非线性控制系统的特性（Ⅰ）

本文采用与线性系统理论相比较的方法，阐述非线性控制系统理论。文中通过一些例子来分析非线性控制系统在能控性、能观性、抗干扰性、解耦和稳定性等方面的特性，从而进一步说明非线性控制系统理论在提法、论述和结论上的特点。第一部分介绍非线性系统的能控性和能观性。     

A Global Control Algorithm in the Plane

The controllability theory may at times lead to a control law as can be seen in the control theory literature. In this paper, a global control algorithm is proposed for nonlinear systems in the so-called linear-analytic form in the plane. The algorithm is motivated by a theorem by Hunt, which gives sufficient conditions for the global controllability of linear-analytic systems on a 2-dimensional manifold. It is verified that the algorithm is globally convergent under the given assumptions. A computational form of the algorithm is presented. Some computational aspects are also discussed.     

Optimum approximation of high-order systems by low-order models†

A method has been proposed for the determination of optimum low-order models for a high-order system which minimize a specified error criterion for a given order of the model. The method is based on the pattern-search algorithm of Hooke and Jeeves. Starting from an approximate first or second-order model, an optimum model of that order is determined, and the process is continued with the order increasing progressively. As an example of the application of the method, optimum second-order models of a seventh-order system have been obtained using a number of different criteria for optimization. A third and a fourth-order optimum model have then been derived for a given criterion.     

周期性系统的能控性理论

主要探讨周期性系统(包括连续和离散两种情形)的能控性问题,对文献中有关周期为To的连续周期性系统的能控性结论进行了完善,推导出系统能控等价于单周期(0,To)内能控的结论,并将这些结论直接推广到离散周期性系统;然后讨论了离散前后周期性系统能控性保持不变的可能性,证明在采用不等间距采样方式时,离散前后周期性系统的能控性保持不变。     

Control of nonholonomic systems with extended base space dynamics

This paper extends certain results in Reference 1 to a more general class of nonholonomic systems with extended base space dynamics. This extension is important in applications for which control actuator dynamics are significant. These nonlinear control systems are referred to as nonholonomic control systems owing to certain nonintegrability assumptions which are made. The class of systems considered in this paper are characterized by general nonlinear base space dynamics that are input-output decouplable. Controllability results for this class of nonholonomic control systems are presented.     

分布参数系统的能控性

本文对一个控制量以分布方式在作用于系统的齐次项的同时,也作用于系统导数项的一阶分布参数系统讨论能控性问题。     

Null controllability of planar bimodal piecewise linear systems

This article investigates the null controllability of planar bimodal piecewise linear systems, which consist of two second order LTI systems separated by a line crossing through the origin. It is interesting to note that even when both subsystems are controllable in the classical sense, the whole piecewise linear system may be not null controllable. On the other hand, a piecewise linear system could be null controllable even when it has uncontrollable subsystems. First, the evolution directions from any non-origin state are studied from the geometric point of view, and it turns out that the directions usually span an open half space. Then, we derive an explicit and easily verifiable necessary and sufficient condition for a planar bimodal piecewise linear system to be null controllable. Finally, the article concludes with several numerical examples and discussions on the results and future work.     

Adaptive Dynamic Output Feedback Stabilisation of Nonlinear Systems

An adaptive dynamical output feedback controller is introduced for a class of nonlinear non‐minimum phase systems. This adaptive controller achieves practical stabilisation, that means the output will asymptotically tend to a pre‐specified neighbourhood of the origin. In case of linear systems, we can even prove adaptive stabilisation.     

Regional constrained controllability problem: Approaches and simulations

The aim of this paper is to deal with an output controllability problem. It consists in driving the state of a distributed parabolic system toward a state between two prescribed functions on a boundary subregion of the system evolution domain with minimum energy control. Two necessary conditions are derived. The first one is formulated in terms of subdifferential associated with a minimized functional. The second one is formulated as a system of equations for arguments of the Lagrange systems. Numerical illustrations show the efficiency of the second approach and lead to some conjectures. Recommended by Editorial Board member Fumitoshi Matsuno under the direction of Editor Jae Weon Choi. Zerrik El Hassan is a Professor at the university Moulay Ismail of Meknes in Morocco. He was an Assistant Professor in the faculty of sciences of Meknes and researcher at the university of Perpignan (France). He got his doctorat d etat in system regional analysis (1993) at the University Mohammed V of Rabat, Morocco. Professor Zerrik wrote many papers and books in the area of systems analysis and control. Now he is the Head of the research team MACS (Modeling Analysis and Control of Systems) at the university Moulay Ismail of Meknes in Morocco. Ghafrani Fatima is a Researcher at team MACS at the University Moulay Ismail of Meknes in Morocco. She wrote many papers in the area of systems analysis and control.     

对称非线性控制系统的能控性

本文采用微分几何方法,研究了具有对称结构的非线性控制系统的能控性。本文证明:若对称非线性控制系统在某点能控,那么该系统在此点所属的轨道上的所有点均能控。     

The regulator problem with indefinite quadratic cost for boundary control systems: the finite horizon case

In this paper we study the finite horizon non-standard LQ-problem for an abstract dynamics, which models a large class of hyperbolic-like partial differential equations. We provide necessary/sufficient conditions for finiteness of the value function corresponding to the control problem. Sharpness of sufficient conditions is shown by means of counterexamples. The specific features of the finite, in contrast to infinite, horizon case are illustrated.