Class Of Uncertain Discrete-time Systems Research Articles

Event‐triggered robust adaptive control for discrete time uncertain systems with unmodelled dynamics and disturbances

In practice, modelling errors caused by high-order unmodelled dynamics and external disturbances are unavoidable. How to ensure the robustness of an adaptive controller with respect to such modelling errors is always a critical concern. In this study, the authors consider the design of event-triggered robust adaptive control for a class of discrete-time uncertain systems which involve such modelling errors and also are allowed to be non-minimum phase. Unlike some existing event-triggered control schemes, the developed controllers do not require that the measurement errors meet the corresponding input-to-state stable condition. Global stability of the closed-loop system which means that all the signals are bounded is established in the presence of unmodelled dynamics and disturbances. Besides, in contrast to existing robust adaptive schemes, the designed adaptive controller does not involve parameters related to unmodelled dynamics and disturbances which are difficult to be chosen for ensuring such stability. An example is given to verify the effectiveness of the proposed control strategy.

Event‐triggered distributed fault detection over sensor networks in finite‐frequency domain

In this study, the event-triggered distributed fault detection problem is investigated for a class of discrete-time uncertain systems in the finite frequency domain. A sensor network is utilised to collect the information of interest, and an event-triggered communication scheme is adopted to alleviate the communication burden. For the addressed problem, a distributed fault detection filter is designed based on the measurement information from its neighbouring nodes and itself by the given topology. In addition, a fashionable index, named as H - /H ∞ performance, is employed in order to simultaneously achieve the residual sensitivity to faults and the robustness against disturbances. By resorting to Euler's formula combined with Lyapunov stability theory, some sufficient conditions are established to satisfy the desired performance over a given finite-frequency domain, and the distributed fault detection filter gains are explicitly characterised by solving a series of linear matrix inequalities. A simulation example is conducted to illustrate the feasibility of the proposed filter design technique.

Robust Guaranteed Cost Control Under Digital Communication Channels

This paper investigates the feedback guaranteed cost control problem for a class of uncertain discrete-time systems with input quantization. The plant with polytope type uncertainties is considered. The input signal will be quantized by a dynamic quantizer before it is transmitted from the controller to the system under digital communication channels. First, a design method of the feedback control for the quantized closed-loop system is given to attain the same guaranteed cost performance as the one without signal quantization. Then, by introducing some useful auxiliary scalars, the dynamic parameter of the quantizer is also designed effectively so that the desired performance level can be achieved. A simulation example is provided to show the effectiveness of the proposed design method.

Observer-Based Finite-Time Nonfragile Control for Nonlinear Systems With Actuator Saturation

This paper considers a design problem of dissipative and observer-based finite-time nonfragile control for a class of uncertain discrete-time system with time-varying delay, nonlinearities, external disturbances, and actuator saturation. In particular, in this work, it is assumed that the nonlinearities satisfy Lipschitz condition for obtaining the required results. By choosing a suitable Lyapunov–Krasovskii functional, a new set of sufficient conditions is obtained in terms of linear matrix inequalities, which ensures the finite-time boundedness and dissipativeness of the resulting closed-loop system. Meanwhile, the solvability condition for the observer-based finite-time nonfragile control is also established, in which the control gain can be computed by solving a set of matrix inequalities. Finally, a numerical example based on the electric-hydraulic system is provided to illustrate the applicability of the developed control design technique.

Modelling and Estimation for Uncertain Systems with Transmission Delays, Packet Dropouts, and Out-of-Order Packets

The study focuses on the modelling and estimation of a class of discrete-time uncertain systems, including network-induced random delays, packet dropouts, and out-of-order packets during the data transmission from the plant to the estimator. In order to improve system performance, event-triggered signal selection method is used to establish the system model. Based on this model, a distributed measurement and centralized fusion estimation scheme is designed using a robust finite horizon Kalman-type filter. Since the phenomena caused by the network-induced deteriorate estimation accuracy, a time-based reorganization measurement is employed to design a linear delay compensation strategy based on estimation. Moreover, in order to obtain the optimal linear estimation, weighted fusion estimation approach is used to perform information collaboration through the error cross-covariance matrix. Simulation results demonstrate that the proposed method has higher estimation performance than the existing methods in this study.

Robust discrete-time nonlinear sliding mode controller with plant uncertainties

This paper addresses the new control algorithm, by designing the asymptotically stable nonlinear sliding surface with investigation of the states. This proposed algorithm leads to solve the problem of unstable systems, by proving the asymptotic stability of a class of uncertain discrete-time systems. A particular linear transformation is being defined to transform the discrete-time system and asymptotic stability is proved for designed nonlinear sliding surface, which leads to show stability of the system. The states of the plant’s will be brought down on a proven asymptotic stable nonlinear sliding surface by the proposed control law and they will be remained on stable nonlinear sliding surface for all future times. This proposed technique will be more useful for enhancing the stability of the real world nonlinear systems. The application of proposed algorithm in magnetic tape drive-servo motors and avionic systems, where the parametric uncertainties are occurring frequently.Keywords: Discrete-time system, linear matrix inequality (LMI), nonlinear system. nonlinear sliding surface, sliding mode control

Robust preview control for a class of uncertain discrete-time systems with time-varying delay

This paper proposes a concept of robust preview tracking control for uncertain discrete-time systems with time-varying delay. Firstly, a model transformation is employed for an uncertain discrete system with time-varying delay. Then, the auxiliary variables related to the system state and input are introduced to derive an augmented error system that includes future information on the reference signal. This leads to the tracking problem being transformed into a regulator problem. Finally, for the augmented error system, a sufficient condition of asymptotic stability is derived and the preview controller design method is proposed based on the scaled small gain theorem and linear matrix inequality (LMI) technique. The method proposed in this paper not only solves the difficulty problem of applying the difference operator to the time-varying matrices but also simplifies the structure of the augmented error system. The numerical simulation example also illustrates the effectiveness of the results presented in the paper.

一类时变时滞不确定离散系统的预见跟踪控制

一类时变时滞不确定离散系统的预见跟踪控制

Iterative Kalman Filter and Related Algorithms for Non-linear Systems

This paper proposes a comparative analysis of different state estimation techniques on linear and non-linear systems. Estimation is the process of finding a value that is usable even if the subject of interest is uncertain, delayed or corrupted due to noise. An Iterative Kalman Filter has been developed for a class of uncertain discrete-time system with delay. It extends, the KF and EKF to the case in which the underlying system is subjected to norm-bounded uncertainties and constant state delay. The IKF is a robust version of KF, but with the necessary modification to account for the parameter uncertainty as well as delay.

Study on the sliding mode fault tolerant predictive control based on multi agent particle swarm optimization

For a class of uncertain discrete-time systems with time varying delay, the problem of robust fault-tolerant control for such systems is studied by combining the design of sliding mode control (SMC) and model predictive control (MPC). A sliding mode fault tolerant predictive control based on multi agent particle swarm optimization (PSO) is presented, and the design, analysis and proof of the scheme are given in detail. Firstly, the sliding mode prediction model of the system is designed by assigning poles of the output error of the system. The model has time varying characteristics, and it can improve the motion quality of the system while ensuring the sliding mode is stable. Secondly, a new discrete reference trajectory considering time-delay systems subjected simultaneously to parameter perturbations and disturbances is proposed, which not only can ensure that the state of the system has good robustness and fast convergence in the process of approaching sliding mode surface, but also can inhibit chattering phenomenon. Thirdly, the multi agent PSO improves the receding-horizon optimization, which can quickly and accurately solve the control laws satisfying the input constraints, and can effectively avoid falling into local extrema problem of the traditional PSO. Finally, the theoretical proof of robust stability of the proposed control scheme is given. Experimental results of quad-rotor helicopter semi physical simulation platform show that the state of uncertain discrete-time systems with time varying delay is stable under the action of the proposed control scheme in this paper. The advantages of fast response, less overshoot and small control chattering prove the feasibility and effectiveness of the proposed control scheme.

Criteria for stability of uncertain discrete-time systems with time-varying delays and finite wordlength nonlinearities

This paper considers the problem of global asymptotic stability of a class of uncertain discrete-time systems under the influence of finite wordlength nonlinearities (quantization and/or overflow) and time-varying delays. The parameter uncertainties are assumed to be norm-bounded. Utilizing the concept of a Wirtinger-based inequality and a reciprocally convex method, two delay-dependent stability criteria are presented. The selection of the criteria depends on the type of the nonlinearities, that is, a combination of quantization and overflow or saturation overflow nonlinearities involved in the present systems. The approach presented in this paper yields less conservative results and reduces the computational burden as compared to previously reported criteria. Numerical examples are given to illustrate the effectiveness of the presented approach.

Design of a robust H∞ preview controller for a class of uncertain discrete-time systems

The robust preview tracking control problem of uncertain discrete-time systems satisfying matching conditions is considered. First, we use the difference between a system state and its steady-state value, instead of the usual difference between system states, to derive an augmented error system that includes the future information on the reference signal and disturbance signal to transform the tracking problem into a regulator problem. Then, a robust preview controller of the augmented error system is proposed by integrating Lyapunov stability theory and LMI approach. Research shows that the preview controller gain matrix can be determined by solving a LMI. The proposed robust preview controller in this paper cannot only guarantee the asymptotic stability of the closed-loop system, but also enhance the interference rejection properties. An integrator is applied to make sure that the output tracks the reference signal with no static error. The numerical simulation example also illustrates the effectiveness of the results presented in the paper.

D-stability and disturbance attenuation properties for networked control systems: switched system approach

Both D-stability and finite L2-gain properties are studied for a class of uncertain discrete-time systems with time-varying network-induced delays. By using coordinate transform and delay partition, the D-stability and H ∞ performance problems for such networked control systems (NCSs) are equivalently transferred into the corresponding problems for switching systems with arbitrary switching. Then, a sufficient condition for the existence of the robust D-stabilizing controllers is derived in terms of linear matrix inequality (LMI), and the design method is also presented for the state feedback controllers which guarantee that all the closed-loop poles remain inside the specified disk D(α, r) and the desired disturbance attenuation level. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed results.

Robust preview tracking control for a class of uncertain discrete-time systems

AbstractThe robust preview control problem of uncertain discrete-time systems satisfying matching conditions is considered. First, for the nominal system, we use the difference between a system state and its steady-state value, instead of the usual difference between system states, to derive an augmented error system that includes the future information on the reference signal and disturbance signal to transform the tracking problem into a regulator problem. Then, the robust controller design problem based on the optimal controller of the augmented error system is proposed for uncertain system. And the proposed robust preview control law is obtained in terms of the linear matrix inequality (LMI) technique and the Lyapunov stability theory. Bringing the resulting controller back to the original system, a controller with preview actions achieving robust tracking performance is presented. The numerical simulation example also illustrates the effectiveness of the results presented in the paper.

Stability Criteria for Uncertain Discrete-Time Systems under the Influence of Saturation Nonlinearities and Time-Varying Delay

The problem of global asymptotic stability of a class of uncertain discrete-time systems in the presence of saturation nonlinearities and interval-like time-varying delay in the state is considered. The uncertainties associated with the system parameters are assumed to be deterministic and normbounded. The objective of the paper is to propose stability criteria having considerably smaller numerical complexity. Two new delay-dependent stability criteria are derived by estimating the forward difference of the Lyapunov functional using the concept of reciprocal convexity and method of scale inequality, respectively. The presented criteria are compared with a previously reported criterion. A numerical example is provided to illustrate the effectiveness of the presented criteria.

Robust Reliable Control for a Class of Uncertain Discrete-Time Systems with Multiple Time-Varying Delays

The robust reliable control design problem of uncertain discrete-time control systems with multiple time-varying delays is addressed in this article. Uncertainty in system is assumed to satisfy the norm-bounded condition and the time-delay parameter is time-varying unstructured. Under the proposed concepts of exponentially robust stability and exponentially robust stabilization, the delay-dependent exponential stability condition for the robust reliable control system is derived and a new delay-dependent state feedback controller design method is provided. The relationship between system stability and time-delays is also studied. Simulation study shows the effectiveness and feasibility of the proposed controller design method.

Robust stability criteria for a class of uncertain discrete-time systems with time-varying delay

In this paper, we consider the problem of delay-dependent robust stability of a class of uncertain discrete-time systems with time-varying delay using Lyapunov functional approach. Two categories of time-varying uncertainties are considered for the robust stability analysis: viz., (i) nonlinear perturbations and (ii) norm-bounded uncertainties. In the proposed stability analysis, by exploiting a candidate Lyapunov functional, and using minimal number of slack matrix variables, less conservative stability criteria are developed in terms of linear matrix inequalities (LMIs) for computing the maximum allowable bound of the delay-range, within which, the uncertain system under consideration remains asymptotically stable in the sense of Lyapunov. The effectiveness of the proposed stability criteria is demonstrated using standard numerical examples.

Adaptive sliding mode control for a class of uncertain discrete-time systems using multi-rate output measurement

This article is concerned with the design of an adaptive sliding mode control (SMC) for a class of uncertain discrete-time systems using the multi-rate output measurement. The states of the discrete-time systems are assumed to be taken in the multi-rate output measurement by the contamination with measurement noise. The uncertainties are assumed not to satisfy the matching condition, and are expressed in a parameterised form. A least squares estimator (LSE) to take the estimates for the un-measurable states and the uncertainties is designed in a batch form by using the noisy multi-rate output measurement. The proposed adaptive SMC is designed by using the sliding surface expressed as the linear state function and the estimates obtained from the LSE. It is proved that the estimation errors converge to zero as time tends to infinite, and the states of the system are bounded under the action of the proposed adaptive SMC. The effectiveness of the proposed method is indicated through the simulation experiment in a simple system.

Improved Robust Stability and Stabilization Conditions of Discrete-time Delayed System

The problem of robust stability and robust stabilization for a class of discrete-time uncertain systems with time delay is investigated. Based on Tchebychev inequality, by constructing a new augmented Lyapunov function, some improved sufficient conditions ensuring exponential stability and stabilization are established. These conditions are expressed in the forms of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Compared with some previous results derived in the literature, the new obtained criteria have less conservatism. Two numerical examples are provided to demonstrate the improvement and effectiveness of the proposed method. Keywords—Robust stabilization, robust stability, discrete-time system, time delay.

Novel Optimal Guaranteed Cost Control of Uncertain Discrete Systems with Both State and Input Delays

The problem of the guaranteed cost control (GCC) for a class of uncertain discrete-time systems with both state and input delays is considered in this paper. A novel LMI-based approach is proposed for the existence of a state feedback controller which guarantees not only the asymptotic stability of the closed-loop system, but also an adequate performance bound over all the possible parameter uncertainties. A convex optimization algorithm is given to design the state feedback controller which minimizes a bound on a quadratic performance index. The result exhibits some favorable features in computation as shown by a numerical example.