Observer-based fault detection for uncertain nonlinear systems

This paper addresses L₂ observer-based fault detection issues for a class of nonlinear systems in the presence of parametric and dynamic uncertainties, respectively. To this end, three different types of uncertain affine nonlinear system models studied in this paper are described first. Then, the integrated design schemes of L₂ observer-based fault detection systems are derived with the aid of Hamilton–Jacobi inequalities (HJIs), respectively. Numerical examples are also provided in the end to demonstrate the effectiveness of the proposed results.     

Observer-based terminal sliding mode control of non-affine nonlinear systems: Finite-time approach

This paper studies the problem of observer based fast nonsingular terminal sliding mode control schemes for nonlinear non-affine systems with actuator faults, unknown states, and external disturbances. A hyperbolic tangent function based extended state observer is considered to estimate unknown states, which enhances robustness by estimating external disturbance. Then, Taylor series expansion is employed for the non-affine nonlinear system with actuator faults, which transforms it to an affine form system to simplify disturbance observer and controller design. A finite time disturbance observer is designed to address unknown compound disturbances, which includes external disturbances and system uncertainties. A fast nonsingular terminal sliding mode with exponential function sliding mode is proposed to address output tracking. Simulation results show the proposed scheme is effective.     

Observer-based adaptive fuzzy control of a class of MIMO non-strict feedback nonlinear systems

This paper investigates the adaptive fuzzy control design problem of multi-input and multi-output (MIMO) non-strict feedback nonlinear systems. The considered control systems contain unknown control directions and dead zones. Fuzzy logic systems (FLSs) are utilized to approximate the unknown nonlinear functions, and the state observers are designed to estimate immeasurable states. By constructing a dead zone compensator and introducing a Nussbaum gain function into the backstepping technique, an adaptive fuzzy output feedback control method is developed. The proposed adaptive fuzzy controller is proved to guarantee the semi-globally uniformly ultimately bounded (SGUUB) of the closed-loop system, and can solve the control design problems of unmeasured states, unknown control directions and dead zones. The simulation results are given to demonstrate the effectiveness of the proposed control method.     

Observer-based fuzzy adaptive stabilization of uncertain switched stochastic nonlinear systems with input quantization

This paper proposes an observer-based fuzzy adaptive output feedback control scheme for a class of uncertain single-input and single-output (SISO) nonlinear stochastic systems with quantized input signals and arbitrary switchings. The SISO system under consideration contains completely unknown nonlinear functions, unmeasured system states and quantized input signals quantized by a hysteretic quantizer. By adopting a new nonlinear disposal of the quantized input, the relationship between the control input and the quantized input is established. The hysteretic quantizer that we take can effectively avoid the chattering phenomena. Furthermore, the introduction of a linear observer makes the estimation of the states possible. Based on the universal approximation ability of the fuzzy logic systems (FLSs) and backstepping recursive design with the common stochastic Lyapunov function approach, a quantized output feedback control scheme is constructed, where the dynamic surface control (DSC) is explored to alleviate the computation burden. The proposed control scheme cannot only guarantee the boundedness of signals but also make the output of the system converge to a small neighborhood of the origin. The simulation results are exhibited to demonstrate the validity of the control scheme.     

Adaptive tracking control for quantized nonlinear systems via backstepping design technique

In this paper, the adaptive tracking control problem for a class of strict-feedback nonlinear systems with quantized input signal is investigated. The hysteretic quantizer is introduced to avoid the chattering phenomenon and the backstepping method is used to design the controller. The tracking errors are guaranteed to be bounded in a small neighborhood of zero via appropriate design parameters. Finally, two simulation examples are given, and the simulation results further demonstrate the effectiveness of the proposed method.     

Observer-based control for singular nonhomogeneous Markov jump systems with packet losses

This paper is concerned with the observer-based H_∞ control for a class of singular Markov jump systems over a finite-time interval, where the transition probability (TP) is time-varying and is limited to a convex hull. Due to the limited capacity of network medium, packet losses are presented in the underlying systems. Firstly, using a stochastic Lyapunov functional, a sufficient condition on singular stochastic H_∞ finite-time boundedness for the corresponding closed-loop error systems is provided. Subsequently, a linear matrix inequality (LMI) condition on the existence of the H_∞ observer-based controller is developed from a new perspective. Finally, three numerical examples are provided to illustrate the effectiveness of the proposed controller design method, wherein it is shown that the proposed method yields less conservative results than those in the literature.     

Observer-based exponential stabilization for time-delay systems via augmented weighted integral inequality

In this paper, we design observer-based feedback control for a class of linear systems. The novelty of the paper comes from the consideration of an augmented weighted based integral inequality involving quadratic functions with an exponential term which is less conservative than the celebrated weighted integral inequality employed in the context of time-delay systems. By using appropriately chosen Lyapunov–Krasovskii functional (LKF), together with the derived integral inequality, a new sufficient condition for exponential stability in terms of linear matrix inequalities (LMIs) is proposed for the delayed linear systems with state feedback control. Finally, the applicability and superiority of the proposed theoretical results over the existing ones are analyzed in virtue of numerical examples.     

Observer-based output regulation of cooperative-competitive high-order multi-agent systems

In this paper, a coopetitive output regulation problem is considered for general linear multi-agent systems with antagonistic interactions, where not all the agents have access to the state, the output, the system matrix and the output matrix of the exogenous system or exosystem. In this sense, the internal model incorporation of the system matrix of the exosystem is also only available to some agents. Thus, we propose distributed observers for each agent: (i) To estimate the state, the output, the system matrix and the output matrix, and (ii) the unavailable internal model of the exosystem. Then, a distributed dynamic output feedback controller is proposed for each agent to solve the coopetitive output regulation problem. The exponential stability of the closed-loop system is analyzed with the output regulation theory. Finally, some simulation results are presented to validate the proposed control strategy.     

Observer design for a class of nonlinear fractional-order systems with unknown input

A full order fractional-order observer is designed for a class of Lipschitz continuous-time nonlinear fractional-order systems with unknown input. Sufficient conditions of existence for the designed observer and stability of state estimation error system are developed by reconstructing state and using general quadratic Lyapunov function. By applying fractional-order extension of Lyapunov direct method, the stability of the fractional-order state estimation error system is analyzed. Due to the conditions involving a nonlinear matrix inequality, a new sufficient condition with linear matrix inequality (LMI) is reformulated, which makes the full order fractional-order observer implemented easily by using Matlab LMI toolbox. Examples are taken to show the effectiveness of the proposed approach by numerical simulations.     

Impulsive observer design for a class of switched nonlinear systems with unknown inputs

This paper investigates hybrid observer design of a class of unknown input switched nonlinear systems. The distinguishing feature of the proposed method is that the stability of all subsystems of the error switched systems is not necessarily required. First, an output derivative-based method and time-varying coordinate transformation are considered to eliminate the unknown input. Then in order to maintain a satisfactory estimation performance, an impulsive full-order and switched reduced-order observer are developed with a pair of upper and lower dwell time bounds and constructing time-varying Lyapunov functions combined with convex combination technique. In addition, the time-varying Lyapunov functions method is also used to analyze the stability of a class of error switched nonlinear systems with stable subsystems. Finally, two examples are presented to demonstrate the effectiveness of the proposed method.     

Fault-tolerant safe control design of switched and interconnected nonlinear systems

This paper provides novel fault-tolerant safe control (FTSC) strategies for switched and interconnected nonlinear systems. With several switching and interconnection situations considered, the proposed corresponding strategies ensure that the state never enters the unsafe set and asymptotically converges to the origin in the presence of faults. This relies on a proposed concept named “fault-tolerant control Lyapunov-Barrier functions (FTCLBF)”. Two practical examples are taken to demonstrate the efficiency of the proposed method.     

Adaptive iterative learning protocol design for nonlinear multi-agent systems with unknown control direction

This paper investigates a new adaptive iterative learning control protocol design for uncertain nonlinear multi-agent systems with unknown gain signs. Based on Nussbaum gain, adaptive iterative learning control protocols are designed for each follower agent and the adaptive laws depend on the information available from the agents in the neighbourhood. The proper protocols guarantee each follower agent track the leader perfectly on the finite time interval and the Nussbaum-type item can seek control direction adaptively. Furthermore, the formation problem is studied as an extension. Finally, simulation examples are given to demonstrate the effectiveness of the proposed method in this article.     

Event-triggered fault detection filter design for nonlinear networked systems via fuzzy Lyapunov functions

This paper investigates the problem of event-triggered fault detection filter design for nonlinear networked control systems with both sensor faults and process faults. First, Takagi–Sugeno (T–S) fuzzy model is utilized to represent the nonlinear systems with faults and disturbances. Second, a discrete event-triggered communication scheme is proposed to reduce the utilization of limited network bandwidth between filter and original system. At the same time, considering network-induced delays and event-triggered scheme, a novel T–S fuzzy fault detection filter is constructed to generate a residual signal, which has nonsynchronous premise variables with the original T–S fuzzy system. Then, the fuzzy Lyapunov functional based approach and the reciprocally convex approach are developed such that the obtained sufficient conditions ensure that the fuzzy fault detection system is asymptotically stable with H_∞ performance and is less conservative. All the conditions are given in terms of linear matrix inequalities (LMIs), which can be solved by LMI tools in MATLAB environment. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed results.     

Adaptive neural design frame for uncertain stochastic nonlinear non-lower triangular pure-feedback systems with input constraint

This paper dedicates to dealing with the adaptive neural design problem for uncertain stochastic nonlinear systems with non-lower triangular pure-feedback form and input constraint. On the basis of the mean-value theorem, the pure-feedback structure is first transformed into the desired affine structure, and then the well-known backstepping technology is applied to construct the actual input signal of the controller. Although the considered system has a fairly complex structure, a new adaptive neural tracking controller design frame is established via the flexible application of radial basis function (RBF) neural networks’ (NNs’) structural characteristics. The proposed design frame guarantees the control objective of this paper can be achieved. Finally, a simulation example is given to further illustrate the availability of the proposed control scheme.     

Observer-based event-triggered tracking consensus of non-ideal general linear multi-agent systems

In this paper, the leader-following consensus problem of general linear multi-agent systems without direct access to real-time state is investigated. A novel observer-based event-triggered tracking consensus control scheme is proposed. In the control scheme, a distributed observer is designed to estimate the relative full states, which are used in tracking consensus protocol to achieve overall consensus. And an event-triggered mechanism with estimated state-dependent event condition is adopted to update the control signals so as to reduce unnecessary data communication. Based on the Lyapunov theorem and graph theory, the proposed event-triggered control scheme is proved to implement the tracking consensus when real-time state cannot direct obtain. Moreover, such scheme can exclude Zeno-behavior. Finally, numerical simulations illustrate the effectiveness of the theoretical results.     

Dissipative observers for discrete-time nonlinear systems

This paper addresses the problem of designing a state observer for a class of nonlinear discrete-time systems using the dissipativity theory. We show that the dissipative observation methodology, originally proposed by one of the authors for continuous-time nonlinear systems, can be extended to the discrete-time case. For constructing a convergent observer, the methodology is applied to the nonlinear estimation error dynamics, which is decomposed into a discrete-time Linear Time-Invariant (LTI) subsystem in the forward loop, connected to a time-varying static nonlinearity in the feedback loop. In order to assure asymptotic stability of the closed-loop, complementary dissipativity conditions are imposed on each of the subsystems: (i) the static nonlinearity is required to be dissipative with respect to a quadratic supply rate, and (ii) the observer gains are designed such that the LTI system is dissipative with respect to a complementary supply rate. As in the continuous time framework, the proposed method includes as special cases, unifies and generalizes some observer design methods proposed previously in the literature. A great advantage of the Dissipative Observer Design Method proposed here is that it leads to Matrix Inequalities for the design of the observer gains, and these can be usually converted into Linear Matrix Inequalities (LMI’s). The results are illustrated using Chua’s Chaotic system.     

An improved design strategy for approximation-based adaptive event-triggered tracking of a class of uncertain nonlinear systems

This paper presents an improved adaptive design strategy for neural-network-based event-triggered tracking of uncertain strict-feedback nonlinear systems. An adaptive tracking scheme based on state variables transmitted from the sensor-to-controller channel is designed via only single neural network function approximator, regardless of unknown nonlinearities unmatched in the control input. Contrary to the existing multiple-function-approximators-based event-triggered backstepping control results with multiple triggering conditions dependent on all error surfaces, the proposed scheme only requires one triggering condition using a tracking error and thus can overcome the problem of the existing results that all virtual controllers with multiple function approximators should be computed in the sensor part. This leads to achieve the structural simplicity of the proposed event-triggered tracker in the presence of unmatched and unknown nonlinearities. Using the impulsive system approach and the error transformation technique, it is shown that all the signals of the closed-loop system are bounded and the tracking error is bounded within pre-designable time-varying bounds in the Lyapunov sense.