Control Of Stochastic Systems Research Articles

Controllability of Stochastic Game-Based Control Systems

It is well known that in classical control theory, the controller has a certain objective to achieve, and the plant to be controlled does not have its own objective. However, this is not the case i...

时滞随机控制系统解的估计

时滞随机控制系统解的估计

Partial Approximate Controllability for Linear Stochastic Control Systems

This paper is devoted to studying controllability problems of linear stochastic control systems with controls only in the drift terms. It is well known that such a system is not exactly controllabl...

Convergence rates of stochastic homogeneous systems

This study considers stochastic homogeneous systems and focuses on the relation between their homogeneity and the convergence rates. We give a definition of stochastic homogeneous systems with weighted dilations as an extension of deterministic homogeneous systems. We also introduce the stability properties, such as exponential, rational, and finite-time stability with respect to homogeneous norms. As a main result, we show that their homogeneous degrees imply the convergence rates of asymptotically stable systems. Based on the result, we also deal with the stabilization of stochastic homogeneous control systems. We provide a design method of homogeneous feedback laws with homogeneous control Lyapunov functions, which guarantees the convergence rates.

Viability of an open set for stochastic control systems

The problem of compatibility of a stochastic control system and a set of constraints – the so called viability property – has been widely investigated during the last three decades. Given a stochastic control system, the question is to characterize sets A such that for any initial condition in A there exists a control ensuring that the associated stochastic process remains forever almost surely in A (this is called the viability property of A). When A is closed and the dynamics is continuous, the viability property has been characterized in the literature through several equivalent geometric conditions involving A, the drift and the diffusion of the control system. In this article we give a necessary and sufficient condition involving the boundary of an open set A ensuring the viability property of A, whenever A has a C2,1 boundary and the dynamics are Lipschitz. If moreover a classical convexity condition on the control dynamics holds true, we show that the viability of an open set A is equivalent to the viability of its closure. This last result is rather surprising, because several very elementary examples in the deterministic framework show that, in general, there is no such equivalence for a general open set A. We will also discuss examples illustrating that the above equivalence is wrong when either the boundary of A does not have enough regularity, or the dynamics are not Lipschitz continuous.

Approximate controllability of semilinear fractional stochastic control system

The objective of this paper is to present some sufficient conditions for approximate controllability of semilinear fractional stochastic control system with delay. The results hold when the nonlinear function is Lipschitz continuous. Sufficient conditions are obtained by separating the given fractional semilinear stochastic system into two systems namely a semilinear fractional system and a fractional linear stochastic system. To prove our results, the Schauder fixed point theorem is applied. At the end, one example is given to illustrate the results.

Computer simulation of control contour of unmanned aviation complex to provide robustness and controllability

The article describes an approach to ensuring stability and controllability of unmanned aerial vehicle (UAV) with unknown aerodynamic characteristics by computer simulation of the airplane flight along a given route in the meteorological standard atmosphere. This computer model takes into account the programmed flight of an unmanned aerial vehicle in the meteorological atmosphere along a given route with waypoints. For this purpose the model incorporates 5 feedback systems (FS) with autopilot (AP) that ensure the stability and controllability of an airplane. Besides the autopilot and the airplane glider the control system encompasses the Kalman filter and a strapdown inertial navigation system. The appropriate structure and parameters of the control system of the model were chosen on the basis of practical technical solutions of the de veloped UAVs. The closed control systems of the model are developed according to the equations considering generation of aerodynamic forces and moments, a model of the standard atmosphere, the routing scheme and the feedback system with autopilot. The stability and controllability of the model were analyzed according to the theory of feedback systems with the graphic plotting of Bode magnitude plot and Bode phase plot. With a view to the assessment of dynamic and fluctuation errors of the control systems the model is represented by stochastic differential control system with the Kalman filter and the strapdown inertial navigation system in quaternions. The results of the computer simulation showed that the Kalman filter estimates the measured parameters with the noise reduction under 10 dB. The strapdown inertial navigation system influences the general dynamics of the control system during the assessment of its stability and controllability. Changing the band of the control system at the expense of external perturbations affecting the plane can lead to instability, and in order to avoid it the robust autopilot is recommended.

Fault Diagnosis and Minimum Rational Entropy Fault Tolerant Control of Stochastic Distribution Collaborative Systems.

In this paper, a fault-tolerant control scheme is presented for a class of stochastic distribution collaborative control systems, which are composed of three subsystems connected in series to complete the control target. The radial basis function neural network is used to approximate the output probability density function of the third subsystem, which is also the output of the entire system. When fault occurs in the first subsystem, an adaptive diagnostic observer is designed to estimate the value of fault. However, the first subsystem does not have the ability of self-recovery, minimum rational entropy controllers are designed in the latter subsystems to compensate the influence of the fault and minimize the entropy of the system output. A numerical simulation is given to verify the effectiveness of the proposed scheme.

A stochastic multi-channel revenue management model with time-dependent demand

Abstract E-commerce has seen rapid growth in recent years and many firms (e.g., airline companies) sell directly to their customers through different online channels or agents (e.g., Expedia, Ctrip, Qunar, elong) by paying different proportional fees. Besides the firm's revenue management decision of dynamically allocating its limited inventory to different demand classes, it may also get a different margin for selling the same product through different channels (at the same price). This paper examines the firm's optimal channel control strategy with combining its revenue management decision. We propose a multi-period multi-channel continuous-time model with time-dependent arrival rates. The market prices are different in different periods. The firm needs to decide the protection levels for all periods and the channel control strategy in each period. By developing a stochastic (Hamiltonian) channel control system and using the Maximum Principle, the optimal channel control rules are found and a threshold channel control policy is proposed. Based on the channel control policy, we show that there exist the unique optimal protection levels for all periods.

Minimum rational entropy fault tolerant control for non-Gaussian singular stochastic distribution control systems using T-S fuzzy modelling

ABSTRACTIn this paper, a new fault diagnosis (FD) and fault tolerant control (FTC) algorithm for a non-Gaussian nonlinear singular stochastic distribution control (SDC) system is studied. The rational square-root fuzzy logic model is used to approximate the output probability density function of non-Gaussian processes and a Takagi-Sugeno (T-S) fuzzy model is employed to transform the non-Gaussian nonlinear SDC system into a fuzzy SDC system. An adaptive fuzzy fault diagnosis observer is constructed to achieve reconstruction of system state and fault. Based on the estimated fault information, the controller is reconfigured by minimising the performance index with regard to the rational entropy subjected to mean constraint. Minimum rational entropy fault tolerant control is introduced to make the output of the past-fault SDC system still have the minimum uncertainty. Simulation results are provided to demonstrate the validity of the FD and minimum rational entropy FTC algorithm.

Collaborative operational fault tolerant control for stochastic distribution control system

Based on a class of industrial processes, a new distributed fault diagnosis approach and a collaborative operational fault tolerant control law are proposed for an irreversible interconnected stochastic distribution control (SDC) system with boundary conditions. This control method is different from the existing collaborative fault tolerant controllers which enable the output probability density function (PDF) to track a desired PDF as close as possible. When fault occurs, a setpoint redesigned fault tolerant approach is adopted to accommodate the fault instead of reconstructing the controller. An augmented PID nominal controller and a setpoint compensation item with linear structure are used to obtain a collaborative operational fault tolerant controller via solution of linear matrix inequalities (LMIs). Simulations are included to show the effectiveness of the proposed algorithms where encouraging results have been obtained.

Dynamic output feedback control for stochastic networked control systems based on a periodic event-triggered mechanism

In this paper, the event-triggered dynamic output feedback control for stochastic networked control systems is investigated. The measurement output signal is periodically sampled but aperiodically transmitted. The time-delay system method is utilized to model the stochastic networked control system under the periodic event-triggered mechanism, then the corresponding stability criteria are obtained. Based on the stability criteria, the suitable output-based controller and event-triggered parameters are co-designed. Two air vehicle systems are presented to illustrate the efficiency of the proposed control method.

Stochastic maximum principle for delayed doubly stochastic control systems and their applications

ABSTRACTIn this paper, we investigate the optimal control problems for delayed doubly stochastic control systems. We first discuss the existence and uniqueness of the delayed doubly stochastic differential equation by martingale representation theorem and contraction mapping principle. As a necessary condition of the optimal control, we deduce a stochastic maximum principle under some assumption. At the same time, a sufficient condition of optimality is obtained by using the duality method. At the end of the paper, we apply our stochastic maximum principle to a class of linear quadratic optimal control problem and obtain the explicit expression of the optimal control.

Bisimulation Equivalence of Discrete-Time Stochastic Linear Control Systems

In this paper, we propose a definition of equivalence via stochastic bisimulation for the class of discrete-time stochastic linear control systems with possibly degenerate normally distributed disturbances. The notion is inspired by the notion of probabilistic bisimulation for probabilistic chains. Geometric necessary and sufficient conditions for checking this notion are derived. Model reduction via Kalman-like decomposition is also proposed. Connections with stochastic reachability are discussed and with finite horizon stochastic safety problems established. A discussion on the use of stochastic bisimulation equivalence for control design is given, and an application to optimal control problems with stochastic reachability specifications is finally presented.

Special focus on modeling, analysis and control of stochastic systems

Special focus on modeling, analysis and control of stochastic systems

Design of Event-Triggered Fault-Tolerant Control for Stochastic Systems with Time-Delays

This paper proposes two novel, event-triggered fault-tolerant control strategies for a class of stochastic systems with state delays. The plant is disturbed by a Gaussian process, actuator faults, and unknown disturbances. First, a special case about fault signals that are coupled to the unknown disturbances is discussed, and then a fault-tolerant strategy is designed based on an event condition on system states. Subsequently, a send-on-delta transmission framework is established to deal with the problem of fault-tolerant control strategy against fault signals separated from the external disturbances. Two criteria are provided to design feedback controllers in order to guarantee that the systems are exponentially mean-square stable, and the corresponding -norm disturbance attenuation levels are achieved. Two theorems were obtained by synthesizing the feedback control gains and the desired event conditions in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to illustrate the effectiveness of the proposed theoretical results.

Input-to-State Stabilization in Probability for Nonlinear Stochastic Systems Under Quantization Effects and Communication Protocols.

In this paper, the observer-based stabilization problem is investigated for a class of discrete-time nonlinear stochastic networked control systems (NCSs) with exogenous disturbances. The signal transmission from the sensors to the observer is implemented via a shared digital network, in which both uniform quantization effect and stochastic communication protocol (SCP) are taken into account to reflect several network-induced constraints. The notion of input-to-state stability in probability is introduced to describe the dynamical behaviors of the closed-loop stochastic NCS that is effectively characterized by a general nonlinear stochastic difference equation with Markovian jumping parameters. A theoretical framework is first established to felicitate the dynamics analysis of the closed-loop system in virtue of the switched Lyapunov function method and the stochastic analysis techniques. By making full use of the quantized measurement output under the scheduling of the SCP, the existence conditions for an observer-based controller are established under which the closed-loop system is input-to-state stable in probability. Then, the explicit expression of the gain matrices of the desired controller is given by resorting to a set of feasible solutions of certain matrix inequalities. The effectiveness of the theoretical results is demonstrated by a numerical simulation example.

Optimal control of stochastic functional neutral differential equations with time lag in control

In this work, we consider an optimal control problem of a class of stochastic differential equations driven by additive noise with aftereffect appearing in control. We develop a semigroup theory of the driving deterministic neutral system and identify explicitly the adjoint operator of the corresponding infinitesimal generator. We formulate the time delay equation under consideration into an infinite dimensional stochastic control system without time lag by means of the adjoint theory established. Consequently, we can deal with the associated optimal control problem through the study of a Hamilton–Jacob–Bellman (HJB) equation. Last, we present an example whose optimal control can be explicitly determined to illustrate our theory.

Representation of asymptotic values for nonexpansive stochastic control systems

In ergodic stochastic problems the limit of the value function Vλ of the associated discounted cost functional with infinite time horizon is studied, when the discounted factor λ tends to zero. These problems have been well studied in the literature and the used assumptions guarantee that the value function λVλ converges uniformly to a constant as λ→0. The objective of this work consists in studying these problems under the assumption, namely, the nonexpansivity assumption, under which the limit function is not necessarily constant. Our discussion goes beyond the case of the stochastic control problem with infinite time horizon and discusses also Vλ given by a Hamilton–Jacobi–Bellman equation of second order which is not necessarily associated with a stochastic control problem. On the other hand, the stochastic control case generalizes considerably earlier works by considering cost functionals defined through a backward stochastic differential equation with infinite time horizon and we give an explicit representation formula for the limit of λVλ, as λ→0.

Try-once-discard scheduling for stochastic networked control systems

ABSTRACTIn practical networked control systems (NCS), such as smart grids, cooperative robotics, and sensor networks, often multiple control applications share a communication infrastructure, requiring a smart and efficient scheduling mechanism to coordinate the access to the capacity-limited communication medium. In this article we consider the problem of event-based scheduling design for NCSs consisting of multiple control loops over a shared communication medium. We extend the notion of Try-Once-Discard (TOD), which is one of the basic deterministic event-based scheduling protocols for resource constrained NCSs, to the case of multiple stochastic control systems coupled via a shared communication medium subject to capacity limitation and stochastic packet delivery failure. Showing that the overall network-induced error is a homogeneous Markov chain in our stochastic set-up, we first study stability properties of such networked systems under the TOD scheduling scheme employing the concepts of stochastic stability. Then, we derive sufficient stability conditions under the TOD rule assuming that the communication channel is not ideal, i.e. a scheduled data packet for transmission might be lost in the communication channel with a non-zero probability. Furthermore, we derive analytic performance bounds by finding uniform upper-bounds for an average quadratic cost function. The numerical simulations are performed for variety of system parameters and NCS set-ups to strengthen our stability claim as well as illustrating performance bounds. Additionally, we show that the TOD scheduling rule outperforms the conventional time-triggered, and uniform and non-uniform random channel access arbitration mechanisms, in terms of efficient coordination of channel access in stochastic NCSs.