基于LMI方法的时滞分布参数控制系统的镇定

针对常时滞、多个常时滞及多个变时滞的分布参数控制系统,提出一种与现有研究分布参数控制系统不同的方法．该方法通过构造平均Lyapunov函数,利用LMI和矩阵不等式知识,在只要求系统本身所固有的系数是负定矩阵的条件下,给出了所研究的分布参数系统镇定的充分条件．当模型中时滞为常时滞时,所得的充分条件与时滞无关;当模型中时滞为变时滞时,所得模型的镇定准则依赖于时滞．此外,该方法一个显著优点是所获得的条件容易检验,因而易于应用．     

Boundary geometric control of a linear Stefan problem

This paper addresses the geometric control of the position of a liquid–solid interface in a melting process of a material known as Stefan problem. The system model is hybrid, i.e. the dynamical behavior of the liquid-phase temperature is modeled by a heat equation while the motion of the moving boundary is described by an ordinary differential equation. The control is applied at one boundary as a heat flux and the second moving boundary represents the liquid–solid interface whose position is the controlled variable. The control objective is to ensure a desired position of the liquid–solid interface. The control law is designed using the concept of characteristic index, from geometric control theory, directly issued from the hybrid model without any reduction of the partial differential equation. It is shown by use of Lyapunov stability test that the control law yields an exponentially stable closed-loop system. The performance of the developed control law is evaluated through simulation by considering zinc melting.     

Bounded control of feedforward nonlinear systems subject to input time‐delay

This article is concerned with the global stabilization problem of a family of feedforward nonlinear time‐delay systems whose linearized system consists of multiple distinct oscillators. To fully utilize the delayed information and maintain the state decoupling property in the controller design, the considered nonlinear feedforward system is first transformed into a new system which contains time delays in both its input and states based on a novel model transformation containing time delays, and then the stabilizing saturated controller for the transformed system is designed based on the recursive design method. Meanwhile, explicit stability conditions are also provided. When the linearized system is a cascade of multiple oscillators and multiple integrators, a modified saturated feedback control utilizing not only the current state but also the delayed state is also established for the corresponding global stabilization problem. Two examples, including a practical one, are given to show the effectiveness and superiority of the proposed approaches.     

Bounded control of feedforward time‐delay systems with linearized systems consisting of chain of oscillators

For the global stabilization of a family of feedforward nonlinear time‐delay systems whose linearized systems consist of a chain of identical oscillators, a saturated feedback control is established based on a special canonical form. The proposed control laws use not only the current states but also the delayed states for feedback, which helps maintain the decoupling property in the recursive design. Moreover, explicit conditions guaranteeing the stability of the closed‐loop system are provided. When the nonlinear terms vanish and even the oscillators are distinct, a modified saturated feedback control can still be established for the corresponding global stabilization problem. Two numerical examples are given to illustrate the effectiveness of the proposed approaches.     

Nonlinear control under wave actuator dynamics with time‐ and state‐dependent moving boundary

We consider the stabilization of nonlinear ODE systems with actuator dynamics modeled by a wave PDE whose boundary is moving and is a function of time and of the ODE's state. Such a problem is inspired by applications in oil drilling where the position of the drill bit is a state variable in the ODE modeling the friction‐dominated drill bit dynamics while at the same time being the position of the moving boundary of the wave PDE that models the distributed torsional dynamics of the drillstring. For moving boundaries that depend only on time, we extend the global result recently developed by Bekiaris‐Liberis and Krstic for constant boundaries. For moving boundaries that also depend on the ODE's state, we develop a local result where the initial condition is restricted in such a way that it is ensured that the rate of movement of the boundary (both ‘leftward’ and ‘rightward’) is bounded by unity in closed‐loop. For strict‐feedforward systems under wave actuator dynamics with moving boundaries, the predictor‐based feedback laws are obtained explicitly. The feedback design is illustrated through an example. Copyright © 2013 John Wiley & Sons, Ltd.     

Compensation of time‐varying input delay for discrete‐time nonlinear systems

We consider general discrete‐time nonlinear systems (of arbitrary nonlinear growth) with time‐varying input delays and design an explicit predictor feedback controller to compensate the input delay. Such results have been achieved in continuous time, but only under the restriction that the delay rate is bounded by unity, which ensures that the input signal flow does not get reversed, namely, that old inputs are not felt multiple times by the plant (because on such subsequent occasions, the control input acts as a disturbance). For discrete‐time systems, an analogous restriction would be that the input delay is non‐increasing. In this work, we do not impose such a restriction. We provide a design and a global stability analysis that allow the input delay to be arbitrary (containing intervals of increase, decrease, or stagnation) over an arbitrarily long finite period of time. Unlike in the continuous‐time case, the predictor feedback law in the discrete‐time case is explicit. We specialize the result to linear time‐invariant systems and provide an explicit estimate of the exponential decay rate. Carefully constructed examples are provided to illustrate the design and analytical challenges. Copyright © 2015 John Wiley & Sons, Ltd.     

一类具有变时滞不确定分布参数系统的滑动模控制

研究一类不确定变时滞分布参数系统的滑动模控制问题．首先设计一种无记忆功能的变结构控制器;然后分析了在滑动模切换面上滑动模控制系统关于不确定量的不变性特征;最后给出了从任意初始位置出发的轨线到达滑动模态区的时间估计．研究表明,所设计的控制器结构简单．容易实现．     

Tuning functions‐based robust adaptive tracking control of a class of nonlinear systems with time delays

In this paper, an adaptive backstepping tracking control scheme is proposed for a class of nonlinear state time‐varying delay systems, which are subject to parametric uncertainties and external disturbances. The bounds of the time delays and their derivatives are assumed to be unknown. Tuning functions method is exploited to construct the control law and adaptive laws. Unknown time‐varying delays are compensated by using appropriate Lyapunov–Krasovskii functional. It is shown that the proposed controller can guarantee the boundedness of all the closed‐loop signals. The tracking performance can be adjusted by choosing suitable design parameters. At the end, a simulation example is provided to illustrate the effectiveness of the design procedure. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust Stability and Stabilization Criteria for Discrete Singular Time‐Delay LPV Systems

This paper is concerned with establishing robust stability and stabilization criteria for discrete singular time‐delay linear parameter varying (LPV) systems. Firstly, a robust stability criterion is obtained for this class of systems by a delay‐partition approach, and thereby a less conservative sufficient condition which guarantees discrete singular time‐delay LPV systems to be admissible is given. Secondly, a class of state feedback controllers for stabilizing discrete singular time‐delay LPV systems is designed. Finally, compared with existing results, the numerical results of several examples illustrate the effectiveness of the approach proposed in this paper. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Observer-based event-triggered containment control of multi-agent systems with time delay

This paper studies the containment control of general linear multi-agent systems with or without time delay. The observer-based event-triggered control schemes will be considered. For the conventional distributed containment control protocol, we will not update the relative state continuously, i.e. the relative state will be updated by some events which happen intermittently. A completely decentralised event trigger will be designed for leader–follower systems. Under the proposed protocol, if we design some appropriate feedback gain matrices, all followers will asymptotically converge to the convex hull spanned by the dynamic leaders. Numerical simulations are also provided and the results show highly consistent with the theoretical results.     

On the backstepping design procedure for multiple input nonlinear systems

In a recent paper, we developed a structural decomposition for multiple input multiple output nonlinear systems that are affine in control but otherwise general. In this paper, we exploit the structural properties of such a decomposition in the application of the backstepping design technique on multiple input nonlinear systems. In particular, this decomposition simplifies the conventional backstepping design and motivates new backstepping design procedures that are able to stabilize systems on which the conventional backstepping procedure is not applicable. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust control of uncertain distributed delay systems with application to the stabilization of combustion in rocket motor chambers

The problems of robust stability and robust stabilization of uncertain linear systems with distributed delay occurring in the state variables are studied in this paper. The essential requirement for the uncertainties is that they are norm-bounded with known bounds. Conditions for the robust stability of distributed time delay systems are given and a design method for the robust stabilizing control law of the uncertain systems is presented. The proposed method is applied to the stabilization of combustion in the chamber of a liquid monopropellant rocket motor. It is found that the combustion can be robustly stabilized when the two parameters pressure exponent γ and maximal time lag r vary in specified intervals, respectively.     

Generalization of Tychonov''s Theorem with applications to adaptive control of SISO delay systems

This paper deals with single-input single-output delay systems with unknown transfer function parameters, including unknown, non-commensurate, real delays. A generalization of Tychonov's Theorem is obtained. This generalization is used to show the stability of a smooth adaptive controller when applied to a large class of delay systems. This paper generalizes the results in [1,2].     

Global stabilization of discrete‐time feedforward time‐delay systems by bounded controls

This paper studies the problem of global stabilization of a family of discrete‐time feedforward time‐delay systems with bounded controls. Two classes of nonlinear control laws are established based on a special canonical form of the considered system. The proposed control laws use not only the current states but also the delayed states for feedback and, moreover, contain some free parameters. These advantages can help to improve the transient performance of the closed‐loop system significantly. A practical example is given for illustration.     

Disturbance decoupling for time delay systems

In this paper the disturbance decoupling problem associated with a class of linear and nonlinear time delay systems is considered. The solution to this problem is given in terms of the relative degrees associated with the input and the disturbance of the corresponding time delay systems. A stability study using some results due to Pontryagin is presented for the resultant closed-loop system when the delay system is linear. Also, an approximate causal solution is proposed for the nonlinear time delay system based on its linearization around an equilibrium point. © 1997 by John Wiley & Sons, Ltd.     

Output-feedback stabilization for stochastic high-order nonlinear systems with time-varying delay

This paper investigates output-feedback control for a class of stochastic high-order nonlinear systems with time-varying delay for the first time. By introducing the adding a power integrator technique in the stochastic systems and a rescaling transformation, and choosing an appropriate Lyapunov-Krasoviskii functional, an output-feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability and the output can be regulated to the origin almost surely. A simulation example is provided to show the effectiveness of the designed controller.     

Well-posed problem of nonlinear singular distributed parameter systems and nonlinear GE-semigroup

According to the well-posed problem of nonlinear singular distributed parameter systems, first of all, the nonlinear GE-semigroup induced by a continuous （possibly nonlinear） operator is introduced in Banach space, which is a generalization of GE-semigroup （i.e., generalized operator semigroup）, and the properties of nonlinear GE-semigroup are discussed; and then the existence, uniqueness and constructive expression for the strong solution of nonlinear singular distributed parameter system are discussed by nonlinear GE-semigroup; at last, the exponential stability of nonlinear singular distributed parameter system is studied by using nonlinear GE-semigroup, functional analysis and operator theory in Banach space.     

Lyapunov tools for predictor feedbacks for delay systems: Inverse optimality and robustness to delay mismatch

We consider LTI finite-dimensional, completely controllable, but possibly open-loop unstable, plants, with arbitrarily long actuator delay, and the corresponding predictor-based feedback for delay compensation. We study the problem of inverse-optimal re-design of the predictor-based feedback law. We obtain a simple modification of the basic predictor-based controller, which employs a low-pass filter, and has been proposed previously by Mondie and Michiels for achieving robustness to discretization of the integral term in the predictor feedback law. The key element in our work is the employment of an infinite-dimensional “backstepping” transformation, and the resulting Lyapunov function, for the infinite dimensional systems consisting of the state of the ODE plant and the delay state. The Lyapunov function allows us to quantify the Lyapunov stability properties under the modified feedback, the inverse optimality of the feedback, and its disturbance attenuation properties. For the basic predictor feedback, the availability of the Lyapunov function also allows us to prove robustness to small delay mismatch (in both positive and negative directions).     

Comparing the Adomian decomposition method and the Runge–Kutta method for solutions of the Stefan problem

The solution of the one-phase Stefan problem is presented. A Stefan's task is first approximated with a system of ordinary differential equations. A comparison between the Adomian decomposition method and the fourth-order Runge–Kutta method for solving this system is then presented.     

Reduced‐order observer‐based output‐feedback tracking control of nonlinear systems with state delay and disturbance

In this paper, we investigate the problem of output‐feedback tracking control for a class of nonlinear SISO systems in the strick‐feedback form, which are subject to both uncertain delay‐related functions and disturbances. A reduced‐order observer is first introduced to provide the estimates of the unmeasured states. Then, an output‐feedback controller is recursively designed based on the backsteppng method. By constructing an appropriate Lyapunov–Krasovskii functional, we prove that all the signals in the closed‐loop system are bounded. The tracking performance is guaranteed by suitably choosing the design parameters. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed control algorithm. Copyright © 2009 John Wiley & Sons, Ltd.