Controllability and observability of impulsive hybrid dynamic systems

Corresponding author, Email: cbsoh{at}auto.eee.ntu.ac.sg This paper considers the controllability and observability ofhybrid dynamic systems with impulsive switching of the otherwisecontinuously evolving state. It derives necessary and sufficientconditions for impulsive hybrid dynamic systems to be controllableand observable.     

Solvability,controllability, and observability of singular systems

The problems of solvability, controllability, and observability for the singular systemKx(t)=Ax(t)+Bu(t) are studied, whereK is a singular, square matrix andu(t) is a complex vector function sufficiently differentiable. The classical theories of matrix pencils are first related to the solvability of singular systems. Then, the concepts of reachability, controllability, and observability of regular systems are extended to singular systems. Finally, the set of reachable states is described. The proposed matrix conditions for testing the controllability and observability of singular systems are simple and always feasible.     

Controllability questions for nonlinear systems in abstract spaces

In abstract spaces, we consider certain constrained controllability and approximate controllability properties of a nonlinear system that can be deduced from various controllability properties of its associated linear system. Several examples involving partial differential operators and functional delay operators are given to illustrate the theory.The research of the second author was supported in part by NSF Grant DMS-85-088651 and by the University of Tennessee Science Alliance Award.     

Two-end observability of elastic vibrations in distributed and lumped parameter systems

The boundary observation problems (initial state reconstruction) of vibrations in objects with distributed and lumped parameters are solved. The vibrations in an object with distributed parameters are described by boundary value problems with boundary conditions of various types. An object with lumped parameters is described by a second-order ordinary differential equation.     

The monotone method for controllability of the nonlinear evolution systems

In this paper,we study the controllability of the nonlinear evolution systems.We establish the controllability results by using the monotone operator theory.No compactness assumptions are imposed in the main results.We present an example to illustrate our results.     

CONTROLLABILITY AND OBSERVABILITY FOR A CLASS OF FRACTIONAL-ORDER IMPULSIVE SYSTEMS

This paper studies the controllability and observability for a class of fractionalorder impulsive systems.First,the basic acknowledgement of fractional-order systems is presented.Then the solution of the fractional-order impulsive systems is given.Finally,necessary and sufficient criteria for controllability and observability are obtained.     

Exact Controllability of Semilinear Evolution Systems and Its Application

In this paper, we obtain several abstract results concerning the exact controllability of semilinear evolution systems. First, we prove the null local exact controllability of semilinear first-order systems by means of the contraction mapping principle; in this case, we do not assume any compactness. Next, we derive the global and/or local exact controllability of semilinear second-order systems by means of the Schauder fixed-point theorem; in this case, we assume only the embedding of the related spaces having some compactness, which is reasonable for many concrete problems. Our main result shows that the observability of the dual of the linearized system implies the exact controllability of the original semilinear system. Finally, we apply our abstract results to the exact controllability of the semilinear wave equation.     

组合系统的行为化方法

在行为框架下研究线性微分组合系统的建模问题 .建立了 n个子系统串、并联组合系统的行为化模型 ,给出了其能控性、能观性的判别条件 .分析过程表明用行为化方法对组合系统的研究有着比传统方法更便捷、适用的模型类更广等优点 .     

Approximate controllability for trajectories of semilinear control systems

We treat an abstract semilinear control system and study the controllability problem for its trajectories. Assuming a range condition of the control action operator and an inequality condition on the system parameters, we can show that the reachable trajectory set of the semilinear system is equivalent to that of its corresponding linear system.The author wishes to express his deep appreciation to Prof. T. I. Seidman for his many helpful suggestions and to Prof. W. Takahashi for many stimulating conversations.     

Controllability of delay systems with restrained controls

Using a geometric growth condition, we characterize both the function space and Euclidean controllability of a nonlinear delay system which has a compact and convex control set. This extends analogous results for ordinary differential systems, and it yields conditions under which perturbed nonlinear delay controllable systems are controllable.This research was supported by the National Aeronautics and Space Administration under Contract No. NSG 1445Now on leave of absence as Professor, Department of Mathematics, University of Jos, Jos, Nigeria.     

Factor release in two-dimensional system models

The possibility of factor release in two-dimensional system models is examined. Confirmation of this condition as a consequence of parameter variations is explored.     

Controllability properties of constrained linear systems

In this paper, we present results on constrained controllability for linear control systems. The controls are constrained to take values in a compact set containing the origin. We use the results on reachability properties discussed in Ref. 1.We prove that controllability of an arbitrary pointp inR ⁿ is equivalent to an inclusion property of the reachable sets at certain positive times. We also develop geometric properties ofG, the set of all nonnegative times at whichp is controllable, and ofC, the set of all controllable points. We characterize the setC for the given system and provide additional spectrum-dependent structure.We show that, for the given linear system, several notions of constrained controllability of the pointp are the same, and thus the setC is open. We also provide a necessary condition for small-time (differential or local) constrained controllability ofp.This work was supported in part by NSF Grant ECS-86-09586.     

Boundary Controllability and Observability of a One-Dimensional Nonuniform SCOLE System

A hybrid system, composed of an elastic beam governed by an Euler-Bernoulli beam equation with variable coefficients and a linked rigid body governed by an ordinary differential equation, is considered. Various controllability/observability properties of the system under bounday control/observation are studied. It is shown that an open-loop smooth/singular controller of either torque control or force control is sufficient to make the system exactly controllable in arbitrarily short time duration. The work was carried out with the support of the National Natural Science Foundation of China and the Russian Foundation for Fundamental Researches, Grant 02-01-00554.     

Controllability of semilinear systems

The most general results known about controllability of semilinear systems are found in Refs. 1 and 2. The authors of these papers used different approaches, and no connection between them has ever been pointed out. The purpose of this paper is to present a general theorem under which these results easily follow.This paper is taken from a chapter of the author's doctoral thesis written at University of California, Los Angeles, California.     

On the null-controllability of linear discrete-time systems with restrained controls

This paper is devoted to the null-controllability problem for linear, autonomous, discrete-time systems with restrained controls, i.e., systems described by the equationx _k+1=Ax _k+u _k,u _k , where 0 , but is not necessarily an interior point of . Some criteria for local and global null controllability are given with proofs. These results can be considered as extensions to discrete-time systems of the known corresponding criteria for linear, continuous-time systems.     

非线性控制系统的梯度扩张的能达性

研究了仿射非线性控制系统的梯度扩张系统.利用非线性控制系统的微分几何理论,通过计算梯度扩张系统的输出函数沿着输入向量场和系统向量场的李导数,讨论仿射非线性控制系统的梯度扩张系统的能达性分布,研究了非线性控制系统和它的梯度扩张系统的能达性之间的关系,证明了如果梯度扩张系统是能达的,则原非线性控制系统也是能达的.