STOCHASTIC STABILIZATION AND H∞ CONTROL FOR DISCRETE JUMPING SYSTEMS WITH TIME DELAYS

In this paper, robust stochastic stabilization and H_∞ control for a class of uncertain discrete‐time linear systems with Markovian jumping parameters are considered. Based on a new bounded real lemma derived upon an inequality recently proposed, a new iterative state‐feedback controller design procedure for discrete time‐delay systems is presented. Sufficient conditions for stochastic stabilization are derived in the form of linear matrix inequalities (LMIs) based on an equivalent model transformation, and the corresponding H_∞ control law is given. Finally, numerical examples are given to illustrate the solvability of the problems and effectiveness of the results.     

ADAPTIVE ROBUST CONTROL OF UNCERTAIN SYSTEMS WITH TIME‐VARYING STATE DELAY

In this paper, a new adaptive robust control scheme is developed for a class of uncertain dynamical systems with time‐varying state delay, unknown parameters and disturbances. By incorporating adaptive techniques into the robust control method, we propose a continuous adaptive robust controller which guarantees the uniform boundedness of the system and at the same time, the regulating error enters an arbitrarily designated zone in a finite time. The proposed controller is independent of the time‐delay, hence it is applicable to a class of dynamical systems with uncertain time delays. The paper includes simulation studies demonstrating the performance of the proposed control scheme.     

DIRECT ADAPTIVE CONTROL FOR NONLINEAR MATRIX SECOND‐ORDER SYSTEMS WITH TIME‐VARYING AND SIGN‐INDEFINITE DAMPING AND STIFFNESS OPERATORS

A direct adaptive control framework for a class of nonlinear matrix second‐order systems with time‐varying and sign‐indefinite damping and stiffness operators is developed. The proposed framework guarantees global asymptotic stability of the closed‐loop system states associated with the plant dynamics without requiring any knowledge of the system nonlinearities other than the assumption that they are continuous and bounded. The proposed adaptive control approach is used to design adaptive controllers for suppressing thermoacoustic oscillations in combustion chambers.     

INTERNET‐BASED REAL‐TIME CONTROL ARCHITECTURES WITH TIME‐DELAY/PACKET‐LOSS COMPENSATION

The main objective of this paper is to demonstrate the feasibility of Internet‐based real‐time control. A novel client/server‐based architecture for Internet‐based supervisory control with a Common Gateway Interface/Hyper Text Markup Language (CGI/HTML) interface is presented. A real‐time operating environment was established for closed‐loop control over Ethernet. We conceived of an autoregressive (AR) prediction scheme and a novel compensation algorithm to compensate for network‐induced time delays and data‐packet losses simultaneously. We constructed an open‐loop unstable ball magnetic‐levitation (maglev) setup as a test bed to validate the two proposed control architectures. Experimental results proved the feasibility of Internet‐based real‐time control and verified the effectiveness of the proposed time‐delay/packet‐loss compensation algorithm in networked feedback control systems.     

时变时滞系统的参数辨识及自适应控制

基于最小二乘法一类辨识算法的自适应控制,一般只适用于时滞已知且时不变的被控过程,本文提出了一种包括可估计时变时滞在内的参数辨识方法,该方法扩展了最小二乘一类辨识算法及相应的自适应控制的应用范围,文中通过一个实例讨论了该方法在自适应控制中的应用,并谈及下一步的研究工作。     

OPTIMAL AND ROBUST SLIDING MODE CONTROL FOR LINEAR SYSTEMS WITH MULTIPLE TIME DELAYS IN CONTROL INPUT

This paper presents the optimal regulator for a linear system with multiple time delays in control input and a quadratic criterion. The optimal regulator equations are obtained using the duality principle, which is applied to the optimal filter for linear systems with multiple time delays in observations. Performance of the obtained optimal regulator is verified in the illustrative example against the best linear regulator available for linear systems without delays. Simulation graphs and comparison tables demonstrating better performance of the obtained optimal regulator are included. The paper then presents a robustification algorithm for the obtained optimal regulator based on integral sliding mode compensation of disturbances. The general principles of the integral sliding mode compensator design are modified to yield the basic control algorithm oriented to time‐delay systems, which is then applied to robustify the optimal regulator. As a result, the sliding mode compensating control leading to suppression of the disturbances from the initial time moment is designed. The obtained robust control algorithm is verified by simulations in the illustrative example.     

ADAPTIVE COORDINATED DECENTRALIZED CONTROL OF STATE DELAYED SYSTEMS WITH ACTUATOR FAILURES

This paper develops an adaptive state feedback coordinated decentralized control scheme for a class of dynamic systems with state delay in subsystems and in the interconnections and in the presence of unknown actuator failures in each subsystem. The main contributions of this paper are the development of a new controller parametrization which attempt to anticipate the future states and failures, the introduction of an appropriate Lyapunov‐Krasovskii type functional to design the adaptation algorithms, and a stability proof.     

STATE‐SPACE DIGITAL PID CONTROLLER DESIGN FOR MULTIVARIABLE ANALOG SYSTEMS WITH MULTIPLE TIME DELAYS

This paper presents a discrete‐time state‐space methodology for optimal design of digital PID controllers for multivariable analog systems with multiple time delays. The multiple time‐delayed multivariable analog systems are formulated in a state‐space generic form so that the exact discrete‐time state‐space model can be constructed. Then, the optimal digital PID controller is designed via a state‐feedback and state‐feedforward LQR approach. The developed PID controller can be applied to a general time‐delayed multivariable analog system represented by a semi‐proper or strictly proper transfer function matrix. Illustrative examples are given to compare the performance of the proposed approach with alternative techniques.     

OPTIMAL TRACKING CONTROL FOR DISCRETE TIME‐DELAY SYSTEMS WITH PERSISTENT DISTURBANCES

Optimal tracking control (OTC) for discrete time‐delay systems affected by persistent disturbances with quadratic performance indexes is considered. Optimal tracking controller is designed based on a sensitivity approximation approach. By introducing a sensitivity parameter, we transform the original OTC problem into a series of difference equations without time‐advance on time‐delay terms. The obtained OTC law consists of analytic feedback and feedforward terms, and a compensation term, which is the sum of the infinite series of adjoint vectors. The compensation term can be obtained with an iterated formula for the adjoint vectors. A simulation example shows that the approximation approach is effective in tracking the reference input and robust with respect to exogenous persistent disturbances.     

INDIRECT ADAPTIVE CONTROL FOR NONLINEAR SYSTEMS WITH SYSTEM PERTURBATION

This paper presents an indirect adaptive control scheme for a class of input-output linearizable nonlinear systems subjected to system perturbations. System parameters are unknown and estimated recursively by a parameter estimator to obtain approximate system output and output derivatives, and then to derive an adaptive control law. In the parameter estimator, a dead-zone approach is used to avoid the parameter drift problem. A positive switching gain is also set to decrease the dead-zone value to obtain better output tracking performance. Under some assumptions, the indirect adaptive control scheme is proved to be stable.     

SIMPLE INSTABILITY CRITERION FOR A CLASS OF SINGULAR SYSTEMS WITH MULTIPLE TIME DELAYS

In this paper, the instability for a class of singular systems with discrete and distributed time delays is investigated. Simple instability criterion, which is a delay‐dependent criterion, is derived to guarantee the instability of such systems. Finally, a numerical example is given to illustrate the use of the main result.     

具有多个时变时滞的不确定系统的时滞相关稳定性

研究了具有多个时变时滞的不确定系统的 稳定性问题, 利用Razumikhn定理与向量不等式的方法, 给出了不确定时滞系统稳定的充分 条件. 所得的条件与时滞相关, 在很大程度上降低了现有结果的保守性. 文末给出了一个应 用的算例, 并与已有的结果作了比较.     

ROBUST ADAPTIVE CONTROL FOR STRICT‐FEEDBACK NONLINEAR SYSTEMS

In this paper, we propose a robust adaptive tracking control based on the backstepping strategy for strict‐feedback nonlinear systems with nonparametric uncertain nonlinearities. It is shown that one can design a stable adaptive control system provided that the uncertain nonlinearities can be decomposed by unknown bounded nonlinear functions and known nonlinear functions. The proposed method can deal with uncertain nonlinearities that appear at the control input term too. It is also shown that suitable choice of design parameters guarantees the convergence of tracking error to any desired bound.     

NETWORK‐INDUCED DELAY‐DEPENDENT H∞ CONTROLLER DESIGN FOR A CLASS OF NETWORKED CONTROL SYSTEMS

This paper is concerned with the problem of robust H_∞ controller design for a class of uncertain networked control systems (NCSs). The network‐induced delay is of an interval‐like time‐varying type integer, which means that both lower and upper bounds for such a kind of delay are available. The parameter uncertainties are assumed to be normbounded and possibly time‐varying. Based on Lyapunov‐Krasovskii functional approach, a robust H_∞ controller for uncertain NCSs is designed by using a sum inequality which is first introduced and plays an important role in deriving the controller. A delay‐dependent condition for the existence of a state feedback controller, which ensures internal asymptotic stability and a prescribed H_∞ performance level of the closed‐loop system for all admissible uncertainties, is proposed in terms of a nonlinear matrix inequality which can be solved by a linearization algorithm, and no parameters need to be adjusted. A numerical example about a balancing problem of an inverted pendulum on a cart is given to show the effectiveness of the proposed design method.     

A GRADIENT BASED ADAPTIVE CONTROL ALGORITHM FOR DUAL‐RATE SYSTEMS

In this paper, using a polynomial transformation technique, we derive a mathematical model for dual‐rate systems. Based on this model, we use a stochastic gradient algorithm to estimate unknown parameters directly from the dual‐rate input‐output data, and then establish an adaptive control algorithm for dual‐rate systems. We prove that the parameter estimation error converges to zero under persistent excitation, and the parameter estimation based control algorithm can achieve virtually asymptotically optimal control and ensure the closed‐loop systems to be stable and globally convergent. The simulation results are included.     

NEURAL NETWORK‐BASED OPTIMAL ADAPTIVE TRACKING USING GENETIC ALGORITHMS

This paper presents the use of neural networks (NNs) and genetic algorithms (GAs) to enhance the output tracking performance of partly known robotic systems. Two of the most potential approaches of adaptive control, i.e., the concept of variable structure control (VSC) and NN‐based adaptive control, are ingeniously combined using GAs to achieve high‐performance output tracking. GA is used to make the maximum use of different performance characteristics of two self‐adaptive NN modules by finding the switching function which best combines them. The method will be valid for any rigid revolute robot system. Computer simulations on our active binocular head are included for illustration and verification.     

DIRECT ADAPTIVE FEEDBACK DESIGN FOR LINEAR DISCRETE‐TIME UNCERTAIN SYSTEMS

In this paper, we develope a direct adaptive control framework for linear discrete‐time uncertain MIMO systems, based on assumptions that the system is controllable and the difference of the unknown system matrix from the stable solution is bounded by a given value. The proposed framework is Lyapunov‐based, and the controller guarantees adaptive stabilization. In addition, the adaptive laws are characterized by means of Kronecker calculus. Furthermore, the results can easily be extended to time‐varying cases, where the deviation from the stable solution is bounded, and the controllability assumption holds. The controller not only tolerates plant deviation, but also guarantees asymptotical stability of the closed‐loop system. Two numerical examples are provided to demonstrate the performance of the controller.     

线性离散时变系统的鲁棒自适应控制

利用滑模控制的概念,提出一种线性离散时变系统的自适应控制设计方法.在等价控制信号外,用两个补偿项代替切换信号,避免了传统滑模控制中的抖动现象.文中证明了自适应闭环系统的稳定性.     

CONTROL LAW FOR QUADRATIC STABILIZATION OF PERTURBED FUZZY TIME‐DELAY LARGE‐SCALE SYSTEMS VIA LMI

In this paper, the perturbed continuous‐time large‐scale system with time delays is represented by an equivalent Takagi‐Sugeno type fuzzy model. First, two types of decentralized state feedback controllers are considered in this paper. Based on the Riccati‐type inequality, the Razumikhin theorem, and the delay‐dependent Lyapunov functional approach, some controller design approaches are proposed to stabilize the whole fuzzy time‐delay system asymptotically. In these design methods, both the delay‐independent and delay‐dependent stabilization criteria are derived. By Schur complement, these sufficient conditions can be easily transformed into the problem of LMI's. Moreover, the systems with all the time‐delays τ^l_ij (t) are the same for all rules (i.e., τ^l_ij (t) = τ^m_ij (t) = τ_ij for all l =m); the authors also propose a simpler and less conservative stabilizing criteria. A numerical example is given to illustrate the control design and its effectiveness.