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In this paper, the adaptive fuzzy control of switched stochastic nonlinear systems with set-time prescribed performance based on event-driven mechanism is studied. The creative part of this paper is that based on the set-time performance function, a modified event-triggered strategy that considers asynchronous switching to deteriorate system performance without strict assumptions is presented, which avoids Zeno behavior and saves communication resources. Then, by using backstepping recursive design technique, It $\hat {o}$ ’s differential lemma and mode-dependent average dwell time (MDADT) method, a novel adaptive performance control scheme is proposed, which can ensure that all the variables in the system are semiglobally uniformly ultimately bounded (SGUUB) in probability and the tracking error gets into prescribed boundary no later than an arbitrarily adjusted setting time. Finally, the proposed algorithm is applied to a RLC circuit and its practicability is verified via simulation results. [ABSTRACT FROM AUTHOR]

For a class of nontriangular nonlinear systems in presence of unknown disturbances, we propose a predictor-based neural dynamic surface control (PNDSC) strategy in this paper. This nontriangular system is transformed via the mean value theorem, and a predictor is then constructed. To avoid an algebraic loop problem, partial state vectors are employed as input signals of neural networks (NNs) for approximating unknown dynamics, and compensation items are designed to compensate for approximation errors from NNs. Different from the traditional NDSC, the PNDSC in this paper utilizes prediction errors to update learning parameters for improving NNs’ learning behaviors with overlarge adaptive gains. On the basis of improved NNs’ approximation behaviors, a predictor-based NNs disturbance observer (PNNDO) is constructed for compensation for external disturbances and approximation errors from NNs. Furthermore, with predictors, a normalization method of weights is developed to reduce the number of online learning parameters. On the basis of the aforementioned result, measurement noises are taken into account in our predictor-based neural control strategy. We employ predictor states, rather than measurement information paralyzed by noises, in design of our control strategy. This reduces high-frequency oscillations in control input. A Lyapunov-based stability analysis shows that all signals are ultimately bounded in the closed-loop system. Finally, the effectiveness of the proposed control strategy is verified by a numerical example and a permanent magnet brushless DC motor system. [ABSTRACT FROM AUTHOR]

In this paper, a Takenaka-Malmquist (TM) basis function based equivalent data-model is established by an adaptive rational decomposition for the finite-time interval trajectory tracking control and real-time control of a class of nonlinear systems in the frequency domain. This data model can adaptively learn and match the control process of nonlinear systems. As a result, the proposed trajectory tracking as well as real-time control method can reflect the feature of adaptive learning in order-by-order decomposition, and the feasibility of the proposed method is guaranteed by the convergence of adaptive decomposition by TM basis function under the maximum selection principle (MSP) in Hardy space $H^{2}(\mathbb {D})$. Compared with the traditional model-free control method, this data learning model which matches the control process has obvious advantages in the system model expression and control accuracy. Simulation results at the end of this paper show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we consider the identification problem for nonlinear state-space models with skewed measurement noises. The generalized hyperbolic skew Student’s t (GHSkewt) distribution is employed to describe the skewed noises and formulate the hierarchical model of the considered system. A unified framework for estimating unknown states and model parameters is presented based on expectation-maximization (EM) algorithm, in which the forward filtering backward simulation with rejection sampling (RS-FFBSi) is employed to efficiently estimate the smoothing densities of the hidden states, and optimization method is adopted to update model parameters. One numerical study and the electro-mechanical positioning system (EMPS) are employed to verify the effectiveness of the developed approach. [ABSTRACT FROM AUTHOR]

This paper investigates the leader-following consensus control problem for a class of nonlinear multiagent systems subject to sensor and actuator faults under a fixed directed graph. First, a fault compensation mechanism is proposed because of multiple faults wherein the adaptive parameters substitute the fault coefficients. Then, the command filtering method is employed to avoid the burst of complexity rendered by the duplicative differentiation of the virtual control signal. Furthermore, the neural networks-based state observers are designed to reconstruct the unmeasurable states of the nonlinear multiagent systems. According to the given design approach, a switching threshold-based event-triggered adaptive fault-tolerant control strategy is developed and ensures all the signals in the closed-loop system are semiglobally uniformly ultimately bounded (SGUUB). Finally, the simulation result is provided to demonstrate the validity of the presented method. [ABSTRACT FROM AUTHOR]

In this paper, global event-triggered adaptive prescribed tracking output feedback control is investigated for a class of nonlinear uncertain systems with unknown control direction. Different from the existing works, the design of the tracking error-dependent normalized function and prescribed boundary is based on our uniformly defined blow-up function rather than a specific function, and the asymmetric constraint requirements on tracking error can be achieved by appropriately selecting the blow-up function. By utilizing the Kalman filter ($K$ -filter) and dynamic gain technique, a new reduce-order observer is proposed, which can make the estimated error exponentially converge to zero. In addition, by introducing a dynamic signal into the trigger condition, a novel event-triggered mechanism is proposed, which can extend the trigger time interval and completely counteract the event-triggered errors in terms of asymptotic stability by sacrificing part of the system transient performance. Furthermore, an adaptive controller is designed based on the backstepping method, which ensures the boundedness of the state of the closed-loop system, while regulating the tracking error meets the global prescribed performance requirements and approaches to zero asymptotically. Two examples are given to illustrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper studies the prescribed-time input-to-state stabilization problem of normal nonlinear systems. With the help of some key properties of a class of parametric Lyapunov equations, the prescribed-time input-to-state stabilization problem of normal nonlinear systems under matched uncertainties is studied. Some bounded time-varying controllers are proposed. It is shown that the closed-loop systems are prescribed-time input-to-state stable. Finally, the effectiveness of the established methods is illustrated by two physical systems. [ABSTRACT FROM AUTHOR]

In this paper, a novel saturation-based control method is proposed for high-order sliding mode (HOSM) dynamics with upper-triangular nonlinearities. Firstly, a new HOSM dynamics with upper-triangular nonlinearities is constructed based on the traditional HOSM dynamics, so as to reduce the uncertainties in the control input channel. Then, a HOSM controller is established by means of the adding a power integrator method such that the new HOSM dynamics is locally stabilized. Finally, the saturation-based controller is constructed by a combination of the saturation technique and the local HOSM controller to guarantee that the sliding variables can converge into a domain of attraction in a finite time and retain inside it thereafter. The rigorous stability analysis is made by the Lyapunov theory. A simulation example is also given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper investigates the fixed-time stabilization problem for a class of nonlinear systems via event-triggered control. The event-triggered mechanism can be applied to the nonlinear system with the coexistence of low-order and high-order nonlinearities. In order to deal with these low-order and high-order terms as well as achieve the objective of fixed-time stabilization, the initial value of the system is divided into two cases, and then the event-triggered controller is designed, respectively. By switching control theory, it is proved that the nonlinear system is globally fixed-time stable under the designed controller and the Zeno behavior can be excluded. Finally, two simulations show that the proposed technology is effective. [ABSTRACT FROM AUTHOR]

This paper investigates global stabilization via adaptive event-triggered output feedback for a class of uncertain nonlinear systems. Typically, unknown polynomial-function rate is admitted in the unmeasurable-state dependent growth of the systems. This calls for an advanced compensation strategy based on dynamic high gain, which in turn requires more intelligent execution in the event-triggered control architecture. To this end, a novel event-triggering mechanism is designed with two events separately evaluating the behaviors of dynamic gain and the controller signal. Particularly, the event on controller signal is enforced to suspend for a certain time after each execution to guarantee a positive lower bound for the inter-execution intervals. More importantly, the suspension time and the threshold therein are both online adjusted according to dynamic gain (rather than pre-specified), which could become small enough as the dynamic gain increases. This ensures timely execution for the effectiveness of adaptive compensation. Then, with the dynamic gain delicately designed to counteract the influence of the execution error, an event-triggered controller via adaptive output feedback is proposed to make the original system states and observer states converge to zero. Further attempt is performed for more efficient resource saving and disturbance tolerance. [ABSTRACT FROM AUTHOR]

In this paper, the output feedback based periodic event-triggered control problem is considered for a class of nonminimum-phase nonlinear systems via dynamic event-triggering mechanism. When only the sampled-data output is known, a new periodic event-triggered control method is proposed via output feedback and the control input updates based on a discrete-time dynamic event-triggering condition. Despite the unstable zero dynamics, the proposed control method can asymptotically stabilize the hybrid control systems by closing the loop only when it is necessary. In contrast to the continuous-time static one, the proposed dynamic triggering condition has several advantages including the easier digital implementation and the larger average inter-event time interval. The delicate analysis gives the explicit expression of the maximum allowable sampling period, and the global asymptotic stability can be achieved for the hybrid control systems. Finally, the effectiveness of the proposed periodic event-triggered control method is verified by a numerical simulation. [ABSTRACT FROM AUTHOR]

In this paper, the observer based neural adaptive finite-time containment control strategy for non-strict feedback nonlinear multi-agent systems is studied. The finite-time command filter is used to overcome the explosion of complexity problem and the established fractional power based error compensation signal is applied to compensate the filtering error caused by the filter. The distributed finite-time command filtered backstepping control method combines with the neural adaptive control technology and state observer is given, which ensures the containment control errors reach to the desired neighborhood of the origin in finite-time in the presence of uncertain dynamics and unmeasurable states in the system. The given numerical simulations show the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

This paper investigates the secure consensus tracking problem for continuous-time nonlinear multiagent systems with sensor attacks. By designing a secure data selector, the unattacked output data is extracted from a group of output measurements under sparse sensor attacks. Then, by virtue of the obtained data and neural networks, a state observer is constructed to estimate the unavailable system states, where the convex combination theory is introduced to reduce the difficulty of solving observation gains. To utilize the limited communication resources reasonably, a novel saturated threshold event-triggered control strategy is proposed to reduce control updates, and then each update is encoded into a binary signal (0 or 1) to further reduce the occupation of communication bandwidth. The designed control scheme ensures that all closed-loop signals are semi-globally uniformly ultimately bounded, and its effectiveness is verified via a simulation of attitude control of unmanned aerial vehicles. [ABSTRACT FROM AUTHOR]

This paper discusses the distributed fixed-time containment control for networked nonlinear systems via the event/self-triggered approaches over directed graphs. A distributed event-triggered control protocol without continuous control updates is first proposed. In order to relieve the chattering effect, a modified distributed event-triggered control law is developed. To further overcome the drawback of continuous state monitoring and reduce the communication frequency between neighboring agents, a distributed chattering-free self-triggered control strategy is accordingly designed. A favorable aspect of our work is that the unnecessary resource utilizations of computation, communication as well as control updates can be saved while sustaining the desired control properties and excluding the Zeno behavior. Another distinct feature of this paper lies in that the containment control objective is realized in fixed time and the estimate of settling time can be prescribed without dependence on initial states of networked agents. Finally, some simulation results are provided to illustrate the effectiveness of the theoretical control schemes. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the adaptive fast finite-time tracking control problem for a class of uncertain nonlinear strict-feedback systems by using backstepping technique and fast finite-time stable theory. Dynamic surface control approach is introduced to reduce the computational complexity because of the repeated differentiation of virtual signals in the traditional backstepping algorithm. By employing the approximation of fuzzy logic systems, a fuzzy-based adaptive fast finite-time output tracking control approach is presented, which can guarantee the convergence of tracking error and the boundedness of all closed-loop signals in the fast finite-time. In the final, the validity of the developed control method is proved by the simulation results. [ABSTRACT FROM AUTHOR]

In this study, the probabilistic-constrained $\mathcal {H}_{\infty }$ tracking control problem is addressed for a class of stochastic nonlinear systems subject to measurement outliers, stochastic nonlinearities and DoS attacks. The considered systems have the following characters: 1) an unequal redundant-channel communication protocol is adopted to resist the DoS attacks and enhance the reliability of packet transmission. Different from some existing redundant-channel approaches, the considered two channels have different transmission abilities. 2) The measurement outliers (e.g., some unexpected large amplitude disturbances) are concerned and a saturation-function-based observer is proposed to avert the side effects from measurement outliers. 3) The DoS jamming attacks are considered in this paper, and an aperiodic DoS model is utilized. 4) Both sector-bounded nonlinear function and stochastic nonlinear function are involved in the considered systems, which makes the considered systems more general. To compensate the negative effect of the DoS jamming attacks and enhance the reliability of the packet transmission, a novel redundant-channel-based switching protocol is proposed to schedule data transmission when the plant suffers malicious cyber attacks. The primary objective of the present study is to design tracking controller such that the prescribed $\mathcal {H}_{\infty }$ control performance is reached and probabilistic constraints on the tracking error are satisfied simultaneously. To achieve this objective, a probabilistic-constrained $\mathcal {H}_{\infty }$ tracking control algorithm is established to obtain tracking controller gains and minimize the prescribed set of the constraint. Finally, two simulation examples are used to validate the practicability of our devised strategy. [ABSTRACT FROM AUTHOR]

Aiming at a class of switched uncertain nonlinear strict-feedback systems under the action of average dwell time switching signal, this paper proposes a novel adaptive neural network output feedback tracking control based on the consideration of the full state constraints. The controller is proposed based on neural networks. One of the key characteristics of the system discussed is that the state variables cannot be measured and the system states need to be kept within the constraint ranges. For the sake of estimating the unmeasured states, the observer is constructed. In order to ensure all states which are within the time-varying boundary, the tangent barrier Lyapunov function (BLF-Tan) is selected in the design process. The boundedness of the closed-loop signals with average dwell time is guaranteed by the designed controllers and all the states limit in their constrained sets. It has been proved that the output tracking error converge to a small neighborhood of zero. In addition, the significance of the presented control strategy is verified and tested by a simulation example. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of observer-based fault estimation (FE) for discrete-time nonlinear systems via a weighted switching approach. A pair of variable weights is introduced in an efficient but straight-forward way, and thus, the space spanned by the prescribed normalized fuzzy weighting function can be divided into a set of non-overlapping subspaces. A new fuzzy switching FE observer is proposed by designing exclusive FE observer gain matrices for each non-overlapping subspaces, and thus, less conservative off-line designed conditions for the proposed fuzzy switching FE observer are obtained than the previous results by adequately taking advantage of the characteristic information of each non-overlapping subspaces. More importantly, the process of on-line deciding the current subspace’s index at each sampled point is very straightway and some previous time-consuming online operation is avoided, i.e., it can be said that the on-line computational burden also is alleviated in this paper. Finally, the proposed theoretical result is applied to a tunnel diode circuit and the advantages over existing literature are validated by means of objective comparisons. [ABSTRACT FROM AUTHOR]

This paper considers the control problem of p-norm stochastic nonlinear systems with output constraints, while the system nonlinearities are completely unknown and the system states are unavailable except the output. A nonlinear observer is constructed to estimate the unmeasurable states. Then, based on the constructed observer and a tan-type barrier Lyapunov function (BLF), an adaptive fuzzy output-feedback control strategy is developed by combining the technique of adding a power integrator with the fuzzy logic systems (FLSs). The proposed scheme enables that all the signals of the considered closed-loop systems are bounded in probability while the prespecified output constraint is not violated. Finally, a numerical example verifies the validation of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, we present an approach to nonlinear system approximation, called the lattice trajectory piecewise linear (LTPWL) model. The approach involves determining a lattice piecewise linear (PWL) approximation to the state trajectory of a nonlinear system. It has been shown in the literature that the lattice PWL expression can represent any PWL function in any dimension. After the LTPWL approximation has been obtained, the order of each model piece is reduced using a Krylov projection technique. Compared to existing trajectory piecewise linear (TPWL) models, which are quasi-PWL in the whole region, LTPWL models are virtually linear in each subregion. Besides, the single output LTPWL model can be seen as a special kind of TPWL model, in which only one weight is 1, and the other weights are 0. In general, for multiple output LTPWL model, the weights set to be 1 for each component are different, which makes the LTPWL model more flexible in approximation of nonlinear function. The proposed strategy is applied to simulate diode circuits, and the experimental results show that the performance of the LTPWL model is better than that of the traditional TPWL model in terms of approximation accuracy and generalization ability. [ABSTRACT FROM AUTHOR]

In this article, we develop a tracking model predictive control (MPC) scheme for nonlinear systems using the linearized dynamics at the current state as a prediction model. Under reasonable assumptions on the linearized dynamics, we prove that the proposed MPC scheme exponentially stabilizes the optimal reachable equilibrium w.r.t. a desired target setpoint. Our theoretical results rely on the fact that, close to the steady-state manifold, the prediction error of the linearization is small, and hence, we can slide along the steady-state manifold toward the optimal reachable equilibrium. The closed-loop stability properties mainly depend on a cost matrix, which allows us to trade off performance, robustness, and the size of the region of attraction. In an application to a nonlinear continuous stirred tank reactor, we show that the scheme, which only requires solving a convex quadratic program online, has comparable performance to a nonlinear MPC scheme while being computationally significantly more efficient. Furthermore, our results provide the basis for controlling nonlinear systems based on data-dependent linear prediction models, which we explore in our companion paper. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of dynamic event-triggered output feedback tracking control for a class of $p$ -normal nonlinear systems with unknown growth rate. To cope with the unknown growth rate imposed on the system nonlinearities, a dynamic gain technique is introduced and a constructive coordinate transformation is given. On the other hand, an event-triggered strategy combining with the dynamic gain is proposed such that the triggering threshold can be adjusted in an adaptive manner. With the help of the proposed event-triggered strategy, a dynamic event-based output feedback controller is developed to ensure that all signals of the closed-loop system are bounded while the tracking error converges to a small neighborhood of the origin. Moreover, it is proved that the Zeno behavior is excluded in the presence of nonsmooth controller. Two examples, including an induction heater circuit system and a numerical example, are provided to indicate the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

In this paper, the locally fixed-time and globally fixed-time $\mathcal {H}_{\infty }$ control problems for the port-controlled Hamiltonian (PCH) systems are investigated via the interconnection and damping assignment passivity-based control (IDA-PBC) technique. Compared with finite-time stabilization, where the convergence time of the closed-loop system's states relies on the initial values, the settling time of fixed-time stabilization can be adjusted to achieve desired equilibrium point regardless of initial conditions. The concepts of fixed-time $\mathcal {H}_{\infty }$ control, fixed-time stability region (or region of attraction), and fixed-time stability boundary are presented in this paper, and the criterions of globally fixed-time attractivity of a prespecified locally fixed-time stability region are obtained. Combining the locally fixed-time stability of an equilibrium point and the globally fixed-time attractivity of a prespecified fixed-time stability region, the globally fixed-time $\mathcal {H}_{\infty }$ control problem of PCH system is effectively solved. Two novel control laws are designed to deal with the globally fixed-time $\mathcal {H}_{\infty }$ control problem, and the conservativeness in estimating the settling time is also briefly discussed. An illustrative example shows that the theoretical results obtained in this paper work very well in the fixed-time $\mathcal {H}_{\infty }$ control design for PCH systems. [ABSTRACT FROM AUTHOR]

This paper investigates the probabilistic-constrained distributed filtering problem for a class of nonlinear stochastic systems with state constraints and cyber attacks. The considered cyber attacks are periodic denial-of-service (DoS) attacks which are modeled by a kind of periodic pulse-width-modulated (PWM) jamming signals. Different from some existing works, by using the proposed filter design method, the probability of the filtering error exceeding a threshold can be guaranteed below a certain level quantitatively. Furthermore, in order to economize the limited bandwidth resources, an event-triggered communication scheme (ETS) is designed for the data transmission. The aim of the problem addressed is to design a time-varying distributed filters such that: 1) the probability of the filtering error restricted to a given ellipsoid is larger than a specified value; and 2) the obtained ellipsoid threshold is minimized in the sense of matrix norm at each time point. To achieve this purpose, a recursive linear matrix inequality method is utilized and sufficient conditions are derived. Moreover, the filter parameters are explicitly determined in terms of the solution to certain matrix inequalities. Finally, the reliability and applicability of the proposed distributed filtering strategy are demonstrated by an illustrative example. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of event-triggered $\mathcal {H}_{\infty }$ control for continuous Takagi-Sugeno fuzzy systems with repeated scalar nonlinearities. A feasible stability solution is first proposed based on the fuzzy-rule-dependent Lyapunov functional methods and positive definite diagonally dominant matrix techniques, which not only reduces the conservativeness of the resulting closed-loop dynamic system, but also ensures the concerned fuzzy system is asymptotically stable with a specified $\mathcal {H}_{\infty }$ disturbance attenuation performance. Then, sufficient conditions are presented for the existence of admissible state-feedback controller, and the cone complementarity linearization approach is employed to convert the non-convex feasibility problem into a sequential minimization one subject to linear matrix inequalities, which can be validly solved by employing standard numerical software. In the end, a numerical example and a Chua’s chaotic circuit system are provided to show the applicability of the proposed theories. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive fuzzy output feedback event-triggered control problem for a class of switched nonlinear systems with sensor faults. Due to that the unknown nonlinearities of the systems are more general and the sensor undergoes faults, the considered problem is difficult to be addressed by existing schemes. Therefore, fuzzy logic systems are employed to approximate unknown nonlinear terms and a fault compensation coefficient is introduced to compensate for the effect of sensor failures. Then, a state observer is established for estimating unmeasured states. By choosing a suitable common Lyapunov function, an adaptive fuzzy output feedback fault-tolerant event-triggered controller is derived. It is proven that the proposed scheme can guarantee that the system output tracks the desired trajectory effectively, all states of the resulting closed-loop system are semi-globally uniformly ultimately bounded, and the Zeno phenomenon is excluded. Finally, two simulation examples, which include a switched RLC circuit system and a numerical example, are presented to show the the effectiveness of the proposed strategy. [ABSTRACT FROM AUTHOR]

In this paper, the synchronization problem for networked nonlinear agents with time-varying control gain is studied under a synchronous periodic data sampling framework. To achieve synchronization, both the state-dependent and time-dependent event-triggered protocols are proposed. The effectiveness of these protocols is justified by Lyapunov stability theorem based on rigorous mathematical proof, facilitated by a delayed differential inequality with time-dependent parameters. Instead of specifying a lower bound for the control gain, as others usually suggested, our criteria rely on its time-average and thus allow higher flexibility in controller design. Numerical simulations are also presented to confirm the reaching of synchronization and demonstrate the wide applicability of the proposed protocols. [ABSTRACT FROM AUTHOR]

This article further considers the abstraction problem of affine control systems proposed in the paper “Consistent abstractions of affine control systems” by Pappas et al. We present a general solution for the problem. Then, constructions in the abovementioned paper are treated as a special case of our results. We also clarify the statement given in the abovementioned paper, claiming that the canonical construction on M gives the desired affine distribution on N, which solves the abstraction problem of smooth affine control systems. Additional assumptions are added to make the statement hold. [ABSTRACT FROM AUTHOR]

In this paper, $H_\infty $ control problem is investigated by off-policy integral reinforcement learning (IRL) method for the nonlinear systems with completely unknown dynamics, disturbances, and constrained-input. Firstly, according to a model-based policy iteration (PI) algorithm, a model-free algorithm is proposed based on the derived iterative equation, and the equivalence of model-based PI algorithm and model-free algorithm is proven. Then, the model-free algorithm is implemented by off-policy IRL technology to solve the Hamilton-Jacobi-Isaacs (HJI) equation with the collected system data by the least-square approach, where three neural networks (NNs) are constructed to approximate the value function, control and the disturbance. Finally, our proposed methods are applied to stabilize an autonomous third-order Chua’s chaotic circuit system and a non-autonomous second-order memristive chaotic circuit system to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Given an unstable hybrid stochastic differential equation (SDE), can we design a feedback control, based on the discrete-time observations of the state at times $0, \tau, 2\tau, \ldots$ , so that the controlled hybrid SDE becomes asymptotically stable? It has been proved that this is possible if the drift and diffusion coefficients of the given hybrid SDE satisfy the linear growth condition. However, many hybrid SDEs in the real world do not satisfy this condition (namely, they are highly nonlinear) and there is no answer to the question, yet if the given SDE is highly nonlinear. The aim of this paper is to tackle the stabilization problem for a class of highly nonlinear hybrid SDEs. Under some reasonable conditions on the drift and diffusion coefficients, we show how to design the feedback control function and give an explicit bound on $\tau$ (the time duration between two consecutive state observations), whence the new theory established in this paper is implementable. [ABSTRACT FROM AUTHOR]

This paper addresses the stability issue of a class of delayed switched cascade nonlinear systems consisting of separate subsystems and coupling terms between them. Some global and local asymptotic stability sufficient conditions are proposed, drawing stability conclusion of the overall cascade system from those of separate systems. These results essentially rely on the following observation: For a general delayed switched nonlinear system being asymptotically stable, the trajectories of the perturbed system asymptotically approach zero if so does the perturbation. This observation is one of the main results in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we propose new algebraic Gramians for continuous-time switched linear systems, which satisfy generalized Lyapunov equations. The main contribution of this paper is twofold. First, we show that the ranges of those Gramians encode the reachability and observability spaces of a switched linear system. As a consequence, a simple Gramian-based criterion for reachability and observability is established. Second, a balancing-based model order reduction technique is proposed and, under some sufficient conditions, stability preservation and an error bound are shown. Finally, the efficiency of the proposed method is illustrated by means of numerical examples. [ABSTRACT FROM AUTHOR]

This paper aims to give a design strategy on the prescribed performance $ {H_{\infty }}$ tracking control problem for a class of strict-feedback stochastic nonlinear systems based on the backstepping technique. Generally, by using the backstepping design method, the stochastic nonlinear systems can only be made to be bounded in probability and it is difficult to achieve the $ {H_{\infty }}$ performance criterion due to the positive constant term appeared in the stability analysis. Thus, a novel concept with regard to the bounded- $ {H_{\infty }}$ performance is proposed in this paper to overcome the design difficulty. By using the new concept and the adaptive neural network technique as well as Gronwall inequality, an adaptive neural network prescribed performance bounded- $ {H_{\infty }}$ tracking controller is designed. Therein, neural networks are used to approximate the unknown packaged nonlinear functions. The assumption that the approximation errors of neural networks are square-integrable in some literature is eliminated. The designed controller guarantees that all the signals in the closed-loop stochastic nonlinear systems are bounded in probability, the tracking error is constrained into an adjustable neighborhood of the origin with the prescribed performance bounds, and the controlled system has a given $ {H_{\infty }}$ disturbance attenuation performance for external disturbances. Finally, the simulation results are provided to illustrate the effectiveness and feasibility of the proposed approach. [ABSTRACT FROM AUTHOR]

The robust control problem of a class of nonlinear systems subject to external disturbances, control gain uncertainty, and nonlinear uncertainties is investigated in this paper using a nonlinearity estimator-based control approach. Different from the existing results, the crucial but highly restrictive hypothesis on the boundedness of nonlinear uncertainties is removed from this paper by means of the tools of semiglobal stabilization. By delicately constructing a specific composite Lyapunov function for the closed-loop system as well as several useful level sets, the rigorous qualitative robustness performance is presented for the closed-loop system. Finally, an example of a single-link manipulator is utilized to demonstrate the performance specification claimed by the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we propose a convex programming based method to address a long-standing problem of inner-approximating backward reachable sets of state-constrained polynomial systems subject to time-varying uncertainties. The backward reachable set is a set of states, from which all trajectories starting will surely enter a target region at the end of a given time horizon without violating a set of state constraints in spite of the actions of uncertainties. It is equal to the zero sublevel set of the unique Lipschitz viscosity solution to a Hamilton–Jacobi partial differential equation (HJE). We show that inner approximations of the backward reachable set can be formed by zero sublevel sets of its viscosity supersolutions. Consequently, we reduce the inner-approximation problem to a problem of synthesizing polynomial viscosity supersolutions to this HJE. Such a polynomial solution in our method is synthesized by solving a single semidefinite program. We also prove that polynomial solutions to the formulated semidefinite program exist and can produce a convergent sequence of inner approximations to the interior of the backward reachable set in measure under appropriate assumptions. This is the main contribution of this paper. Several illustrative examples demonstrate the merits of our approach. [ABSTRACT FROM AUTHOR]

Because of a powerful temporal-difference (TD) with $\lambda $ [TD($\lambda $)] learning method, this paper presents a novel $n$ -step adaptive dynamic programming (ADP) architecture that combines TD($\lambda $) with regular TD learning for solving optimal control problems with reduced iterations. In contrast with a backward view learning of TD($\lambda $) that is required an extra parameter named eligibility traces to update at the end of each episode (offline training), the new design in this paper has forward view learning, which is updated at each time step (online training) without needing the eligibility trace parameter in various applications without mathematical models. Therefore, the new design is called the online model-free $n$ -step action-dependent (AD) heuristic dynamic programming [NSHDP($\lambda $)]. NSHDP($\lambda $) has three neural networks: the critic network (CN) with regular one-step TD [TD(0)], the CN with $n$ -step TD learning [or TD($\lambda $)], and the actor network (AN). Because the forward view learning does not require any extra eligibility traces associated with each state, the NSHDP($\lambda $) architecture has low computational costs and is memory efficient. Furthermore, the stability is proven for NSHDP($\lambda $) under certain conditions by using Lyapunov analysis to obtain the uniformly ultimately bounded (UUB) property. We compare the results with the performance of HDP and traditional action-dependent HDP($\lambda $) [ADHDP($\lambda $)] with different $\lambda $ values. Moreover, a complex nonlinear system and 2-D maze problem are two simulation benchmarks in this paper, and the third one is an inverted pendulum simulation benchmark, which is presented in the supplemental material part of this paper. NSHDP($\lambda $) performance is examined and compared with other ADP methods. [ABSTRACT FROM AUTHOR]

This paper is concerned with the attack-resilient event-triggered controller design problem of a DC microgrid with multiple nonlinear constant power loads and intermittent denial-of-service (DoS) attacks. First, for a resource efficiency purpose, an event-triggering communication scheme is delicately devised in such a way to only invoke the data transmission over the communication line when the DoS attack is inactive. Second, via characterizing the DoS active and inactive time intervals, a new switching piecewise system model for the nonlinear DC microgrid system is presented. Third, a numerically efficient design criterion on the existence of the desired attack-resilient event-triggered controller is established. It is further shown that various performance indices including resource efficiency, attack resilience, robustness against disturbance, sampling performance of the DC microgrid system can be evaluated in a unified framework. Finally, an illustrative example is given to verify the effectiveness of the proposed control design method for the DC microgrid. [ABSTRACT FROM AUTHOR]

This paper provides a new analytic test to check strong accessibility of nonlinear control systems. This test can be applied to nonlinear systems described by meromorphic vector fields (whose components are fractions of analytic functions). The test consists in checking the rank of a certain finite matrix (which extends to a nonlinear case the classical “controllability matrix” of linear systems theory) and, unlike the classical accessibility test, always terminates giving an exhaustive answer (yes/no) within a fixed number of steps. Further, a generic feature of accessibility is proven: the accessibility from a point $p$ of the system analyticity domain implies the accessibility from almost every point of the domain (generic strong accessibility). The paper provides two simple examples, which illustrate the proposed analytic test and its advantages with respect to the existing results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of disturbance attenuation with internal stability for nonlinear, input-affine systems via measurement feedback. The solution to the above-mentioned problem has been provided, three decades ago, in terms of the solution to a system of coupled nonlinear, first-order partial differential equations (PDEs). As a consequence, despite the rather elegant characterisation of the solution, the presence of PDEs renders the control design synthesis almost infeasible in practice. Therefore, to circumvent such a computational bottle-neck, in this paper we provide a novel characterisation of the exact solution to the problem that does not hinge upon the explicit computation of the solution to any PDE. The result is achieved by considering the immersion of the nonlinear dynamics into an extended system for which locally positive definite functions solving the required PDEs may be directly provided in closed form by relying only on the solutions to Riccati-like, state-dependent, algebraic matrix equations. [ABSTRACT FROM AUTHOR]

One often wishes for the ability to formally analyze large-scale systems—typically, however, one can either formally analyze a rather small system or informally analyze a large-scale system. This paper tries to further close this performance gap for reachability analysis of linear systems. Reachability analysis can capture the whole set of possible solutions of a dynamic system and is thus used to prove that unsafe states are never reached; this requires full consideration of arbitrarily varying uncertain inputs, since sensor noise or disturbances usually do not follow any patterns. We use Krylov methods in this paper to compute reachable sets for large-scale linear systems. While Krylov methods have been used before in reachability analysis, we overcome the previous limitation that inputs must be (piecewise) constant. As a result, we can compute reachable sets of systems with several thousand state variables for bounded, but arbitrarily varying inputs. [ABSTRACT FROM AUTHOR]

This paper presents a novel minimum entropy filter design for a class of stochastic nonlinear systems, which are subjected to non-Gaussian noises. Motivated by stochastic distribution control, an output entropy model is developed using a radial basis function neural network, while the parameters of the model can be identified by the collected data. Based upon the presented model, the filtering problem has been investigated, while the system dynamics have been represented. As the model output is the entropy of the estimation error, the optimal nonlinear filter is obtained based on the Lyapunov design, which makes the model output minimum. Moreover, the entropy assignment problem has been discussed as an extension of the presented approach. To verify the presented design procedure, a numerical example is given, which illustrates the effectiveness of the presented algorithm. The contributions of this paper can be summarized as follows: 1) an output entropy model is presented using a neural network; 2) a nonlinear filter design algorithm is developed as the main result; and 3) a solution of the entropy assignment problem is obtained, which is an extension of the presented framework. [ABSTRACT FROM AUTHOR]

This paper studies an adaptive neural network (NN) tracking control method for a class of uncertain nonlinear strict-feedback systems with time-varying full-state constraints. As we all know, the states are inevitably constrained in the actual systems because of the safety and performance factors. The main contributions of this paper are that: 1) in order to ensure that the states do not violate the asymmetric time-varying constraint regions, an adaptive NN controller is constructed by introducing the asymmetric time-varying barrier Lyapunov function (TVBLF) and 2) the amount of the learning parameters is reduced by introducing a TVBLF at each step of the backstepping. Based on the Lyapunov stability analysis, it can be proven that all the signals in the closed-loop system are the semiglobal ultimately uniformly bounded and the time-varying full-state constraints are never violated. Finally, a numerical simulation is given, and the effectiveness of this adaptive control method can be verified. [ABSTRACT FROM AUTHOR]

This paper studies the high-order sliding mode (HOSM) control for a general class of uncertain nonlinear systems. Firstly, the standard sliding mode system is extended to a new sliding mode system subject to mismatched terms. The use of the new sliding mode system can reduce the system uncertainties in the control channel and relax the well defined relative degree assumption. Secondly, the conventional constant upper bounds assumption is relaxed to time-varying positive functions, which enables us to obtain a global result. For the new sliding mode system under the new global assumption, a novel HOSM controller, that has a simple relay polynomial form, is then proposed. By introducing a new continuous component in the controller, the discontinuous component of the controller only needs to be selected to suppress the uncertainties and thus a controller with minimal discontinuous component magnitude can be implemented. Finally, strict Lyapunov analysis is provided to show the globally finite-time stability of the closed-loop sliding mode system and an application to Buck converter is presented. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a method to obtain necessary and sufficient stability conditions for systems governed by one-dimensional nonlinear hyperbolic partial-differential equations with closed-loop integral controllers, when the linear frequency analysis cannot be used anymore. We study the stability of a general nonlinear transport equation where the control input and the measured output are both located on the boundaries. The principle of the method is to extract the limiting part of the stability from the solution using a projector on a finite-dimensional space and then use a Lyapunov approach. This paper improves a result of Trinh, Andrieu, and Xu, and gives an optimal condition for the design of the controller. The results are illustrated with numerical simulations where the predicted stable and unstable regions can be clearly identified. [ABSTRACT FROM AUTHOR]

In this paper, the main issues of model-based control methods are first reviewed, followed by the motivations and the state of the art of the model-free adaptive control (MFAC). MFAC is a novel data-driven control method for a class of unknown nonaffine nonlinear discrete-time systems since neither explicit physical model nor Lyapunov stability theory or key technical lemma is used in the controller design and theoretical analysis except only for the input/output (I/O) measurement data. The basis of MFAC is the dynamic linearization data modeling method at each operating point of the closed-loop system. The established dynamic linearization data model is a virtual equivalent data relationship in the I/O sense to the original nonlinear plant by means of a novel concept called pseudo-partial derivative (PPD) or pseudo-gradient (PG) vector. Based on this virtual equivalent dynamic linearization data model and the time-varying PPD or PG estimation algorithm designed merely using the I/O measurements of a controlled plant, the MFAC system is constructed. The main contribution of this paper is that the theoretical analysis of the bounded-input bounded-output stability, the monotonic convergence of the tracking error dynamics, and the internal stability of the full form dynamic linearization based MFAC scheme are rigorously presented by the contraction mapping principle; the well known PID control and the traditional adaptive control for linear time-invariant systems are explicitly shown as the special cases of this MFAC. The simulation results verify the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper presents a novel scheme of controller design for a cross-coupled multi-input multi-output (MIMO) two link robot manipulator (TLRM) system having time varying uncertainties, disturbances, and nonlinearity by employing fuzzy parallel distributed compensation (PDC) type ${L}_{1}$ adaptive controller. The combination of linear consequence-based fuzzy subsystems are utilized to represent the nonlinear TLRM system. The components of $ {L}_{1}$ adaptive control framework are also realized by combining linear consequence-based fuzzy systems to incorporate the zone-wise controlling of the TLRM system. A fuzzy PDC control has also been augmented to achieve robust stable transient and steady state performances. The stability of each fuzzy systems as well as the overall proposed control scheme is guaranteed by utilizing fuzzy Lyapunov theory-based analysis. The experimental results demonstrate the usefulness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper proposes a less conservative stability criterion for discrete-time Lur'e systems with sector and slope restrictions by constructing a novel Lyapunov functional. Compared with the Lyapunov functional in the literature, this paper fully utilizes the sector and slope restrictions in our Lyapunov functional, which includes integral terms involved with the sector restriction of the nonlinearities $\phi (y_{i})$ and $\phi (y_{i+1})$ , integral terms involved with the slope restriction between $\phi (y_{i})$ and $\phi (y_{i+1})$ , and a quadratic term with an augmented vector related to available vectors for representing upper and lower bounds of all integral terms. The positive definiteness of a matrix appearing in the quadratic term can be relaxed by utilizing the lower bounds of all integral terms. Based on the Lyapunov functional, an improved stability criterion is derived in terms of linear matrix inequalities. Numerical examples show the effectiveness of the proposed criterion. [ABSTRACT FROM AUTHOR]

This paper is concerned with the rate at which a discrete-time, deterministic, and possibly large network of nonlinear systems generates information, and so with the minimum rate of data transfer under which the addressee can maintain the level of awareness about the current state of the network. While being aimed at development of tractable techniques for estimation of this rate, this paper advocates benefits from directly treating the dynamical system as a set of interacting subsystems. To this end, a novel estimation method is elaborated that is alike in flavor to the small gain theorem on input-to-output stability. The utility of this approach is demonstrated by rigorously justifying an experimentally discovered phenomenon. The topological entropy of nonlinear time-delay systems stays bounded as the delay grows without limits. This is extended on the studied observability rates and appended by constructive upper bounds independent of the delay. It is shown that these bounds are asymptotically tight for a time-delay analog of the bouncing ball dynamics. [ABSTRACT FROM AUTHOR]

This paper studies the consensus tracking problem of uncertain Lagrangian systems. In contrast to the existing results where the command signals are sufficiently smooth, we consider a class of nonsmooth command signals generated by a switched command generator, which might be more realistic from the perspective of practical applications. The main technical innovations of this paper are threefold. First, to enable a rigorous problem formulation, some piecewise decaying function sets are defined to precisely describe the steady-state behaviors of the tracking errors. Second, to ensure the stability of the switched nonlinear closed-loop system, a system-based scaling method with the establishment of several lemmas is developed to determine the minimal dwell time of the switching signal. Third, a quantitative analysis is performed to acquire the ultimate bound for the steady-state tracking errors. The proposed control approach is evaluated by a simulation example. [ABSTRACT FROM AUTHOR]

This paper addresses the event-triggered tracking for a class of uncertain nonlinear systems. Essentially different from the related works, the nonlinear systems allow serious (parametric) uncertainties, while no further a priori information, excepting some coarse information, is required on the reference signal to be tracked. This makes event-triggered control more challenging, partially because the sampling error cannot be precisely bounded any more. As main contributions of this paper, new adaptive event-triggered tracking schemes are proposed for the systems in two event-triggering architectures with different roles of the event-triggering mechanism on the information transmitting and control computing/updating. Much importantly, a dynamic gain is incorporated in either scheme not only to counteract the serious uncertainties, but also to overcome the bad influence of the sampling error. Based on the dynamic gain, two adaptive event-triggered controllers are designed with distinct event-triggering mechanisms, respectively. Particularly, to ensure application flexibility, one of the triggering mechanisms is rendered relatively independent of the controller signal. The designed event-triggered controllers are shown to achieve the practical tracking for the systems, that is, the prespecified arbitrary tracking accuracy can be guaranteed (a comparable objective to that via continuous-time control), while avoiding infinitely fast sampling/execution. [ABSTRACT FROM AUTHOR]