FD filter is built. A cyclic-small-gain condition is introduced to guarantee that the resulted augmented FD system is asymptotically stable with a satisfying ${H_{\infty }}$ performance. The comparison results show that the proposed switching-type decentralized FD filter can achieve a better FD performance than linear filters. Finally, the validity and superiority of the proposed method are verified with two examples. [ABSTRACT FROM AUTHOR]

This paper investigates a problem of stability analysis for a class of nonlinear systems with a time-varying delay taking both large and small values in an alternating manner. This problem is a delay-dependent stability analysis one but it shares some features with delay-independent ones. Hence, traditional stability analysis techniques for systems with delay are not applicable. By building upon our previous works, we first introduce the concept of delay-hybrid-dependent stability, which characterizes the delays described above. The considered system is first represented as a system with a switched delay. Then by using switching techniques and Lyapunov–Krasovskii functionals (LKFs), a new stability criterion is developed. Next, in the linear context, it is shown how the needed LKFs can be constructed by developing an original design of LKFs. [ABSTRACT FROM AUTHOR]

Aiming to solve the cluster lag consensus (CLC) problem of networked nonlinear agents with a switching topologies, this paper proposes a control algorithm based on the measurements of position and velocity. When the network has several clusters of agents, under the conditions that each cluster is a strongly connected digraph including isolated agents, and at least one agent in each cluster can communicate with the common leader each time, a sufficient condition is derived for reaching CLC. Finally, a numerical simulation is demonstrated to validate the proposed control algorithm and the developed conditions. [ABSTRACT FROM AUTHOR]

In this paper, the problems of stability and ${l_{2}}$ -gain analysis are investigated for discrete-time switched systems with mode-dependent average dwell time (DT). By proposing a novel multiple discontinuous Lyapunov function (MDLF) approach, the conditions of stability and weighted ${l_{2}}$ -gain are established for nonlinear systems. Next, the corresponding results for linear switched systems are also proposed by using MDLF. It turns out that our proposed results provide smaller bounds on the DT. Some simulation results are given to show the validity of our approaches. [ABSTRACT FROM AUTHOR]

This paper investigates an adaptive fuzzy output feedback control design problem for the switched multiple-input and multiple-output (MIMO) nontriangular structure nonlinear systems. The discussed system contains the unknown nonlinear dynamics, the unknown backlash hysteresis, the immeasurable states, and the unknown control directions under a class of switching signals. The fuzzy logic systems are utilized to learn the unknown nonlinear dynamics and construct an MIMO fuzzy switched nonlinear observer. By combining the property of the Nussbaum gain function with the Prandtl-Ishlinskii models, a novel observer-based fuzzy adaptive backstepping schematic design algorithm is presented. Furthermore, the stability of the whole controlled system is proved via Lyapunov stability theory and the average dwell time method. The simulation results are presented to verify the validity of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In this paper, the prescribed performance-based consensus problem for nonlinear multiagent systems with unknown control directions and switching networks is investigated. Different from the existing works, the unknown control directions and prescribed performance of consensus errors are considered simultaneously under the switching networks. In this case, the graph Laplacian matrix may be singular and the controllers are interacted. To handle this problem which cannot be dealt with directly using the existing methods, a distributed adaptive observer is introduced so that the controllers are decoupled and the difficulty caused by the unknown control directions can be overcome by adopting the existing Nussbaum functions and the unknown control directions of agents are allowed to be nonidentical. Meanwhile, by utilizing the designed controller, the consensus errors can be guaranteed with the prescribed performance. Finally, a numerical example verifies the validity of the proposed method. [ABSTRACT FROM AUTHOR]

The adaptive fuzzy prescribed performance tracking control design problem is investigator switched stochastic nonlinear systems with unknown control directions in this paper. The Nussbaum-type functions are introduced to handle the issue of unknown control directions. The constructed controller guarantees that all the signals in the closed-loop are bounded in probability, whereas the convergence of the tracking error and the prescribed performance bound are also ensured. Finally, simulations on a mass-spring-damper system with controller switching are performed to illustrate the developed control scheme. [ABSTRACT FROM AUTHOR]

This paper considers the global stabilization problem via sampled-data control for a class of switched nonlinear systems meanwhile taking into account asynchronous switching. First of all, a state feedback sampled-data controller is constructed by backstepping design method. Then, a relationship between the sampling period and the average dwell time is derived, which can guarantee that the closed-loop system is globally asymptotically stable. Finally, two simulation examples are presented to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The derivation and implementation of the natural switching surfaces (NSS) considering certain parametric uncertainties for a flyback converter operating in the boundary conduction mode is the main focus of this paper. The NSS with nominal parameters presents many benefits for the control of nonlinear systems; for example, fast transient response under load-changing conditions. However, the performance worsens considerably when the converter actual parameters are different from the ones used in the design process. Therefore, a novel control strategy for NSS considering the effects of parameter uncertainties is proposed. This control law can estimate and adapt the control trajectories in a minimum number of switching cycles to obtain excellent performances even under extreme parameter uncertainties. The analytical derivation of the proposed adaptive switching surfaces is presented together with simulations and experimental results showing adequate performance under different tests, including comparisons with a standard PI controller. [ABSTRACT FROM AUTHOR]

This part of the paper illustrates the use of the expression derived in Part I for predicting subharmonic oscillation in switching regulators. Six case studies with different control schemes from the recent literature are used to validate the novel approach and the new derived expression, which is benchmarked for these case studies against results obtained using the discrete-time modeling approach or Floquet theory combined with Filippov method. Numerical simulations from the circuit-level switched models, implemented in PSIM software, are used to demonstrate the correctness of the derived closed-form condition. A procedure is presented to apply the approach of the paper to power converters with nonlinear sources, such as photovoltaic (PV) arrays or fuel cells. Experimental measurements from a boost converter prototype for PV applications are also provided to validate the theoretical predictions and the numerical simulations showing a remarkable agreement. [ABSTRACT FROM AUTHOR]

The guaranteed-performance consensualization for high-order linear and nonlinear multiagent systems with switching topologies is respectively realized in a completely distributed manner in the sense that consensus design criteria are independent of interaction topologies and switching motions. This paper first proposes an adaptive consensus protocol with guaranteed-performance constraints and switching topologies, where interaction weights among neighboring agents are adaptively adjusted and state errors among all agents can be regulated. Then, a new translation-adaptive strategy is shown to realize completely distributed guaranteed-performance consensus control and an adaptive guaranteed-performance consensualization criterion is given on the basis of the Riccati inequality. Furthermore, an approach to regulate the consensus control gain and the guaranteed-performance cost is proposed in terms of linear matrix inequalities. Moreover, main conclusions for linear multiagent systems are extended to Lipschitz nonlinear cases. Finally, two numerical examples are provided to demonstrate theoretical results. [ABSTRACT FROM AUTHOR]

This paper proposes a distributed model free adaptive iterative learning control (MFAILC) method for a class of unknown nonlinear multiagent systems to perform consensus tracking. Here, both fixed and iteration-varying topologies are considered and only a subset of followers can access the desired trajectory in each topology. To design the control protocol, the agent’s dynamic is first transformed into a dynamic linearization model along the iteration axis, and then a distributed MFAILC scheme is constructed to guarantee that all agents can track the desired trajectory. Through rigorous analysis, it is shown that under this novel distributed MFAILC scheme, the tracking errors of all agents are convergent along the iteration axis. The main merit of this design is that consensus tracking task can be achieved only utilizing the input/output data of the multiagent system. Three examples are given to validate the effectiveness of the proposed design. [ABSTRACT FROM AUTHOR]