Controllability of nonlinear discrete systems without differentiability assumption

The paper gives another approach to studying controllability of nonlinear discrete systems, which is based on proving the support principle for some boundary problems involving locally Lipschitzian set-valued maps. The approach enables us to develop sufficient conditions for various types of local controllability of nonlinear non-stationary discrete systems without differentiability assumption. For linear discrete systems with constrained states and controls, necessary and sufficient conditions for local controllability are given.     

Constrained Controllability of Fractional Dynamical Systems

The article deals with the controllability results for fractional dynamical systems with prescribed controls represented by the fractional integrodifferential equation in finite dimensional spaces. Sufficient conditions for the controllability results of nonlinear fractional dynamical systems are obtained using the contraction mapping principle. Examples are included to illustrate the theory.     

Global robust controllability of the triangular integro-differential Volterra systems

A solution of the global controllability problem for a class of nonlinear control systems of the Volterra integro-differential equations is presented. It is proven that there exists a family of continuous controls that solve the global controllability problem for this class. The constructed controls depend continuously on the initial and the terminal states. It makes possible to prove the global controllability of the uniformly bounded perturbations of these systems under the global Lipschitz condition for the unperturbed system with respect to the states and the controls.     

Controllability in nonlinear systems

In this paper we obtain an explicit expression for the reachable set for a class of nonlinear systems. This class is described by a chain condition on the Lie algebra of vector fields associated with each nonlinear system. These ideas are used to obtain a generalization of a controllability result for linear systems in the case where multiplicative controls are present.     

Sufficient conditions for the controllability of nonlinear distributed systems

For nonlinear distributed systems representable as a Volterra functional operator equation in a Lebesgue space, sufficient conditions for pointwise controllability with respect to a vector of non-linear functionals are proved. The controls are assumed to be piecewise constant vector functions. The reduction of controlled distributed systems to the functional operator equation under study is illustrated by two examples: a Dirichlet boundary value problem for the diffusion equation and a mixed problem for the transport equation.     

Complete controllability of nonlinear stochastic impulsive functional systems

This paper is concerned with the controllability of a kind of nonlinear stochastic impulsive functional systems. Sufficient conditions for the complete controllability of the nonlinear stochastic impulsive functional systems are obtained by using Schauder fixed-point theorem. A numerical example is given to illustrate the effectiveness of the theoretical results.     

Controllability and controllability with prescribed controls

In this paper, a controllability condition with prescribed controls (that is, a controllability condition for which the initial and final value of the control are givena priori), for classes of nonlinear control process with different controllability criteria, is obtained. The result is achieved by using the fixed-point argument as a crucial tool.     

Exact boundary controllability of nodal profile for quasilinear hyperbolic systems in a tree‐like network

In this paper, the exact boundary controllability of nodal profile is established for quasilinear hyperbolic systems with general nonlinear boundary and interface conditions in a tree‐like network with general topology. The basic principles for giving nodal profiles and for choosing boundary controls are presented, respectively. Copyright © 2011 John Wiley & Sons, Ltd.     

Controllability of Nonlinear Systems in Banach Spaces: A Survey

This paper presents a survey on research using fixed-point theorems and semigroup theory to study the controllability of nonlinear systems and functional integrodifferential systems in Banach spaces. Also discussed is the use of this technique in K-controllability and boundary controllability problems for nonlinear systems and integrodifferential systems in abstract spaces.     

Approximate Controllability of Fractional Differential Equations with State-Dependent Delay

The systems governed by delay differential equations come up in different fields of science and engineering but often demand the use of non-constant or state-dependent delays. The corresponding model equation is a delay differential equation with state-dependent delay as opposed to the standard models with constant delay. The concept of controllability plays an important role in physics and mathematics. In this paper, first we study the approximate controllability for a class of nonlinear fractional differential equations with state-dependent delays. Then, the result is extended to study the approximate controllability fractional systems with state-dependent delays and resolvent operators. A set of sufficient conditions are established to obtain the required result by employing semigroup theory, fixed point technique and fractional calculus. In particular, the approximate controllability of nonlinear fractional control systems is established under the assumption that the corresponding linear control system is approximately controllable. Also, an example is presented to illustrate the applicability of the obtained theory.     

一类混杂动态系统的能控性(Ⅱ)——含单时滞的情形

首次将时滞现象引入到线性切换系统的模型中,研究含时滞的线性切换系统的能控性及其判定条件。全部工作由三部分组成。第Ⅱ部分,主要研究含单时滞的线性切换系统的能控性及其判定准则。首先给出周期型系统的单周期能控性和多周期能控性的定义和充要条件,其次给出非周期系统的能控性的定义和充要条件。     

The controllability problem for nonlinear Volterra systems

We discuss the controllability of systems whose dynamics are governed by a large class of nonlinear Volterra integral equations. The property of controllability is shown to be equivalent to the existence of a fixed point of a certain set-valued map. We show that convexity and seminormality conditions intimately related to those assumed in proofs of existence theorems for optimal controls are sufficient to guarantee controllability. Approximate controllability results are obtained by first introducing generalized solutions and then showing, under only mild additional restrictions, that ordinary solutions are dense in this broader class of trajectories.Dedicated to L. CesariTu se' lo mio maestro e il mio autore: Tu se' solo colui, da cui io tolsi Lo bello stile che m' ha fatto onore. Dante, Canto I: 85–87This work was written while the author was on leave to the Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Göttingen, West Germany.     

Controllability of nonlinear fractional order integrodifferential system with input delay

This paper addressed the controllability of nonlinear fractional order integrodifferential systems with input delay. Firstly, the Caputo fractional derivatives and the Mittag‐Leffler functions are employed. Thereafter, we establish a set of sufficient and necessary conditions for the controllability of the linear fractional system. Furtherly, controllability conditions of the nonlinear integrodifferential fractional order system with input delay are acquired by utilizing Arzela‐Ascoli theorem and Schauder's fixed‐point theorem. Finally, an example is presented to demonstrate our main results.     

Relative approximate controllability of abstract functional systems with infinite delay and delayed control

This paper is concerned with the relative approximate controllability of functional systems with infinite delay and delayed control in Hilbert spaces. In particular, we begin with studying some criteria of the controllability of linear systems. Based on those results, sufficient conditions are derived for the relative approximate controllability of nonlinear functional systems. Finally, an example is included to illustrate the effectiveness of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.     

一类混杂动态系统的能控性(Ⅲ)——含多时滞的情形

首次将时滞现象引入到线性切换系统的模型中,研究含有时滞线性切换系统的能控性及其判定条件。全部工作由三部分组成。第Ⅲ部分,主要研究含多时滞的线性切换系统的能控性及其判定规则。首先给出周期型系统的单周能控性和多周期能控性的定义和充要条件,其次给出非周期系统的能控性的定义和充要条件。最后,研究时滞大小不一致的情形,指出能控性与时滞大小无关。     

Exact Controllability for a Class of Nonlinear Evolution Control Systems

In this paper, we study the exact controllability of the nonlinear control systems. The controllability results by using the monotone operator theory are es-tablished. No compactness assumptions are im...     

One-sided exact boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws

In this paper, the one-sided exact boundary null controllability of entropy solutions is studied for a class of general strictly hyperbolic systems of conservation laws, whose negative (or positive) characteristic families are all linearly degenerate. The authors first prove the well-posedness of semi-global solutions constructed as the limit of ε-approximate front tracking solutions to the mixed initial-boundary value problem with general nonlinear boundary conditions and they establish various properties of both the ε-approximate front tracking solutions and such solutions. By means of essential modifications of the strategy suggested by the first author in [17] originally for the local exact boundary controllability in the framework of classical solutions, the one-sided local exact boundary null controllability of entropy solutions can then be realized via boundary controls acting on one side of the boundary, where the incoming characteristics are all linearly degenerate.     

On Russell's method of controllability via stabilizability

Russell has observed that a linear system is controllable provided it is stabilizable in both positive and negative time. We give a version of this result valid for nonlinear systems, and illustrate its use by giving new proofs of two classical results from control theory, the first involving bounded perturbations of controllable linear systems, and the second involving controllability of linear systems by bounded controls.This research was supported by the Natural Sciences and Engineering Research Council of Canada.     

Relative controllability of fractional dynamical systems with delays in control

This paper is concerned with the controllability of nonlinear fractional dynamical systems with time varying multiple delays and distributed delays in control defined in finite dimensional spaces. Sufficient conditions for controllability results are obtained using the Schauder fixed point theorem and the controllability Grammian matrix which is defined by Mittag–Leffler matrix function. Examples are provided to illustrate the theory.