Complete controllability of impulsive stochastic integro-differential systems

This paper is concerned with the controllability of impulsive stochastic integro-differential systems. Sufficient conditions of complete controllability for impulsive stochastic integro-differential systems are obtained by using Schaefer’s fixed point theorem. A numerical example is provided to show the effectiveness of the proposed results.     

Necessary and sufficient conditions for quadratic controllability of a class of uncertain systems

We introduce a controllability notion for uncertain systems, namely, quadratic controllability. For a specific class of norm bounded uncertain systems, we show that this notion is equivalent to controllability of a nominal system and the satisfaction of a certain structural condition by the uncertainty. For systems in which the uncertain parameters affect all control inputs, this structural condition is simply the familiar matching condition commonly encountered in the literature on robust and adaptive control of uncertain systems.     

Approximate controllability of abstract stochastic impulsive systems with multiple time‐varying delays

This paper investigates the approximate controllability of abstract stochastic impulsive systems with multiple time‐varying delays. The class of stochastic impulsive systems consists of ordinary differential equations effected by impulse and noise environment. We focus first on constructing the control function. With this control function, we present sufficient conditions for approximate controllability problems in Hilbert space. The results are then extended to more easily verified conditions. The methods we choose are mainly Nussbaum fixed point theorem and stochastic analysis techniques combined with a strongly continuous semigroup. Finally, an example is given to illustrate the effectiveness of the results. Copyright © 2012 John Wiley & Sons, Ltd.     

Sample controllability of impulsive differential systems with random coefficients

In this paper, we investigate the controllability of impulsive differential systems with random coefficients. Impulsive differential systems with random coefficients are a different stochastic model from stochastic differential equations. Sufficient conditions of sample controllability for impulsive differential systems with random coefficients are obtained by using random Sadovskii's fixed-point theorem. Finally, an example is given to illustrate our results.     

A notion of possible controllability for uncertain linear systems with structured uncertainty

This paper introduces a notion of possible controllability for a class of uncertain linear systems with structured uncertainty described by averaged integral quadratic constraints. This notion relates to the question of when a state is controllable for some possible value of the uncertainty. The notion of possible controllability is motivated by a desire to extend the theory of minimal realization for linear time invariant systems to the case of uncertain systems with structured uncertainty.     

Controllability of linear stochastic systems

We discuss several concepts of controllability for stochastic systems and derive sufficient (and in most cases also necessary) algebraic conditions for the controllability of the state and the output of white and colored noise linear systems. These criteria reduce to the well known deterministic ones in the absence of noise.     

Stochastic controllability of linear systems with Markovian jumps

The notion of stochastic controllability for linear systems subject to Markovian jumps in parameter values is studied. An algebraic necessary and sufficient condition is obtained in terms of an easily computable rank test.     

Robust exponential stability of uncertain stochastic systems with probabilistic time‐varying delays

This paper is concerned with the problem of delay‐distribution–dependent robust exponential stability for uncertain stochastic systems with probabilistic time‐varying delays. Firstly, inspired by a class of networked systems with quantization and packet losses, we study the stabilization problem for a class of network‐based uncertain stochastic systems with probabilistic time‐varying delays. Secondly, an equivalent model of the resulting closed‐loop network‐based uncertain stochastic system is constructed. Different from the previous works, the proposed equivalent system model enables the controller design of the network‐based uncertain stochastic systems to enjoy the advantage of probability distribution characteristic of packet losses. Thirdly, by applying the Lyapunov‐Krasovskii functional approach and the stochastic stability theory, delay‐distribution–dependent robust exponential mean‐square stability criteria are derived, and the sufficient conditions for the design of the delay‐distribution–dependent controller are then proposed to guarantee the stability of the resulting system. Finally, a case study is given to show the effectiveness of the results derived. Moreover, the allowable upper bound of consecutive packet losses will be larger in the case that the probability distribution characteristic of packet losses is taken into consideration.     

Controllability of impulsive mixed type Volterra–Fredholm stochastic systems with nonlocal conditions

This paper investigates complete controllability of impulsive mixed type Volterra–Fredholm stochastic systems with nonlocal conditions. Sufficient conditions are established for complete controllability of a class of impulsive stochastic integrodifferential systems with nonlocal conditions. The results are obtained by a fixed point approach on condition that the corresponding linear system is completely controllable. Finally, an example is given to illustrate our results. Copyright © 2014 John Wiley & Sons, Ltd.     

Approximate controllability of stochastic delay differential systems driven by Poisson jumps with instantaneous and noninstantaneous impulses

Control systems in which instantaneous and noninstantaneous impulses occur simultaneously are difficult to handle. In this article, we investigate the solvability and approximate controllability for a new category of stochastic differential equations steered by Poisson jumps with instantaneous and noninstantaneous impulses. Utilizing the theory of fundamental solution, stochastic analysis, the measure of noncompactness, and the fixed-point approach, we establish the presence of a mild solution for the proposed system. We have also constructed a new set of sufficient constraints that assures approximate controllability of the considered system. Next, we discuss the existence of a solution and approximate controllability for an impulsive deterministic control system in which the nonlinear term contains spatial derivatives. Lastly, two examples are presented to encapsulate the abstract results.     

基于模型参考和内模原理的线性系统鲁棒控制设计

不确定性因素会使系统性能恶化,它包括系统不确定性参数和各种外部干扰等.本文针对这种不确定性线性系统,利用模型参考和内模原理,建立鲁棒控制系统结构,分析了其能控性条件,通过选择参考模型和内模实现系统能控,在此条件下,将鲁棒控制设计转换为控制系统的LQR问题进行研究,并运用最优控制理论,计算其反馈控制律.仿真结果表明该设计方法将"模型参考"与"内模原理"有机结合起来,提高了系统的鲁棒稳定性,有效抑制干扰,并实现系统性能的改善.     

Controllability of Stochastic Delay Systems with Impulse in a Separable Hilbert Space

In this paper, we study the controllability of a kind of nonlinear stochastic impulsive system with infinite delay in abstract space. Sufficient conditions for the controllability are obtained via the generalization of the contraction mapping principle and with none of the compactness condition restriction on the evolution family of operators for the system. Finally, a numerical example is given to illustrate the effectiveness of our results.     

Controllability of linear stochastic systems

We discuss several concepts of controllability for partially observable stochastic systems: complete controllability, approximate controllability, and stochastic controllability. We show that complete and approximate controllability notions are equivalent, and in turn they are equivalent to the stochastic controllability for linear stochastic systems controlled with Gaussian processes. We derive necessary and sufficient conditions for these concepts of controllability. These criteria reduce to the well-known rank condition     

Theoretical developments in discrete-time control

Significant theoretical developments in discrete-time control over the past 10–15 years are reviewed. Topics reviewed include optimal control, Riccati equations, controllability, stability, robustness, deadbeat control, minimum-time systems, sampling, quantization, microprocessor implementation, and stochastic systems. Emphasis is placed on topics that are peculiar to discrete-time systems and do not generalize from continuous-time theory.     

On the quasi-balanceable class of linear quantum stochastic systems

This paper is concerned with the characterization of the quasi-balanceable class of linear quantum stochastic systems (i.e., systems that can be approximated via the recently proposed quasi-balanced truncation method). It has previously been shown that the quasi-balanceable class of systems includes the class of completely passive systems. In this work, we refine the previously established characterization of quasi-balanceable systems and show that the class of quasi-balanceable systems is strictly larger than the class of completely passive systems. We derive a novel characterization of completely passive linear quantum stochastic systems solely in terms of the controllability Gramian of such systems. Exploiting this result, we prove that all linear quantum stochastic systems with a pure Gaussian steady state (active systems included) are all quasi-balanceable, and establish a new complete parameterization for this important class of systems. Examples are provided to illustrate our results.     

Controllability of non-linear impulsive stochastic systems

In this article, we consider the finite-dimensional dynamical control systems described by non-linear impulsive stochastic differential equations. Sufficient conditions for the complete and approximate controllability of non-linear impulsive stochastic systems are formulated and proved under the natural assumption that the corresponding linear system is appropriately controllable.     

具有非线性滞后关联的随机大系统的分散镇定

本文通过利用李雅普诺夫函数和李雅普诺夫矩阵方程的性质，对具有非线性滞后关联的一类随机大系统建立了分散鲁棒镇定的判据，所得闭环随机大系统的和稳定性不依赖于任意实数滞后，并对不确定系数矩阵和随机扰动强度具有鲁棒性。     

A new recursive identification algorithm for singularity free adaptive control

Reportedly, guaranteeing the controllability of the estimated system is a crucial problem in adaptive control. In this paper, we introduce a least-squares-based identification algorithm for stochastic SISO systems, which secures the uniform controllability of the estimated system and presents closed-loop identification properties similar to those of the least-squares algorithm. The proposed algorithm is recursive and, therefore, easily implementable. Its use, however, is confined to cases in which the parameter uncertainly is highly structured.     

On stochastic controllability for nonlinear systems

Both the stochastic ε-controllability and the stochastic controllability with probability one are first defined. Second, by using a stochastic Lyapunov-like approach, several theorems are developed which give sufficient conditions for the stochastic controllability defined for an important class of nonlinear stochastic systems. A theorem of stochastic uncontrollability is also presented, giving sufficient conditions for stochastic uncontrollability for a class of nonlinear systems. Finally, the relation between the deterministic controllability and the stochastic one is comparatively discussed.