Conservative boundary control systems

We study continuous time linear dynamical systems of boundary control/observation type, satisfying a Green-Lagrange identity. Particular attention is paid to systems which have a well-defined dynamics both in the forward and the backward time directions. As we change the direction of time we also interchange inputs and outputs. We show that such a boundary control/observation system gives rise to a continuous time Livšic-Brodski? (system) node with strictly unbounded control and observation operators. The converse is also true. We illustrate the theory by a classical example, namely, the wave equation describing the reflecting mirror.     

Infinite-horizon boundary control of distributed systems

For a boundary controlled dynamic system, algorithms for solving the problem of tracking reference motion and the problem of tracking reference control are described. The algorithms are robust to information noise and computational errors. The solution method is based on the extremal shift method from the theory of positional differential games.     

Stabilization of nonlinear systems with a dither control

In this paper a new approach is taken to analyze stabilization of a general nonlinear system with a dither input. Given the original system with a control, an autonomous relaxed system is constructed. It is shown that if the relaxed system is stable, then the original system with dither control would be stable in the finite time. An algorithm is given for constructing the dither control. The technique used here is general and does not have the limitations of the Dual Input Describing Function technique. Furthermore, in many cases it is possible to guarantee global contractive stability as well. Two examples are solved in detail using computer simulations for demonstration of the technique.     

Stabilization of affine control systems with periodic coefficients

We obtain new sufficient conditions for the uniform global asymptotic stabilization of the zero solution of an affine control system with periodic coefficients and some corollaries for bilinear control systems.     

Euler-Bernoulli梁方程基于边界分数阶导数反馈控制的镇定

研究具有边界控制的Euler-Bernoulli梁方程基于边界分数阶导数反馈控制的镇定问题.首先,给出开环系统在Salamon意义下的适定性;其次,运用半群方法和LaSalle不变原理,证明了闭环系统生成C_0-半群并且闭环系统是渐近稳定的;最后,设计了一个未知输入类型的状态观测器,其观测器状态渐近收敛于原系统的状态.     

Stabilization of stationary affine control systems with discrete time

We obtain new sufficient conditions for the local and global asymptotic stabilization of the zero solution of a nonlinear affine control system with discrete time and with constant coefficients by a continuous state feedback. We assume that the zero solution of the free system is Lyapunov stable. For systems with linear drift, we construct a bounded control in the problem of global asymptotic state and output stabilization. Corollaries for bilinear systems are obtained.     

Stabilization of linear distributed control systems with unbounded delay

In this paper we study the asymptotic stabilization of linear distributed parameter control systems with unbounded delay. Assuming that the semigroup of operators associated with the uncontrolled and nondelayed equation is compact and that the phase space is a uniform fading memory space, we characterize those systems that can be stabilized using a feedback control. As consequence we conclude that every system of this type is stabilizable with an appropriated finite dimensional control.     

Stabilization of nonlinear switched systems using control Lyapunov functions

In this paper, we study the stabilization of general nonlinear switched systems by using control Lyapunov functions. The concept of control Lyapunov function for nonlinear control systems is generalized to switched control systems. The first part of our contribution provides a necessary and sufficient condition of stabilization. The main idea is to use a common control Lyapunov function; this is achieved with the converse Lyapunov theorem dedicated to switched systems. In the second part, an explicit construction of a common control Lyapunov function is addressed with respect to a finite family of switched systems. The approach uses a family of control Lyapunov functions attached to the subsystems.     

Stabilization and synchronization of chaotic systems via intermittent control

In this paper, we consider the stabilization and synchronization of chaotic systems via intermittent control with time varying control period and control width. Compared to existing results, some less conservative conditions are derived to guarantee the stabilization of nonlinear system. An effective adaptive-intermittent control law is also presented. Two examples are given to verify our proposed results.     

Stabilization of unbounded bilinear control systems in Hilbert space

We consider bilinear control systems of the form y^′(t)=Ay(t)+u(t)By(t) where A generates a strongly continuous semigroup of contraction (etA)_t?0 on an infinite-dimensional Hilbert space Y whose scalar product is denoted by 〈.,.〉. We suppose that this system is unbounded in the sense that the linear operator B is unbounded from the state Y into itself. Tacking into account eventual control saturation, we study the problem of stabilization by (possibly nonquadratic) feedback of the form u(t)=−f(〈By(t),y(t)〉). Applications to the heat equation is considered.     

Adaptive servomechanism design for boundary control systems

In this paper we consider the design of adaptive servomechanismfor boundary control systems in the case of the input and outputoperators being collocated. An adaptive servomechanism is constructedby the concept of high-gain output feedback and the estimationmechanism of the unknown parameters for the bounded disturbances.Moreover, a controller is designed to be inverse optimal. Itminimizes a meaningful cost functional that incorporates integralpenalty on the tracking error state, the control and the parametererror.     

Stabilization for hybrid stochastic systems by aperiodically intermittent control

In this paper, the mean-square exponential stabilization for stochastic differential equations with Markovian switching is studied. Specifically, a new set of sufficient conditions is derived to obtain the aperiodically intermittent control design which exponentially stabilizes the addressed hybrid stochastic differential equations. Further, stabilization problem by periodically intermittent control can be deduced as a special case from the developed results. As an application, we consider the Hopfield neutral network model with simulations to illustrate the effectiveness of developed aperiodically intermittent control design.     

Approximate positive controllability of positive boundary control systems

This paper is devoted to the study of the approximate positive controllability for linear systems with positive boundary controls. The results are applied to an abstract transport equation and controlled flows in networks.     

Stabilization and tracking control for a class of nonlinear systems

This paper discusses stabilization and tracking control using linear matrix inequalities for a class of systems with Lipschitz nonlinearities. A nonlinear state feedback stabilization control is proposed for systems containing a more general case of Lipschitz nonlinearity. The main objective of the present study is to provide, for multi-input multi-output nonlinear systems, a tracking control approach based on nonlinear state feedback, which guarantees global asymptotic output and state tracking with zero tracking error in the steady state. Further, the tracking control is formulated for optimal disturbance rejection, using $L_2$ gain reduction based performance criteria. The proposed methodologies are illustrated herein using two simulation examples of chaotic and unstable dynamical systems.     

Stabilization and control of distributed systems with time-dependent spatial domains

This paper considers the problem of the stabilization and control of distributed systems with time-dependent spatial domains. The evolution of the spatial domains with time is described by a finite-dimensional system of ordinary differential equations, while the distributed systems are described by first-order or second-order linear evolution equations defined on appropriate Hilbert spaces. First, results pertaining to the existence and uniqueness of solutions of the system equations are presented. Then, various optimal control and stabilization problems are considered. The paper concludes with some examples which illustrate the application of the main results.This work was supported by the Air Force Office of Scientific Research, Grant No. AFOSR 86-0132, by the National Science Foundation, Grant No. 87-18473, and by the Jet Propulsion Laboratory, Pasadena, California.     

Optimal control of impulsive systems with nonlocal boundary conditions

In this paper we study an optimal control problem, where states of a control system are described by impulsive differential equations with nonlocal boundary conditions. With the help of the contraction principle we prove the existence and uniqueness of a solution to the corresponding boundary value problem with fixed admissible controls. We calculate the first and second variation of the functional. Using the variation of controls, we establish various necessary optimality conditions of the second order.     

Stabilization of bilinear control systems in Hilbert space with nonquadratic feedback

We consider bilinear control systems of the form y′(t) = Ay(t) + u(t)By(t) where A generates a strongly continuous semigroup of contraction (e ^{t A} ) _t⩾0 on an infinite-dimensional Hilbert space Y whose scalar product is denoted by 〈.,.〉. The function u denotes the scalar control. We suppose that B is a linear bounded operator from the state Y into itself. Tacking into account the control saturation, we study the problem of stabilization by feedback of the form u(t)=−f(〈By(t), y(t)〉). Application to the heat equation is considered.      

Stabilization of linear control systems in Hilbert space with nonlinear feedback

This paper considers the problem of stabilization of linear control systems in Hilbert space with nonlinear feedback. Extensions of known results in the linear feedback case to the nonlinear one are given.     

Stabilization of switched linear systems using an improved event-triggered control scheme

This paper is concerned with the event-triggered control of switched linear systems. The coupling of system switching and event-triggered communication raises two phenomena: (1) the update of controller cannot always catch up with the active subsystem; (2) the switching may lead to additional triggers. The first phenomenon is called the asynchronous switching induced by network communication and the second one brings great difficulty to avoid the Zeno behavior of event-triggered mechanism (ETM). To address the above problem, we propose a new ETM which contains the switching signal of models and controllers and the discontinuity of triggering error at switching time instants. A relative threshold strategy, combined with a jump function, is designed as a new threshold function. By introducing a compensation term, the linear feedback control law is extended to avoid the Zeno behavior of ETM and improve the solvability of control algorithm. Based on the proposed event-triggered control scheme, the exponential stabilization of switched systems is achieved with relaxed constraints on the triggering and switching conditions. The obtained results are validated by a numerical example.