Controllability of nonlinear systems consisting of a bilinear mode with time-varying delays in control

Sufficient conditions are established for the global relative controllability of nonlinear system consisting of a bilinear mode with time-varying delays in control. The results are a generalization of previous results and are obtained by using Schauder's fixed point theorem.     

Controllability of stochastic systems with distributed delays in control

In this article, we are concerned with the problem of relative controllability for non-linear stochastic systems with distributed delays in control in finite-dimensional spaces. Sufficient criteria for the relative controllability of the non-linear stochastic system are established. Some special cases are also considered. The results are obtained by using the Banach fixed point theorem. An example is provided to illustrate the technique.     

Controllability of fractional dynamical systems with distributed delays in control using ψ-Caputo fractional derivative

This research investigates the controllability of linear and non-linear fractional dynamical systems with distributed delays in control using the $\psi$-Caputo fractional derivative. For controllability of linear systems, the positive definiteness of Grammian matrix, which is characterized by Mittag–Leffler functions, is used to provide necessary and sufficient conditions. For the controllability of non-linear systems, the iterative technique with the completeness of $X$ is used to obtain sufficient conditions. Using the $\psi$-Caputo fractional derivative, this study is new since it investigates the ideas of controllability. A couple of numerical results are offered to explain the theoretical results.     

Controllability of linear systems with multiple delays in control

The controllability of linear systems with multiple time delays in the control function is investigated.     

滑模控制一类非线性分布式时滞系统

针对一类状态不可测的非线性不确定分布式时滞系统, 给出了系统滑动模态鲁棒渐近稳定的充分条件. 设计了一类滑模观测器, 同时采用线性矩阵不等式的处理方法给出了该观测器存在的充分条件. 再应用滑模控制的趋近率方法和基于观测器所得到的估计状态, 综合了一类滑模控制器. 该控制器同时保证了估计状态下的滑模面和估计误差状态下的滑模面的渐近可达性.     

Controllability of nonlinear systems with delay in control

Sufficient conditions for global relative controllability of certain types of nonlinear time-varying systems with time-variable delay in control are given. The results are obtained by using Schauder's fixed-point theorem. The results obtained are a generalization of Davison [3].     

Optimal control of distributed bilinear systems

The optimal control problem for a bilinear distributed parameter system subject to a quadratic cost functional is solved. It is shown that the optimal control is given by a convergent power series in the state with tensor coefficients.     

Controllability of fractional-order damped systems with time-varying delays in control

Frontiers of Information Technology & Electronic Engineering - In this study, we focus on the controllability of fractional-order damped systems in linear and nonlinear cases with multiple...     

Controllability of switched bilinear systems

The controllability of switched bilinear systems (SBLSs) is considered. Three kinds of controllabilities, including weak controllability, approximate controllability, and global controllability, are investigated one by one. Sets of easily verifiable sufficient conditions are obtained for each case, which are applicable to a large class of switched bilinear systems.     

Controllability results for nonlinear impulsive integrodifferential evolution systems with time-varying delays

In this paper, we study the controllability results for the nonlinear impulsive integrodifferential evolution systems with time-varying delays in Banach spaces. The sufficient conditions of exact controllability is proved under without assuming the compactness of the evolution operator. The results are obtained by using the semigroup theory and the Schafer fixed point theorem.     

Controllability of nonlinear stochastic control systems

In the paper sufficient conditions for ‘deterministic weak controllability’ of nonlinear Itô equations of the form are given.     

Variable structure sliding mode control for a class of uncertain distributed parameter systems with time-varying delays

This article considers sliding mode control of a class of parabolic linear uncertain distributed parameter systems with time-varying delays. The sliding mode controller design does not contain time delay terms and drives the state trajectory of the system to the sliding manifold in finite time. A sufficient condition of asymptotic stability for the sliding motion is derived. A simulation example is presented to illustrate effectiveness of the proposed method.     

A note on control of a class of discrete-time stochastic systems with distributed delays and nonlinear disturbances

This paper is concerned with the state feedback control problem for a class of discrete-time stochastic systems involving sector nonlinearities and mixed time-delays. The mixed time-delays comprise both discrete and distributed delays, and the sector nonlinearities appear in the system states and all delayed states. The distributed time-delays in the discrete-time domain are first defined and then a special matrix inequality is developed to handle the distributed time-delays within an algebraic framework. An effective linear matrix inequality (LMI) approach is proposed to design the state feedback controllers such that, for all admissible nonlinearities and time-delays, the overall closed-loop system is asymptotically stable in the mean square sense. Sufficient conditions are established for the nonlinear stochastic time-delay systems to be asymptotically stable in the mean square sense, and then the explicit expression of the desired controller gains is derived. A numerical example is provided to show the usefulness and effectiveness of the proposed design method.     

Sliding mode control for a class of nonlinear discrete-time networked systems with multiple stochastic communication delays

In this article, a sliding mode control problem is studied for a class of uncertain nonlinear networked systems with multiple communication delays. A sequence of stochastic variables obeying Bernoulli distribution is applied in the system model to describe the randomly occurring communication delays. The discrete-time system considered is also subject to parameter uncertainties and state-dependent stochastic disturbances. A novel discrete switching function is proposed to facilitate the sliding mode controller design. The sufficient conditions are derived by means of the linear matrix inequality (LMI) approach. It is shown that the system dynamics in the specified sliding surface is robustly exponentially stable in the mean square if two LMIs with an equality constraint are feasible. A discrete-time SMC controller is designed that is capable of guaranteeing the discrete-time sliding-mode reaching condition of the specified sliding surface. Finally, a simulation example is given to show the effectiveness of the proposed method.     

Relative controllability of nonlinear systems with delays in control

Relative controllability of nonlinear time-varying systems with time-variable delays in control is considered. Using Schauder's fixed point theorem, sufficient conditions for global relative controllability are given. The results obtained are a generalization of Davison [3], and Klamka [7].     

Optimum control of distributed parameter systems with time delays

This paper discusses the optimum control of distributed parameter systems with time delays which are governed by a set of partial differential-difference equations. The technique of dynamic programming is used to derive the functional equations associated with optimization. Specific results are derived for linear systems with quadratic performance index. Also, an explicit condition for the complete null controllability of linear systems is given. The paper concludes with a discussion on the approximate solutions for the minimum energy control of a simple linear parabolic system with a time delay.     

Euclidean null-controllability of linear systems with distributed delays in control

J. Klamka derives a necessary and sufficient condition for the relative controllability of linear systems with distributed delays in control. In this paper the author discusses the Euclidean null-controllability of system described by the equationdot{x}(t) = A(t)x(t) + intliminf{-h}limsup{0} dH(t,s)u(t+s)satisfied almost everywhere on [t_{0},infty). If the systemdot{x}(t)=A(t)x(t)is uniformly asymptotically stable and the controlled systemdot{x}(t) = A(t)x(t) + intliminf{-h}limsup{0} dH(t,s)u(t+s)is proper then the system is null-controllable.     

Controllability of linear time-varying systems with delays

The necessary and sufficient condition for the controllability of linear time-varying systems with delays in both the control and the state is obtained.     

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.