Controllability and Observability of Stochastic Singular Systems in Banach Spaces

Exact(approximate)controllability and exact(approximate)observability of stochastic singular systems in Banach spaces are discussed.Firstly,the condition for the existence and uniqueness of the mild solution to stochastic singular systems is given by GE-semigroup in Banach spaces.Secondly,the necessary and sufficient conditions for the exact(approximate)controllability and exact(approximate)observability of the systems considered are derived in terms of GE-semigroup,and the dual principle is given.Thirdly,an illustrative example is given.

Impulse Controllability and Impulse Observability of Stochastic Singular Systems

This paper discusses the impulse controllability and impulse observability of stochastic singular systems.Firstly,the condition for the existence and uniqueness of the impulse solution to stochastic singular systems is given by Laplace transform.Secondly,the necessary and sufficient conditions for the impulse controllability and impulse observability of systems considered are derived in terms of matrix theory.Finally,an example is given to illustrate the effectiveness of the obtained theoretical results.

State Estimation of Discrete Stochastic Singular System

In this paper, a state estimation problem in discrete\|time stochastic singular systems is investigated. It has been proved that the optimal state estimation problem of a discrete\|time stochastic singular system is equivalent to the optimal control problem of a deterministic singular system.

Robust H-infinity filter design for uncertaintime-delay singular stochastic systems withMarkovian jump

This paper deals with the problem of H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump. Based on the extended It6 stochastic differential formula, sufficient conditions for the solvability of these problems are obtained. Furthermore, It is shown that a desired filter can be constructed by solving a set of linear matrix inequalities. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method.

Time evolution of information entropy for a stochastic system with double singularities driven by quasimonochromatic noise

This paper deals with the time evolution of information entropy for a stochastic system with double singularities driven by quasimonochromatic noise. The dimension of the Fokker Planck equation is reduced by the linear transfor- mation. The exact expression of the time dependence of information entropy is obtained based on the definition of Shannon＇s information entropy. The relationships between the properties of dissipative parameters, system singularity strength parameter, quasimonochromatic noise, and their effects on information entropy are discussed.

Upper bound for the time derivative of entropy for a stochastic dynamical system with double singularities driven by non-Gaussian noise

A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transformation. Based on the definition of Shannon＇s information entropy and the Schwartz inequality principle, the upper bound for the time derivative of entropy is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculations can be used to interpret the effects of the system dissipative parameter, the system singularity strength parameter, the noise correlation time and the noise deviation parameter on the upper bound.

Receding Horizon Control-Based Stabilization of Singular Stochastic Systems with State Delay

For a class of discrete-time singular stochastic systems with multi-state delay,the stabilization problem of receding horizon control(RHC)is concerned.Due to the difficulty in solving the proposed optimization problem,the RHC stabilization for such systems has not been solved.By adopting the forward and backward equation technique,the optimization problem is solved completely.A sufficient and necessary condition for the optimization controller to have a unique solution is given when the regularization and pulse-free conditions are satisfied.Based on this controller,an RHC stabilization condition is derived,which is in the form of linear matrix inequality.It is proved that the singular stochastic system with multi-state delay is stable in the mean-square sense under appropriate assumptions when the terminal weighting matrix satisfies the given inequality.Numerical examples show that the proposed RHC method is effective in stabilizing singular stochastic systems with multi-state delay.

A CLASS OF STATIONARY MODELS OF SINGULAR STOCHASTIC CONTROL

A class of stationary models of singular stochastic control has been studied, in which the state is extended to solution of a class of S.D.E. from Wiener process. The existence of optimal control has been proved in all cases under some weaker conditions, and the structure of optimal control may be characterized.

Observer-Based Controller Design for Singular Stochastic Markov Jump Systems with State Dependent Noise

This paper is concerned with the problem of observer-based controller design for singular stochastic Markov jump systems with state-dependent noise. Two concepts called "non-impulsiveness"and "mean square admissibility" are introduced, which are different from previous ones. Sufficient conditions for the open-and closed-loop singular stochastic Markov jump systems with state-dependent noise to be mean square admissible are provided in terms of strict LMIs. The controller gain and the observer gain which guarantee the resulting closed-loop error system to be mean square admissible are obtained in turn by solving the strict LMIs. A numerical example is presented to show the efficiency of the design approach.

A New Method of State Estimation for Singular Discrete-time Stochastic Linear System

Using theory of Bayesian Dynamic Models and Forecasting , this paper mainly deals with the problem on state estimation for singular discrete time stochastic linear system. And a new method of state estimation linear Bayes estimation (LBE for short) has been proposed.

A New Approach to Optimal Filtering for SingularDiscrete-Time Stochastic Linear System

Based on the theory of Bayes forecasting, this paper mainly deals with the problem onthe state estimation for singular discrete-time stochastic linear system. And a new approach to optimalfiltering-linear Bayes estimation (LBE) has been proposed.

ON SUFFICIENT AND NECESSARY OF EXISTENCE FOR A CLASS OF SINGULAR OPTIMAL STOCHASTIC CONTROL

We study a class of discounted models of singular stochastic control. In thiskind of models, not only the structure of cost function has been extended to some general type, butalso the state can be represented as the solution of a class of stochastic differential equationswith nonlinear drift and diffusion term. By the various methods of stochastic analysis, we derivethe sufficient and necessary conditions of the existence of optimal control.

A Mean-Field Necessary and Sufficient Conditions for Optimal Singular Stochastic Control

This paper studies singular optimal control problems for systems described by nonlinear-controlled stochastic differential equations of mean-field type(MFSDEs in short),in which the coefficients depend on the state of the solution process as well as of its expected value.Moreover,the cost functional is also of mean-field type.The control variable has two components,the first being absolutely continuous and the second singular.We establish necessary as well as sufficient conditions for optimal singular stochastic control where the system evolves according to MFSDEs.These conditions of optimality differs from the classical one in the sense that here the adjoint equation turns out to be a linear mean-field backward stochastic differential equation.The proof of our result is based on convex perturbation method of a given optimal control.The control domain is assumed to be convex.A linear quadratic stochastic optimal control problem of mean-field type is discussed as an illustrated example.

Stochasticst ability and Hopf bifurcation analysis of a singular bio-economic model with stochastic fluctuations

In this paper,we study a class of singular stochastic bio-economic models described by differential-algebraic equations due to the influence of economic factors.Simplifying the model through a stochastic averaging method,we obtained a two-dimensional diffusion process of averaged amplitude and phase.Stochastic stability and Hopf bifurcations can be analytically determined based on the singular boundary theory of diffusion process,the Maximal Lyapunov exponent and the invariant measure theory.The critical value of the stochastic Hopf bifurcation parameter is obtained and the position of Hopf bifurcation drifting with the parameter increase is presented as a result.Practical example is presented to verify the effectiveness of the results.