On controllability and near-controllability of discrete-time inhomogeneous bilinear systems without drift

In this paper, controllability and near-controllability of discrete-time inhomogeneous bilinear systems without drift are studied. Necessary and sufficient conditions for controllability and near-controllability of the systems are respectively presented. In particular, algorithms for computing the control inputs to achieve the transition of a given pair of states for the controllable systems and nearly controllable systems are also provided. Examples are shown to demonstrate the conceptions and results of the paper.     

Controllability of a class of discrete time bilinear systems

In this paper the controllability of a class of discrete time bilinear systems is discussed. Necessary and sufficient conditions for complete controllability are derived. In addition a complete characterization of the controllable regions of this class of systems, when not completely controllable, is made.     

Parallel Control for Continuous-Time Linear Systems: A Case Study

In this paper, a new parallel controller is developed for continuous-time linear systems. The main contribution of the method is to establish a new parallel control law, where both state and control are considered as the input. The structure of the parallel control is provided, and the relationship between the parallel control and traditional feedback controls is presented. Considering the situations that the systems are controllable and incompletely controllable, the properties of the parallel control law are analyzed. The parallel controller design algorithms are given under the conditions that the systems are controllable and incompletely controllable. Finally, numerical simulations are carried out to demonstrate the effectiveness and applicability of the present method.      

Canonical forms of decouplable and controllable linear systems

In this paper, we present the canonical forms of decouplable and controllable linear systems. Some of the non-zero elements in Gilbert's canonically decoupled structure, which remain undetermined, are explicitly determined by a complete set of invariances. Our result constitutes the key step to characterization of the whole class of nonlinear systems that are feedback—equivalent to decouplable and controllable linear systems.     

Minimal controllability for systems with delays†

In this paper we consider the problem of minimal controllability for a general class of linear spectrally controllable systems. We show that the smallest number of controls that are necessary in order that spectral controllability may hold depends only upon the matrices of the uncontrolled system and that it is equal to the smallest number of outputs necessary for the dual problem of ‘spectral observability’; moreover, any spectrally controllable system can be made minimally controllable by acting upon the control matrix only, and any spectrally observable system can be made minimally observable by acting upon the output matrix only. In the sequel this result is explained in the cases of the delayed systems and of some kind of generalized systems.     

On strong controllability for planar affine nonlinear systems

Different to linear systems, a controllable nonlinear system does not generally imply that it is strongly controllable. This paper will investigate the strong controllability of planar affine nonlinear systems and obtain its necessary and sufficient condition by introducing the variation function of the control curve. These conditions are imposed on the system structure only. In addition, we also point out that, for a class of polynomial systems, their strong controllability is equivalent to their controllability. Finally, some examples are given to show the application of our results.     

On small-controllability and controllability of a class of nonlinear systems

In this paper, small-controllability and controllability of a class of nonlinear systems are studied. Both the discrete-time case and continuous-time case are considered. By proposing an implicit function approach, sufficient conditions for the systems respectively to be small-controllable and controllable are obtained. Examples are also provided to illustrate the results of the paper.     

广义系统的最小能控结构

本文通过线性变换的Drazin逆理论讨论了广义系统的最小能控结构问题,给出了广义 系统四种主要能控性的最小能控结构定理.     

On the controllability of a nonlinear control system

This paper considers the problem of controllability of a class of nonlinear systems. Sufficient conditions are given for a nonlinear system to be locally controllable and globally completely controllable. In the case of a linear time-invariant system, these conditions are also necessary. Furthermore, our result reveals that, for a nonlinear control system, there is a relationship among controllability, stability and optimality.     

Finite-time stabilization and stabilizability of a class of controllable systems

In this paper, finite-time control problem of a class of controllable systems is considered. Explicit formulae are proposed for the finite-time stabilization of a chain of power-integrators, and then discussions about a generalized class of nonlinear systems are given.     

Controllability on principal fibre bundles with compact structure group

In this paper we consider the controllability problem for systems defined on principal fibre bundles, in which the set of associated vector fields is invariant under the action of the structure group, and projects down on to a set of vector fields on the base space. It is shown that if the system is accessible, and the structure group is compact, then the system is controllable if and only if the system is controllable when projected onto the base space. The connection between these systems and systems admitting symmetries generated by free and proper group actions is described, and various examples are given relating to systems on homogeneous spaces.     

Reliability model for hierarchical systems: Regenerative approach

Most of real technical systems and biological objects with sufficiently high organization are complex hierarchical partially controllable systems. In the paper for modeling and analysis of reliability of such systems the method of decomposable semi-regenerative processes is used. A simple example illustrates our approach.     

Observability and decentralized control of fuzzy discrete-event systems

Fuzzy discrete-event systems as a generalization of (crisp) discrete-event systems have been introduced in order that it is possible to effectively represent uncertainty, imprecision, and vagueness arising from the dynamic of systems. A fuzzy discrete-event system has been modeled by a fuzzy automaton; its behavior is described in terms of the fuzzy language generated by the automaton. In this paper, we are concerned with the supervisory control problem for fuzzy discrete-event systems with partial observation. Observability, normality, and co-observability of crisp languages are extended to fuzzy languages. It is shown that the observability, together with controllability, of the desired fuzzy language is a necessary and sufficient condition for the existence of a partially observable fuzzy supervisor. When a decentralized solution is desired, it is proved that there exist local fuzzy supervisors if and only if the fuzzy language to be synthesized is controllable and co-observable. Moreover, the infimal controllable and observable fuzzy superlanguage, and the supremal controllable and normal fuzzy sublanguage are also discussed. Simple examples are provided to illustrate the theoretical development.     

Controllability of Laguerre and Jacobi equations

In this paper we study the controllability of the controlled Laguerre equation and the controlled Jacobi equation. For each case, we find conditions which guarantee when such systems are approximately controllable on the interval [0,?t ₁]. Moreover, we show that these systems can never be exactly controllable.     

Determination of generic dimensions of controllable subspaces and its application

The controllable subspace and its dimension of a structured linear system vary as a function of the free parameters. However, the dimension is stable in the sense that it takes, for almost any system parameters, some maximal constant which is the generic rank of the controllability matrix. In this paper, this maximal constant is called the generic dimension of the controllable subspace. Two simple methods for determining generic dimensions of controllable subspaces are derived. As an application, the results are applied to the determination of system types of linear multivariable unity feedback systems.     

感应电动机系统的能控性与能观测性分析

分析了感应电动机系统的能控性与能观测性。结果表明系统是弱能控与弱能观的。而且,采用非线性状态反馈解耦控制和非线性坐标变换后的局部闭环解耦线性系统是能控与能观的。     

Comments on "Instability of optimal-aim control"

This note discusses the conclusions of the above paper on the instability of optimal-aim strategies relative to controllable linear systems. Contrary to these conclusions, it is proved that under fully implemented optimal-aim strategies, all controllable linear systems are stabilized.     

Finite spectrum assignment and observer for multivariable systems with commensurate delays

This paper is concerned with control of multivariable systems with commensurate delays. The purpose of this paper is to enlarge the class of finite spectrum assignable systems to spectrally controllable multivariable systems with commensurate delays. By overcoming an infinite number of eigenvalues which are contained in the system and make control very complex, it is proved that if the system is spectrally controllable, there is a delayed feedback matrix such that the closed-loop system is spectrally controllable through a single input. Combining this result with previous ones about single-input systems, it is verified that spectral controllability is equivalent to finite spectrum assignability for multivariable systems with commensurate delays. An observer for the system with delayed outputs is presented. By using these results, the multivariable system can be regulated as desired without preliminary knowledge of open-loop eigenvalues and a stability test of transcendental functions whenever the system is spectrally controllable and spectrally observable.