Truncated predictor feedback for linear systems with long time-varying input delays

In this paper we study the problem of stabilizing a linear system with a single long time-varying delay in the input. Under the assumption that the open-loop system is stabilizable and not exponentially unstable, a finite dimensional static time-varying linear state feedback controller is obtained by truncating the predictor based controller and by adopting the parametric Lyapunov equation based controller design approach. As long as the time-varying delay is exactly known and bounded, an explicit condition is provided to guarantee the stability of the closed-loop system. It is also shown that the proposed controller achieves semi-global stabilization of the system if its actuator is subject to either magnitude saturation or energy constraints. Numerical examples show the effectiveness of the proposed approach.     

Pseudo-predictor feedback stabilization of linear systems with time-varying input delays

This paper is concerned with stabilization of (time-varying) linear systems with a single time-varying input delay by using the predictor based delay compensation approach. Differently from the traditional predictor feedback which uses the open-loop system dynamics to predict the future state and will result in an infinite dimensional controller, we propose in this paper a pseudo-predictor feedback (PPF) approach which uses the (artificial) closed-loop system dynamics to predict the future state and the resulting controller is finite dimensional and is thus easy to implement. Necessary and sufficient conditions guaranteeing the stability of the closed-loop system under the PPF are obtained in terms of the stability of a class of integral delay operators (systems). Moreover, it is shown that the PPF can compensate arbitrarily large yet bounded input delays provided the open-loop (time-varying linear) system is only polynomially unstable and the feedback gain is well designed. Comparison of the proposed PPF approach with the existing results is well explored. Numerical examples demonstrate the effectiveness of the proposed approaches.     

On Asymptotic Stabilizability of Linear Systems With Delayed Input

This paper examines the asymptotic stabilizability of linear systems with delayed input. By explicit construction of stabilizing feedback laws, it is shown that a stabilizable and detectable linear system with an arbitrarily large delay in the input can be asymptotically stabilized by either linear state or output feedback as long as the open-loop system is not exponentially unstable (i.e., all the open-loop poles are on the closed left-half plane). A simple example shows that such results would not be true if the open-loop system is exponentially unstable. It is further shown that such systems, when subject to actuator saturation, are semiglobally asymptotically stabilizable by linear state or output feedback.     

一类含有输入时滞的不确定切换系统的鲁棒指数镇定

针对一类含有输入时滞的不确定切换系统,讨论了鲁棒指数镇定问题,提出了可行的切换控制器和切换信号的设计方法．首先,运用还原法将具有时滞的切换系统转化为无时滞的切换系统;然后,基于线性矩阵不等式,给出了系统在切换控制器和切换信号作用下鲁棒指数可镇定的充分条件,并利用多Ｌｙａｐｕｎｏｖ函数方法给出了定理的详细证明;最后,利用数值仿真例子验证了该方法的有效性．     

Stabilisation and consensus of linear systems with multiple input delays by truncated pseudo-predictor feedback

This paper provides a new approach referred to as pseudo-predictor feedback (PPF) for stabilisation of linear systems with multiple input delays. Differently from the traditional predictor feedback which is from the model reduction appoint of view, the proposed PPF utilises the idea of prediction by generalising the corresponding results for linear systems with a single input delay to the case of multiple input delays. Since the PPF will generally lead to distributed controllers, a truncated pseudo-predictor feedback (TPPF) approach is established instead, which gives finite dimensional controllers. It is shown that the TPPF can compensate arbitrarily large yet bounded delays as long as the open-loop system is only polynomially unstable. The proposed TPPF approach is then used to solve the consensus problems for multi-agent systems characterised by linear systems with multiple input delays. Numerical examples show the effectiveness of the proposed approach.     

Truncated predictor feedback control for exponentially unstable linear systems with time-varying input delay

The stabilization of exponentially unstable linear systems with time-varying input delay is considered in this paper. We extend the truncated predictor feedback (TPF) design method, which was recently developed for systems with all poles on the closed left-half plane, to be applicable to exponentially unstable linear systems. Assuming that the time-varying delay is known and bounded, the design approach of a time-varying state feedback controller is developed based on the solution of a parametric Lyapunov equation. An explicit condition is derived for which the stability of the closed-loop system with the proposed controller is guaranteed. It is shown that, for the stability of the closed-loop system, the maximum allowable time-delay in the input is inversely proportional to the sum of the unstable poles in the plant. The effectiveness of the proposed method is demonstrated through numerical examples.     

Delay compensation for linear systems with both state and distinct input delays

This paper is concerned with the stabilization of linear systems with both state and distinct input delays. Nested predictor feedback controllers are designed to predict the future states such that the distinct input delays that can be arbitrarily large yet bounded are compensated completely. It is shown that the compensated closed‐loop system possesses the same characteristic equation as the closed‐loop system without distinct input delays. Both continuous‐time and discrete‐time time‐delay systems are studied in this paper. Moreover, the safe implementation problem for the continuous‐time nested predictor feedback controller is solved via adding input filters. Three numerical examples show the effectiveness of the proposed approaches.     

Delay‐range‐dependent control of nonlinear time‐delay systems under input saturation

This paper describes a delay‐range‐dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time‐delay systems under input saturation. By employing a Lyapunov–Krasovskii functional, properties of nonlinear functions, local sector condition and Jensen's inequality, a sufficient condition is derived for stabilization of nonlinear systems with interval delays varying within a range. Novel solutions to the delay‐range‐dependent and delay‐dependent stabilization problems for linear and nonlinear time‐delay systems, respectively, subject to input saturation are derived as specific scenarios of the proposed control strategy. Also, a delay‐rate‐independent condition for control of nonlinear systems in the presence of input saturation with unknown delay‐derivative bound information is established. And further, a robust state feedback controller synthesis scheme ensuring L₂ gain reduction from disturbance to output is devised to address the problem of the stabilization of input‐constrained nonlinear time‐delay systems with varying interval lags. The proposed design conditions can be solved using linear matrix inequality tools in connection with conventional cone complementary linearization algorithms. Simulation results for an unstable nonlinear time‐delay network and a large‐scale chemical reactor under input saturation and varying interval time‐delays are analyzed to demonstrate the effectiveness of the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.     

Stabilization of linear systems with time‐varying input delay by event‐triggered delay independent truncated predictor feedback

This article deals with the problem of stabilization of linear systems with time‐varying input delay by an event‐triggered delay independent truncated predictor feedback law, either of the state feedback type or the output feedback type. Only the information of a delay bound rather than the delay itself is required in the design of both control laws and event‐triggering strategies. For both the state feedback case and the output feedback case, an admissible delay bound that guarantees the stabilizability of a general linear system is established, and the Zeno behavior is shown to be excluded. For linear systems with all open‐loop poles at the origin or in the open left‐half plane, stabilization can be achieved for a delay under an arbitrarily large bound.     

带传输滞后的线性离散系统的状态反馈镇定

针对存在传输滞后的线性离散系统的状态反馈镇定问题,给出了系统可镇定的一个内部限制条件.为克服这一限制条件,提出了两种方法:一种是充分利用滞后状态的信息,另一种是设计带有递推动态的状态反馈控制器.研究结果表明,若系统在没有传输滞后时能通过状态反馈被镇定,则存在传输滞后时一定也能通过设计新的控制器使系统被镇定.     

Stabilizable regions of receding horizon predictive control with input constraints

Stabilizable regions of receding horizon predictive control (RHPC) with input constraints are examined. A feasible region of states, which is spanned by eigenvectors of the closed-loop system with a stabilizing feedback gain, is derived in conjunction with input constraints. For states in this region, the feasibility of state feedback is guaranteed with the corresponding feedback gain. It is shown that an RHPC scheme with adequate finite terminal weights can guarantee stability for any initial state which can be steered into this region using finite number of control moves in the presence of input saturation. This methodology results in feasible regions which are infinite (in certain directions) even in the case of open-loop unstable systems. It is shown that the proposed feasible regions are larger than the ellipsoidal regions which were suggested in earlier works. We formulated the optimization problem in LMI so that it can be solved by semidefinite programming.     

Control of discrete-time systems with actuator non-linearities: An LMI approach

This paper considers the problem of stabilization of discrete-time systems with actuator non-linearities. Specifically, full-state feedback and dynamic, output feedback control designs for discrete-time systems with time-varying, sector-bounded, input non-linearities are addressed. The proposed framework is based on a linear matrix inequality approach and directly accounts for robust stability and robust performance over the class of actuator non-linearities. Furthermore, it is directly applicable to actuator saturation control and provides state feedback and dynamic, output feedback controllers with guaranteed domains of attraction. The effectiveness of the approach is illustrated by two numerical examples.     

Time-varying feedback laws for decentralized control

Decentralized control schemes are considered for time-invariant, finite dimensional, linear systems with know state equations. It is assumed that the systems are reachable and observable at a fictitious centralized control station, and that there is strong connectivity between the decentralized control stations via the system where necessary. It is shown that whether or not there are decentralized fixed modes in the open-loop system, periodically varying feedback gains at all but one of the control stations permit the remaining control station to observe and control the system given knowledge of the control laws implemented at the other control stations. Certain time-invariant systems which cannot be stabilized by decentralized time-invariant controllers, namely those with unstable decentralized fixed modes, can thus be stabilized by decentralized time-varying controllers.     

Simultaneous stabilization of a collection of single‐input nonlinear systems based on CLFs

This paper considers the simultaneous stabilization problem of a collection of single‐input nonlinear systems. Based on the technique of control Lyapunov functions (CLFs), a sufficient condition for the existence of a simultaneously stabilizing state feedback controller is proposed. It is shown that a collection of feedback linearizable systems in canonical form can be simultaneously globally asymptotically stabilized by a single state feedback controller. Moveover, for a set of three‐order chaotic dynamical systems, the simultaneous stabilization problem is considered and a similar result is derived. All the proposed simultaneously stabilizing state feedback controllers are explicitly constructed. Numerical examples are provided to illustrate the effectiveness of the proposed schemes. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

具有输入饱和的组合系统的分散控制

研究了一类具有饱和输入的组合系统的分散可镇定问题. 运用M-矩阵方法, 通过线性分散状态反馈得出具有饱和输入组合系统的可镇定的充分条件. 对于具有对称结构的组合系统, 给出了更为简单的镇定条件.     

Pseudo‐predictor feedback control of discrete‐time linear systems with a single input delay

This paper studies the problems of stabilization of discrete‐time linear systems with a single input delay. By developing the methodology of pseudo‐predictor feedback, which uses the (artificial) closed‐loop system dynamics to predict the future state, memoryless state feedback control laws are constructed to solve the problem. Necessary and sufficient conditions are obtained to guarantee the stability of the closed‐loop system in terms of the stability of a class‐difference equations. It is also shown that the proposed controller achieves semi‐global stabilization of the system if its actuator is subject to either magnitude saturation or energy constraints under the condition that the open‐loop system is only polynomially unstable. Numerical examples have been worked out to illustrate the effectiveness of the proposed approaches. Copyright © 2015 John Wiley & Sons, Ltd.     

Consensus of high-order multi-agent systems with large input and communication delays

We study in this paper the consensus problem for multi-agent systems with agents characterized by high-order linear systems with time delays in both the communication network and inputs. Provided that the open-loop dynamics of the agents is not exponentially unstable, but may be polynomially unstable, and the communication topology contains a directed spanning tree, a truncated predictor feedback approach is established to solve the consensus problem. It is shown that, if the delays are constant and exactly known, the consensus problems can be solved by both full state feedback and observer based output feedback protocols for arbitrarily large yet bounded delays. If it is further assumed that the open-loop dynamics of the agents only contains zero eigenvalues, the delays are allowed to be time-varying and unknown. Numerical examples are worked out to illustrate the effectiveness of the proposed approaches.     

Observer based output feedback regulation of a class of feedforward nonlinear systems with uncertain input and state delays using adaptive gain

We consider a global regulation problem of a class of feedforward nonlinear systems with uncertain delays by output feedback. The considered system is a generalized feedforward time-delay nonlinear system in the sense that an additional uncertain constant delay exists in the main control input to the system and feedforward nonlinearity includes states and input which have uncertain time-varying delays. Moreover, when feedforward nonlinearity satisfies some restrictive condition, we extend our control problem to the case such that the delay in the main control input is also a time-varying delay. To globally regulate the considered system, we develop an output feedback controller whose gain-scaling factor involves an adaptive dynamic. Two examples are given for illustration.     

Stabilization of input delay constrained systems with delay dependence

The problem of stabilization of input delay constrained systems is considered. Three kinds of feedback stabilizing laws are treated: a state feedback controller, a dynamic controller and an observer controller, respectively. The properties of the matrix measure and the comparison theorem are employed to treat this problem. The results obtained can be used to estimate the size of the delay time t. An example is given to illustrate the proposed controllers