Control Of Stochastic Systems Research Articles

Stochastic maximum principle for delayed backward doubly stochastic control systems

Stochastic maximum principle for delayed backward doubly stochastic control systems

Fault Detection and Diagnosis for Non-Gaussian Singular Stochastic Distribution Systems via Output PDFs

This paper investigates the problem of fault detection and diagnosis (FDD) problem for non-gausian singulat stochastic distribution control (SDC) systems via the output probability density functions(PDFs). The PDFs can be approximated by using square-root B-spline expansion,via this expansions to represent the dynamics weighting systems between the system input and the weights related to the output PDFs. In this works ,an optimal fault detection and diagnosis algorith is present by introducing the parameter-updating .when the fault occurs, an adaptive network parameter-updating law is designed to approximated the fault. Finally, the simulation result are given to show that the approach can detect faults and estimate the size of fault.

Optimal Control Problems of Forward-Backward Stochastic Volterra Integral Equations with Closed Control Regions

Optimal control problems of forward-backward stochastic Volterra integral equations (FBSVIEs, in short) with closed control regions are formulated and studied. Instead of using spike variation method as one may imagine, here we turn to treat the non-convexity of the control regions by borrowing some tools in set-valued analysis and adapting them into our stochastic control systems. A duality principle between linear backward stochastic Volterra integral equations and linear stochastic Fredholm-Volterra integral equations with conditional expectation are derived, which extends and improves the corresponding results in [25], [30]. Some first order necessary optimality conditions for optimal controls of FBSVIEs are established. In contrast with existed common routines to treat the non-convexity of stochastic control problems, here only one adjoint system and one-order differentiability requirements of the coefficients are needed.

Fault tolerant control for a class of nonlinear non-Gaussian singular stochastic distribution systems

New fault diagnosis and active fault tolerant control (FTC) algorithms are proposed for a class of nonlinear singular stochastic distribution control (SDC) systems in this paper. Different from general SDC systems, in singular SDC systems, the relationship between the weights and the control input is expressed by a singular state space model, which increases the difficulty in design of fault diagnosis and fault tolerant control. A non-singular state transformation is made to transform the singular dynamic system into a differential-algebraic system. An adaptive nonlinear observer is designed to estimate the size of the fault occurring in the system. Furthermore, the linear matrix inequality (LMI) approach is applied to establish sufficient conditions for the existence of the observer. Based on the estimated fault information, the active fault tolerant controller is designed to make the post-fault probability density function (PDF) still track the given distribution. At last, an illustrated example is given to demonstrate the effectiveness of the proposed algorithm, and satisfactory results have been obtained.

Fault tolerant control for a class of nonlinear non-Gaussian singular stochastic distribution systems

New fault diagnosis and active fault tolerant control (FTC) algorithms are proposed for a class of nonlinear singular stochastic distribution control (SDC) systems in this paper. Different from general SDC systems, in singular SDC systems, the relationship between the weights and the control input is expressed by a singular state space model, which increases the difficulty in design of fault diagnosis and fault tolerant control. A non-singular state transformation is made to transform the singular dynamic system into a differential-algebraic system. An adaptive nonlinear observer is designed to estimate the size of the fault occurring in the system. Furthermore, the linear matrix inequality (LMI) approach is applied to establish sufficient conditions for the existence of the observer. Based on the estimated fault information, the active fault tolerant controller is designed to make the post-fault probability density function (PDF) still track the given distribution. At last, an illustrated example is given to demonstrate the effectiveness of the proposed algorithm, and satisfactory results have been obtained.

Maximum Principle for Forward-Backward Control System Driven by Itô-Lévy Processes under Initial-Terminal Constraints

This paper investigates a stochastic optimal control problem where the control system is driven by Itô-Lévy process. We prove the necessary condition about existence of optimal control for stochastic system by using traditional variational technique under the assumption that control domain is convex. We require that forward-backward stochastic differential equations (FBSDE) be fully coupled, and the control variable is allowed to enter both diffusion and jump coefficient. Moreover, we also require that the initial-terminal state be constrained. Finally, as an application to finance, we show an example of recursive consumption utility optimization problem to illustrate the practicability of our result.

Optimal control of the two-state Markov process in discrete time

Using the control problem of a two-state Markov process in discrete time as an example, we consider the basic stages concerning the application of theory of conditional Markov processes to synthesize optimal algorithms of the control of stochastic systems. It is assumed that the control changes the statistical properties of the states of a controlled plant. The numerical method for solving the problem and the results of solving particular example are presented. The special features of the solution of this problem compared to the well-known problem in continuous time are discussed.

Linear Quadratic Stochastic Optimal Control of Forward Backward Stochastic Control System Associated with Lévy Process

This paper analyzes one kind of linear quadratic (LQ) stochastic control problem of forward backward stochastic control system associated with Lévy process. We obtain the explicit form of the optimal control, then prove it to be unique, and get the linear feedback regulator by introducing one kind of generalized Riccati equation. Finally, we discuss the solvability of the generalized Riccati equation, and its existence and uniqueness of the solutions are proved in a special case.

Approximate Controllability of Fractional Semilinear Stochastic System of Order α∈ (1,2

A family of dynamical control systems described by nonlinear fractional of order (1,2] stochastic differential equations in Lp spaces is considered. We discussed the approximate controllability of stochastic semilinear fractional control system of order α∈(1,2] under the assumption that the corresponding linear system is approximately controllable. A new set of sufficient conditions for approximate controllability of system are obtained by the theory of strongly continuous α-order cosine family, fixed point theorem, and stochastic analysis techniques. At the end, an example is given to illustrate the theory.

Approximate controllability of a second-order neutral stochastic differential equation with state dependent delay

In this paper, the existence and uniqueness of mild solution is initially obtained by use of measure of noncompactness and simple growth conditions. Then the conditions for approximate controllability are investigated for the distributed second-order neutral stochastic differential system with respect to the approximate controllability of the corresponding linear system in a Hilbert space. We construct controllability operators by using simple and fundamental assumptions on the system components. We use the lemma, which implies the approximate controllability of the associated linear system. This lemma is also described as a geometrical relation between the range of the operator B and the subspaces Ni⊥, i = 1, 2, 3, associated with sine and cosine operators in L2([0, a], X) and L2([0, a], LQ). Eventually, we show that the reachable set of the stochastic control system lies in the reachable set of its associated linear control system. An example is provided to illustrate the presented theory.

Towards scalable synthesis of stochastic control systems

Formal synthesis approaches over stochastic systems have received significant attention in the past few years, in view of their ability to provide provably correct controllers for complex logical specifications in an automated fashion. Examples of complex specifications include properties expressed as formulae in linear temporal logic (LTL) or as automata on infinite strings. A general methodology to synthesize controllers for such properties resorts to symbolic models of the given stochastic systems. Symbolic models are finite abstractions of the given concrete systems with the property that a controller designed on the abstraction can be refined (or implemented) into a controller on the original system. Although the recent development of techniques for the construction of symbolic models has been quite encouraging, the general goal of formal synthesis over stochastic control systems is by no means solved. A fundamental issue with the existing techniques is the known curse of dimensionality, which is due to the need to discretize state and input sets. Such discretization generally results in an exponential complexity over the number of state and input variables in the concrete system. In this work we propose a novel abstraction technique for incrementally stable stochastic control systems, which does not require state-space discretization but only input set discretization, and that can be potentially more efficient (and thus scalable) than existing approaches. We elucidate the effectiveness of the proposed approach by synthesizing a schedule for the coordination of two traffic lights under some safety and fairness requirements for a road traffic model. Further we argue that this 5-dimensional linear stochastic control system cannot be studied with existing approaches based on state-space discretization due to the very large number of generated discrete states.

Controllability of semilinear stochastic control system with finite delay

Controllability of semilinear stochastic control system with finite delay

S-Controllability of a partially observed semilinear integrodifferential stochastic control system

In this article, some sufficient conditions are given for the S-controllability of a partially observed semilinear integrodifferential stochastic control system. Here, we established the controllability result using the separation principle approach in which the given semilinear stochastic control system is splitted into two control systems, namely one is semilinear deterministic control system and another is linear stochastic control system. An example is given to illustrate the result.

Robust fault diagnosis and fault‐tolerant control for non‐Gaussian uncertain stochastic distribution control systems

SummaryThe purpose of fault diagnosis of stochastic distribution control systems is to use the measured input and the system output probability density function to obtain the fault estimation information. A fault diagnosis and sliding mode fault‐tolerant control algorithms are proposed for non‐Gaussian uncertain stochastic distribution control systems with probability density function approximation error. The unknown input caused by model uncertainty can be considered as an exogenous disturbance, and the augmented observation error dynamic system is constructed using the thought of unknown input observer. Stability analysis is performed for the observation error dynamic system, and the H∞ performance is guaranteed. Based on the information of fault estimation and the desired output probability density function, the sliding mode fault‐tolerant controller is designed to make the post‐fault output probability density function still track the desired distribution. This method avoids the difficulties of design of fault diagnosis observer caused by the uncertain input, and fault diagnosis and fault‐tolerant control are integrated. Two different illustrated examples are given to demonstrate the effectiveness of the proposed algorithm. Copyright © 2016 John Wiley & Sons, Ltd.

Dynamic Data Reconciliation for Enhancing Performance of Minimum Variance Control in Univariate and Multivariate Systems

Healthy controllers are required in order for the control systems to maintain a high level of performance. In past research, minimum variance control (MVC) played a crucial role as a benchmark in performance monitoring because of the attractive theoretical and computational properties associated with it. Since the influence of measurement errors has not been explicitly considered in the MVC theory in stochastic control systems, this paper first analyzes the influence of measurement errors on the control performance of MVC in both univariate and multivariate systems. And then the dynamic data reconciliation (DDR) methods are proposed and combined in the procedure of MVC/multivariate MVC (MMVC) to decrease the influence of measurement errors and to enhance the control performance. Considering both random measurement errors and gross errors, the effectiveness of MVC/MMVC combined with DDR on the variances of process outputs is illustrated by two simulated cases, including both univariate and multivariate sys...

Fault Diagnosis and Sliding Mode Fault Tolerant Control for Non‐Gaussian Stochastic Distribution Control Systems Using T‐s Fuzzy Model

AbstractFor the non‐Gaussian stochastic distribution control system using Takagi‐Sugeno fuzzy model, a new fault diagnosis and sliding mode fault tolerant control algorithm is presented. First, a new adaptive fault diagnosis algorithm is adopted to diagnose the fault that occurred in the system, and the observation error system is proven to be uniformly bounded. Second, the sliding mode control algorithm is used to reconfigure the controller, based on the fault estimation information. The post‐fault probability density function can still track the given distribution, leading to fault tolerant control of non‐Gaussian stochastic distribution control systems using Takagi‐Sugeno fuzzy model. Finally, simulation results show the effectiveness of the proposed method.

When Backpressure Meets Predictive Scheduling

Motivated by the increasing popularity of learning and predicting human user behavior in communication and computing systems, in this paper, we investigate the fundamental benefit of predictive scheduling, i.e., predicting and pre-serving arrivals, in controlled queueing systems. Based on a lookahead window prediction model, we first establish a novel equivalence between the predictive queueing system with a \emph{fully-efficient} scheduling scheme and an equivalent queueing system without prediction. This connection allows us to analytically demonstrate that predictive scheduling necessarily improves system delay performance and can drive it to zero with increasing prediction power. We then propose the \textsf{Predictive Backpressure (PBP)} algorithm for achieving optimal utility performance in such predictive systems. \textsf{PBP} efficiently incorporates prediction into stochastic system control and avoids the great complication due to the exponential state space growth in the prediction window size. We show that \textsf{PBP} can achieve a utility performance that is within $O(\epsilon)$ of the optimal, for any $\epsilon>0$, while guaranteeing that the system delay distribution is a \emph{shifted-to-the-left} version of that under the original Backpressure algorithm. Hence, the average packet delay under \textsf{PBP} is strictly better than that under Backpressure, and vanishes with increasing prediction window size. This implies that the resulting utility-delay tradeoff with predictive scheduling beats the known optimal $[O(\epsilon), O(\log(1/\epsilon))]$ tradeoff for systems without prediction.

Adaptive Control for Stochastic Systems with Unknown Parameters and Input Delay

The adaptive dual control problem of a single-in single-out (SISO) stochastic system with unknown parameters and input delay is studied in this paper. The unknown parameters are assumed to be constant but belong to a known finite set. For each group of possible model parameters, a Kalman filter is used to estimate the system state online and the posterior probability of this model can also be calculated accordingly. The optimal control of each model is designed, based on an M steps ahead loss function. The final dual controller is obtained by a weighted sum of all possible optimal control outputs considering the posterior probabilities of each model. Numerical simulations were performed to verify the effectiveness of the proposed controller.

Robust resilient [formula omitted] control for uncertain stochastic systems with multiple time delays via dynamic output feedback

This paper deals with the problem of robust resilient L2−L∞ control for stochastic systems with multiple time delays and norm-bounded parameter uncertainties via dynamic output feedback. Both additive and multiplicative controller gain perturbations are considered. New delay-dependent conditions of robust mean-square exponential stability are developed by applying the Lyapunov–Krasovskii functional method and introducing free-weighting matrices. Two lemmas are given for reducing high-order nonlinearities, with the aid of which sufficient conditions are presented for the solvability of the robust resilient L2−L∞ control problem. The desired controllers can be constructed through the numerical solutions of a set of linear matrix inequalities. The proposed design conditions can be employed to determine reduced-order dynamic output feedback controllers without the need to impose any extra constraints on the system parameters. Numerical examples are provided to illustrate the effectiveness of the obtained results.

Approximate controllability of abstract semilinear stochastic control systems with nonlocal conditions

This paper studies the approximate controllability issue of an abstract semilinear stochastic control system with nonlocal conditions. Sufficient conditions are formulated and proved for the approximate controllability of such systems by splitting the given semilinear system into two systems, namely a semilinear deterministic system and a linear stochastic system. To prove the approximate controllability of semilinear deterministic system, Schauder fixed point theorem has been used. At the end, an example has been presented to illustrate the feasibility of the proposed result.