Class Of Discrete Time-delay Systems Research Articles

Information Fusion Tracking Control for a Class of Discrete-Time Systems With Delays

In this article, the optimal tracking control problem for a class of discrete time-delay systems with disturbance is studied using the information fusion control methodology. First, the disturbance estimation is regarded as a minimization problem, and an information fusion disturbance observer (IFDO) is designed. Second, combining the soft constraint requirement of the output tracking error contained in the performance index function, a fusion filter is constructed to estimate the system co-state and its information weight under system state and input delays. Finally, the obtained co-state and its information weight, the soft constraint requirement of the control input contained in the performance function, as well as the system delay dynamics, are all transformed into the information equations about the control input, and then the information fusion delay controller (IFDC) is directly obtained by fusing these information equations. As a result, the negative effects caused by disturbance and time delays can be effectively compensated at the same time. The convergence of the tracking errors of the closed-loop system is guaranteed by the Lyapunov stability theory. Numerical simulation results have been provided to demonstrate the effectiveness and robustness of the proposed control algorithm.

Moving Horizon Estimation for Networked Time-Delay Systems Under Round-Robin Protocol

This paper is concerned with the moving horizon estimation problem for a class of discrete time-delay systems under the Round-Robin (RR) protocol. The communication between the sensor nodes and the remote state estimator is implemented via a shared network, where only one sensor node is permitted to transmit data at each time instant for the purpose of preventing data collisions. The RR protocol is utilized to orchestrate the transmission order of sensor nodes, under which the selected node obtaining access to the network could be modeled by a periodic function. A lifting technology is introduced to reformulate the system model into a linear system without delays. The aim of the addressed problem is to develop a moving horizon estimator such that the estimation error is ultimately bounded. A sufficient condition is established to ensure the ultimate boundedness in terms of a matrix inequality. Within the established theoretical framework, two optimization problems are proposed to calculate the corresponding estimator parameters according to two different performance requirements (e.g., the smallest ultimate bound and the fastest decay rate). Finally, simulation examples are given to illustrate the effectiveness of the estimator design scheme.

H∞ Tracking Control of Discrete-Time System With Delays via Data-Based Adaptive Dynamic Programming

In this article, the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> tracking control problem for a class of discrete time-delay systems is studied using databased adaptive dynamic programming (ADP) algorithm. First, the controlled system and the reference system are combined to form an augmented discrete time-delay system. Second, we transform it into a discrete time-delay system represented by system measured data, which allows the system state to be completely replaced by the data generated during system operation. Third, a novel data-based Bellman equation is derived according to the Bellman optimality principle. Then, an ADP-based H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> tracking control method is designed by means of the measured data. The simulation example demonstrates the effectiveness of the data-based ADP control method proposed in this article.

Input-to-state stability of discrete time-delay systems with switching and impulsive signals

This paper investigates input-to-state stability (ISS) for a class of discrete time-delay systems with switching and impulsive signals. By the Lyapunov–Krasovskii technique, a dwell-time bound and delay bound are clearly presented to contribute to the ISS for discrete time-delay systems. A significant subsequence method of the switched and impulsive sequence will firstly be applied to study the ISS of discrete systems. Based on this method, some new conditions guaranteeing ISS are presented. Compared with the existing results on related problems, the obtained stability criteria are less conservative as it is only required for the specially designed Lyapunov function to be non-increasing along each of the defined subsequences of the switched and impulsive time. Examples of network control systems are presented to illustrate the main results at the end.

ℓ 2 –ℓ ∞ reliable control for discrete time‐delay systems with fractional uncertainties and saturated package losses

This study deals with the l 2 -l ∞ reliable control problem for a class of discrete time-delay systems. The considered system involves fractional uncertainties, saturated package losses and stochastic non-linearities as well as possible actuator failures. A sensor model is proposed to depict the phenomenon of saturated package losses which better reflect the reality in a networked environment. In addition, stochastic non-linearities with statistical characteristics cover several well-studied non-linear functions as special cases. The focus of this study is placed upon the design of a reliable controller such that the closed-loop system satisfies a prescribed noise attenuation level in an l 2 -l ∞ sense. By utilising stochastic analysis methods, some sufficient conditions are established to guarantee both the exponentially mean-square stability and the l 2 -l ∞ performance. Owing to the obtained conditions with a non-linear equality constraint, the cone complementary linearisation method is exploited to cast them into a convex optimisation problem, which can be readily solved by using standard numerical software. Finally, a simulation example is exploited to demonstrate the applicability of the proposed design approach.

Generating chaos for discrete time-delayed systems via impulsive control

Generating chaos for a class of discrete time-delayed systems via impulsive control is investigated in this paper. With the augmented matrix method, the time-delay impulsive systems can be transformed into a new class of linear discrete impulsive systems. Based on the largest Lyapunov exponent and the boundedness of the systems, some theoretical results about the chaotification for the discrete impulsive systems with time delay are derived and an example is given to visualize the satisfactory control performance.

Saturating composite disturbance-observer-based control and H ∞ control for discrete time-delay systems with nonlinearity

This note is concerned with a saturating composite disturbance-observer-based control (DOBC) and H∞ control for a class of discrete time-delay systems with nonlinearity and disturbances. The disturbances are supposed to include two parts. One in the input channel is generated by an exogenous system with uncertainty, which can represent the harmonic signals with modeling perturbations. The other is supposed to have the bounded H2 norm, which can represent parametric uncertainties and external disturbance existing in the controlled object. The design approaches of reduced-order disturbance observer are presented for the estimation of the disturbance. By composite control law with saturation, the disturbances can be rejected and attenuated, simultaneously, the desired dynamic performances can be guaranteed for discrete time-delay systems with known and unknown nonlinear dynamics, respectively. Simulation for a flight control system is provided to show the effectiveness of the proposed scheme compared with the previous schemes.

Delay-dependent [formula omitted] control for discrete time-delay systems with D-stability constraints

This paper studies the problem of H 2 control for a class of discrete time-delay systems with D-stability constraints. The corresponding sufficient conditions are given in terms of linear matrix inequalities. In particular, the conditions are delay-dependent, and so they are less conservative. The obtained controller can provide an upper bound for the H 2 cost function. A numerical example is given to illustrate the proposed method.

Design of Iterative Learning Controllers for Linear Discrete Systems with Multiple Time Delays

The problem of iterative learning control is considered for a class of linear discrete systems with multiple time delays. In this paper, it is assumed that the initial condition for discrete time-delay systems is unknown at each iteration. For such a class of discrete time-delay systems, a method is presented whereby a class of discrete iterative learning control schemes can be constructed. It is shown that under some given conditions, the constructed iterative learning controllers can guarantee the asymptotic convergence of the output error between the given desired output and the actual output through the iterative learning process. Finally, a numerical example is given to demonstrate the validity of the results.

On the estimation of eigenvalue regions for discrete time-delay systems with a class of highly structured perturbations

By means of norm,M-matrix, and matrix measure techniques, this paper estimates several restricted regions in the complex plane in which all eigenvalues of a class of discrete time-delay systems subjected to highly structured parametric perturbations are located. Both the stability and the instability conditions for these systems are also investigated via the proposed schemes. Two numerical examples are given to verify the correctness and demonstrate the applicability of the quantitative results.

A Control Algorithm for a Class of Discrete Time-delay Systems Based on Staged Transformation and Its Application

In this paper, a stabilizing control algorithm for a class of discrete linear systems with delayed control is presentedbased on staged design idea. A timedelay transformation with past control information is introduced to transform a time-delay system into a linear delay-free system. The stabilizing controller to the primitive time-delay system is derived via a staged design method. The simulation study shows the effectiveness of the presented design method for an industrial electric heater example.