Amplitude-bounded Disturbance Research Articles

Event-based fault estimation and compensation for discrete-time systems via zonotopes

A fault estimation and compensation approach is presented for discrete-time systems with event-triggered scheme based on zonotope techniques in this paper. Instead of energy-bounded uncertainties, the dynamic system is supposed to be subjected to unknown but amplitude-bounded disturbance and noise, which is more in line with engineering practice. By introducing dynamic interval variables, a component-wise dynamic event-triggered strategy is utilized to reduce the consumption of communication resources. With considering the amplitude-bounded uncertainties and event-triggered scheme, a joint state-fault estimator is constructed to estimate the system state as well as possible system faults simultaneously, which are utilized to construct the fault-tolerant controller by compensating the effects of system faults. A co-design approach of the estimator, compensator, and event-triggered strategy is proposed to guarantee the stability and l1 performance of the system, based on which a zonotope-based interval estimation algorithm of system state and possible faults is provided to obtain the tight estimation of system state and faults. Eventually, simulation results on aircraft engine systems indicate that the designed method achieves a satisfactory fault estimation and fault tolerance performance, and also reduce the consumption of communication resources significantly.

Event-triggered L1 filtering for uncertain networked control systems with multiple sensor fault modes

Considering the influence of sensor fault modes on the system performance in communication network, under the discrete event-triggered communication scheme (DETCS), the problems of the robust [Formula: see text] filtering for a class of uncertain networked control systems (NCSs) with multiple sensor fault modes and persistent and amplitude-bounded disturbance constraints are investigated. A set of stochastic variables are adopted to describe the sensor faults, the filtering error system is established, which characterizes the effects of sensor faults and DETCS. By constructing an appropriate delay-dependent Lyapunov-Krasovskii functional, new results on stability and robust [Formula: see text] performance are proposed for the filtering error system according to Lyapunov theory and the integral inequality method, and the co-design method for gaining the desired [Formula: see text] filter parameters and event-triggering parameters is given in terms of linear matrix inequalities (LMIs). We notice that with the structrue of Lyapunov-Krasovskii functional which considers the piecewise-linear sawtooth structure characteristic of transmission delay, a less conservative result is obtained. Finally, three examples are provided to illustrate the feasibility of the proposed method.

Zonotopic Fault Detection for Fuzzy Systems With Event-Triggered Transmission

This article deals with the zonotopic fault detection for fuzzy systems with event-triggered mechanism. An <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _1/h_{\infty }$</tex-math></inline-formula> fault detector design method is deduced with considering the asynchronous premise variables caused by event-triggered transmission, such that the residual signal is sensitive to system failure while robust to amplitude-bounded disturbance, and noise. Then, a novel zonotopic residual evaluation process is constructed by converting the asynchronization of premise variables into system uncertainties. Different from most published works on event-triggered fault detection where constant thresholds are utilized for residual evaluation, zonotopic thresholds for residual signal are designed with taking the influences of disturbance, noise, asynchronous premise variables, and event-based transmission into consideration. Finally, a numerical example is utilized to verify the effective performance of the developed strategy.

L1 control for Itô stochastic nonlinear networked control systems

This paper investigates L1 control problem for a class of nonlinear stochastic networked control systems (NCSs) described by Takagi-Sugeno (T-S) fuzzy model. By exploiting a delay-dependent and basis-dependent Lyapunov-Krasovskii function and by means of the Itô stochastic differential equation technique, results on stability and L1 performance are proposed for the T-S fuzzy stochastic NCS. Specially, attention is focused on the fuzzy controller design that guarantees the closed-loop T-S fuzzy stochastic NCS is mean-square asymptotically stable and satisfies a prescribed L1 noise attenuation level [Formula: see text] with respect to all persistent and amplitude-bounded disturbance input signals. To reduce the conservatism of design, the signal transmission delay, data packet dropout, and quantization have been taken into consideration in the controller design. The corresponding design problem of L1 controller is converted into a convex optimization problem by solving a set of linear matrix inequalities (LMIs). Finally, simulation examples are provided to illustrate the feasibility and effectiveness of the proposed method.

Asynchronous observer design for switched linear systems: a tube-based approach

This paper proposes a tube-based method for the asynchronous observation problem of discrete-time switched linear systems in the presence of amplitude-bounded disturbances. Sufficient stability conditions of the nominal observer error system under mode-dependent persistent dwell-time &#x0028 MPDT &#x0029 switching are first established. Taking the disturbances into account, a novel asynchronous MPDT robust positive invariant &#x0028 RPI &#x0029 set and an asynchronous MPDT generalized RPI &#x0028 GRPI &#x0029 set are determined for the difference system between the nominal and disturbed observer error systems. Further, the global uniform asymptotical stability of the observer error system is established in the sense of converging to the asynchronous MPDT GRPI set, i.e., the cross section of the tube of the observer error system. Finally, the proposed results are validated on a space robot manipulator example.

Quantized L1 filtering for stochastic networked control systems based on T–S fuzzy model

This paper is concerned with the L1 filtering problem for a class of nonlinear Ito^ stochastic networked control systems (NCSs) described by Takagi–Sugeno (T–S) fuzzy model. Considering the disadvantages of network-induced delay and quantization error in information transmission, new results on stability and L1 performance are proposed for T–S fuzzy stochastic NCSs by exploiting a Lyapunov–Krasovskii function and by means of the Ito^ stochastic differential equations. Specially, attention is focused on the design of quantization filters of both the fuzzy-rule-independent and fuzzy-rule-dependent that guarantee a prescribed L1 noise attenuation level γ with respect to all persistent and amplitude-bounded disturbance input signals. Then, when fuzzy-rule-independent filter is employed, a sufficient condition is proposed to guarantee the mean-square asymptotic stability with an L1 performance for the T–S fuzzy filtering error system. The corresponding design problem of L1 filter is converted into a convex optimization problem by solving a set of linear matrix inequalities (LMIs). Further, the parallel results with the fuzzy-rule-dependent filtering case are obtained, which have less conservatism than the fuzzy-rule-independent one. Finally, two simulation examples are provided to illustrate the feasibility and effectiveness of the proposed method.

Distributed Consensus Control of One-Sided Lipschitz Nonlinear Multiagent Systems

This paper addresses the distributed consensus controller design approaches for one-sided Lipschitz nonlinear multiagents by employing relative state feedback. A new treatment for one-sided Lipschitz nonlinearity is rendered from the consensus control point of view. By employing the quadratic inner-boundedness and the one-sided Lipschitz constraints, a sufficient condition for asymptotic consensus of nonlinear systems under strongly connected communication topologies is provided. Further, a robust consensus protocol design scheme for the nonlinear multiagents is derived by ensuring the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> stability of the consensus error system. Furthermore, a novel robust consensus control scheme against amplitude-bounded perturbations is developed that guarantees asymptotic convergence of the consensus error into a compact set. Extensions to the proposed methodologies for the leader-following consensus for a spanning tree communication topology with the leader as the root are addressed. In contrast to the conventional consensus control methodologies, this paper is less conservative and can be applied to a broader class of nonlinear multiagent systems. Moreover, the proposed consensus control approach is less conservative for robustness against disturbances owing to its ability to handle amplitude-bounded disturbances and due to the relaxation of a balanced communication topology. A numerical simulation study is provided for the consensus control of eight mobile agents.

Partial boundedness analysis: a state‐space transformation method for reshaping the estimated domain of stability

This study focuses on the problem of the state upper bound estimation for linear systems subject to amplitude-bounded disturbances. A state-space transformation method is proposed to reshape the estimated domain of stability, which is used to analyse the upper bound of a part of system states. By analysing the estimated domains of stability corresponding to different quadratic Lyapunov functions (QLFs), a universal expression for the upper bounds of a part of system states is obtained. By minimising the universal expression, an appropriate QLF is designed to gain the less conservative estimation on the upper bound of a part of system states. The proposed method provides a novel way of constructing and selecting the appropriate QLF to obtain the less conservative results on the upper bound of a part of system states. The effectiveness of the method is illustrated by two examples.

Basis-dependent and delay-dependent results on robust L1 filtering for networked control systems

Persistent and amplitude-bounded disturbances are nowadays considered for various engineering applications. Whereas the traditional H∞ and L2–L∞ filtering methods under the energy-bounded external disturbances assumption cannot receive good noise suppression effect. To effectively reflect the capability of disturbances suppression, this paper proposes a robust L1 filtering approach for a class of nonlinear networked control systems (NNCSs) described by Takagi–Sugeno (T–S) fuzzy model. According to the analysis of the typical time-delay issue induced by communication network and the parallel distributed compensation (PDC) technique, a fuzzy filtering error system is established. Attention is focused on designing the robust L1 filter that guarantees the fuzzy filtering error system to be asymptotically stable and to have a prescribed L1 noise attenuation level γ with respect to all persistent and amplitude-bounded disturbances. In particular, we concentrate on the delay-dependent case, using a basis-dependent Lyapunov–Krasovskii functional which refers to reducing the conservatism, the peak-to-peak performance criterion is first proposed. The integral inequality method and linear matrix inequality (LMI) technique are adopted during the process of robust L1 stability analysis. Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed method.

Robust L1 dynamic output feedback control for a class of networked control systems based on T–S fuzzy model

This paper investigates the robust L1 dynamic output feedback control problem for a class of nonlinear networked control systems (NCSs) represented by Takagi–Sugeno (T–S) fuzzy model. In consideration with the imperfect networked environment with signal transmission delay and data packet dropout, a fuzzy NCS via dynamic output feedback is established by utilizing the parallel distributed compensation (PDC) technique. The attention is focused on designing the robust L1 controller that guarantees being asymptotically stable of the fuzzy NCS and satisfies a prescribed L1 noise attenuation level γ with respect to all persistent and amplitude-bounded disturbance input signals. In particular, we concentrate on constructing a delay- and basis- dependent Lyapunov–Krasovskii function which is in favor of reducing the conservatism, and furthermore, by using the integral inequality method and the Projection Lemma, the peak-to-peak performance criterion is first established. In this way, the design problem of the admissible L1 dynamic output feedback controller can be converted into a convex optimization problem of solving a set of linear matrix inequalities (LMIs). Simulation results are provided to illustrate the effectiveness of the proposed method.

Anti-windup based dynamic output feedback controller design with performance consideration for constrained Takagi–Sugeno systems

This paper proposes an LMI-based method to guarantee the closed-loop regional stability and performance for Takagi–Sugeno systems that are subject to input saturation, state constraints, and also amplitude-bounded disturbance. Based on the Lyapunov stability tool, the proposed method provides conditions to simultaneously design the dynamic output feedback controller and its anti-windup compensator. By solving a convex optimization problem, these conditions are derived such that a tradeoff between the upper bound on the nominal ℒ2 gain for exogenous disturbance and the minimal size of the domain of attraction can be found. This method is simple and systematic, allowing dealing with a very large class of constrained nonlinear systems. The effectiveness of the proposed method is illustrated with numerical examples.

Robust L1 fixed-order filtering for switched LPV systems with parameter-dependent delays

This paper is concerned with the L1 fixed-order filtering problem for a class of switched linear parameter-varying (LPV) systems in which the system matrices and the time delays are dependent on the real-time measured parameters. The authors׳ attention is concentrated on designing the fixed-order filter that guarantees the filtering error system to be exponentially stable and to satisfy a prescribed L1 disturbance attenuation level with respect to all amplitude-bounded disturbances. Based on the switching logic with the minimum average dwell time (ADT), the delay-dependent L1 performance criterion for the switched LPV systems is first established. As there exists coupling between a Lyapunov function matrix and system parameter matrices, we utilize a slack matrix to decouple it. According to the obtained results, the admissible filter can be solved in terms of parameter linear matrix inequality (PLMI) technology. Using approximate basis function and gridding technique, the L1 filter design can be transformed into finite number of LMIs. A numerical example is presented to verify the effectiveness of the proposed method.

Minimax Control of Linear Systems with Amplitude Bounded Disturbances

Optimal control problem formulated for linear constant-coefficient system subjected to class of amplitude bounded load disturbances