Controllability of nonlinear stochastic control systems

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

Robust controllability of linear stochastic uncertain systems

The paper extends the concept of robust controllability via linear state feedback to stochastic uncertain systems. We show that the controllability of a stochastic uncertain system can be characterized using solutions to a game-type differential Riccati equation.     

H Optimal control for linear stochastic systems

The aim of the present paper is to provide an optimal solution to the H² state-feedback and output-feedback control problems for stochastic linear systems subjected both to Markov jumps and to multiplicative white noise. It is proved that in the state-feedback case the optimal solution is a static gain which is also optimal in the class of all higher-order controllers. In the output-feedback case the optimal H² controller has the same order as the given stochastic system. The realization of the optimal controllers depend on the stabilizing solutions of some appropriate systems of Riccati-type coupled equations. An effective iterative convergent algorithm to compute these stabilizing solutions is also presented. The paper gives some illustrative numerical example allowing to compare the results obtained by the proposed design approach with the ones presented in the recent control literature.     

Controllability of linear systems in Banach spaces

The problem of controllability of linear systems in Banach spaces is considered. First, some properties of dual semigroups with respect to Lebesgue measure is presented. Then, based on the properties, the criteria for controllability in reflexive Banach spaces are extended to general Banach spaces and some new criteria for controllability are established. An example is presented to show that the scope of controllable systems can be enlarged if the non-traditional space of control functions is used.     

A stability and contractiveness analysis of discrete-time Markovian jump linear systems

We propose performance criteria for discrete-time linear systems with Markov jumping parameters. Exact convex conditions for internal stability and contractiveness of such systems are expressed in terms of linear matrix inequalities. These conditions are of the same form as that in the Kalman-Yacubovich-Popov lemma.     

Control configuration selection for linear stochastic systems

An appropriate control configuration selection is identified as one of the key prerequisites for attaining the control objectives in industrial practices. To select a suitable control configuration, it is important to determine which variables should be measured and how the process should be actuated. Therefore, the first step is to determine the optimal locations for the sensors and actuators. For the multivariable processes, this step is followed by choosing the appropriate input and output pairs for the design of SISO (or block) controllers. This is due to the popularity of the distributed and decentralized control in industrial control systems. These issues, which have been studied extensively for deterministic systems, have not been closely studied for stochastic systems. In this paper however the problem of control configuration selection is studied for the linear stochastic systems. The problem of selecting the sensor locations for stochastic systems is viewed as the problem of maximizing the output energy generated by a given state and for the actuator locations is viewed as the problem of minimizing the input energy required to reach a given state. Furthermore, a gramian-based interaction measure for control structure selection of multivariable stochastic systems is proposed. This interaction measure can be used to propose a richer (sparse or block diagonal) controller structure for distributed and partially decentralized control.     

Sliding mode control of singular stochastic hybrid systems

This paper is concerned with the sliding mode control (SMC) of nonlinear singular stochastic systems with Markovian switching. An integral sliding surface function is designed, and the resulting sliding mode dynamics is a full-order Markovian jump singular stochastic system. By introducing some specified matrices, a new sufficient condition is proposed in terms of strict linear matrix inequality (LMI), which guarantees the stochastic stability of the sliding mode dynamics. Then, a SMC law is synthesized for reaching motion. Moreover, when there exists an external disturbance, the ?₂ disturbance attenuation performance is analyzed for the sliding mode dynamics. Some related sufficient conditions are also established.     

Controllability and reachability criteria for switched linear systems

This paper investigates the controllability and reachability of switched linear control systems. It is proven that both the controllable and reachable sets are subspaces of the total space. Complete geometric characterization for both sets is presented. The switching control design problem is also addressed.     

Optimal ensemble control of stochastic time-varying linear systems

We consider the optimal guidance of an ensemble of independent, structurally identical, finite-dimensional stochastic linear systems with variation in system parameters between initial and target states of interest by applying a common control function without the use of feedback. Our exploration of such ensemble control systems is motivated by practical control design problems in which variation in system parameters and stochastic effects must be compensated for when state feedback is unavailable, such as in pulse design for nuclear magnetic resonance spectroscopy and imaging. In this paper, we extend the notion of ensemble control to stochastic linear systems with additive noise and jumps, which we model using white Gaussian noise and Poisson counters, respectively, and investigate the optimal steering problem. In our main result, we prove that the minimum norm solution to a Fredholm integral equation of the first kind provides the optimal control that simultaneously minimizes the mean square error (MSE) and the error in the mean of the terminal state. The optimal controls are generated numerically for several example ensemble control problems, and Monte Carlo simulations are used to illustrate their performance. This work has immediate applications to the control of dynamical systems with parameter dispersion or uncertainty that are subject to additive noise, which are of interest in quantum control, neuroscience, and sensorless robotic manipulation.     

Transition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems

This paper considers the robustness of stochastic stability of Markovian jump linear systems in continuous- and discrete-time with respect to their transition rates and probabilities, respectively. The continuous-time (discrete-time) system is described via a continuous-valued state vector and a discrete-valued mode which varies according to a Markov process (chain). By using stochastic Lyapunov function approach and Kronecker product transformation techniques, sufficient conditions are obtained for the robust stochastic stability of the underlying systems, which are in terms of upper bounds on the perturbed transition rates and probabilities. Analytical expressions are derived for scalar systems, which are straightforward to use. Numerical examples are presented to show the potential of the proposed techniques.     

Controllability of second-order infinite-dimensional systems

In the paper, the approximate controllability of linear abstract second-order infinite-dimensional dynamical systems is considered. It is proved using the frequency-domain method, that approximate controllability of second-order system can be verified by the approximate controllability conditions for the corresponding simplified first-order system. General results are then applied for approximate controllability investigation of a vibratory dynamical system modeling flexible mechanical structure. Some special cases are also considered. Moreover, remarks and comments on the relationships between different concepts of controllability are given. The paper extends earlier results on approximate controllability of second-order abstract dynamical systems.     

On the linear-quadratic regulator problem in one-dimensional linear fractional stochastic systems

In this paper, for one-dimensional stochastic linear fractional systems in terms of the Riemann–Liouville fractional derivative, the optimal control is derived. It is assumed that the state is completely observable and all the information regarding this is available. The formulation leads to a set of stochastic fractional forward and backward equation in the Riemann–Liouville sense. The proposed method has been checked via some numerical simulations which show the effectiveness of the fractional stochastic optimal algorithm.     

Risk sensitive identification of linear stochastic systems

Risk-sensitive identification of AR-processes was first considered in [12]. The purpose of this paper is to extend this original approach to ARMA-processes and even to multi-variable linear stochastic systems. We provide a new definition of a risk-sensitive identification criterion. For this we first consider a recursive identification procedure which is parameterized by a weight-matrix K acting on the stochastic gradient. Using the asymptotic theory of recursive estimation a suitably scaled version of the error process will be approximated by a stationary Gaussian process, see Chapter 4.5, Part II of [1]. The new risk sensitive criterion will be defined in terms of this associated stationary Gaussian process in a familiar manner via an exponential-quadratic cost. The main result of the paper is the minimization of the proposed new criterion with respect to the weight-matrix K over a feasible set E_K, see (22), where the cost function is known to be finite, Theorem 6.1. This results will then be extended to the case when minimization over a feasible set E°_K is considered, see (26), on the complement of which the cost function is known to be infinite, Theorem 6.1. The starting point of our analysis is an expression of the cost function given in LEQG-theory, in particular a result of [10]. A new expression for the cost function will be also given, using stochastic realization theory, as the mutual information rate between two stochastic processes.This research was supported in part by grants from the Swedish Research Council for Engineering Sciences (TFR), the Göran Gustafsson Foundation, the National Research Foundation of Hungary (OTKA) under Grants T015668, T16665, T020984 and T032932.     

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     

仿射非线性系统的能控性

研究仿射非线性系统的能控性问题.利用向量场族对应的积分曲线定义系统的能控性,建立一个新的基于漂移向量场弱泊松稳定的能控性判据,并给出了完整的证明.利用该结论对定义在紧致黎曼流形上的解析系统,给出了漂移向量场为保守场条件下的能控性的充要条件,并用状态流形的紧致性证明了弱泊松稳定性的几个等价条件.进一步利用保守系统的判据给出了一般仿射非线性系统能控的充分条件,井应用所得结论分析了欠驱动航天器姿态系统的能控性.     

Necessary conditions for positive realizability of continuous-time linear systems

This paper deals with the positive realization problem. The problem is to find, from a given transfer function, a state equation in which state variables and the output take nonnegative values whenever initial states and inputs are nonnegative. Necessary conditions are investigated and a new one is given, together with some related results.     

On detectability of stochastic systems

We discuss notions of detectability for stochastic linear control systems of Itô type. A natural concept of detectability requires a non-zero output, if the state process is unstable. We show that this property can equivalently be characterized by a generalized version of the Hautus-test. The proof is based on spectral theory for positive operators.     

Global controllability of linear autonomous systems: A geometric consideration

The global controllability in finite time of a linear autonomous system with restrained controls is investigated. Necessary and sufficient conditions are obtained by an approach based on the consideration of geometric properties of the system.     

Delay-dependent robust stability of stochastic delay systems with Markovian switching

In recent years, the stability of hybrid stochastic delay systems, one of the important issues in the study of stochastic systems, has received considerable attention. However, the existing results do not deal with the structure of the diffusion but estimate its upper bound, which induces conservatism. This paper studies delay-dependent robust stability of hybrid stochastic delay systems. A delay-dependent criterion for robust exponential stability of hybrid stochastic delay systems is presented in terms of linear matrix inequalities （LMIs）, which exploits the structure of the diffusion. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method.