Class Of Stochastic Hybrid Systems Research Articles

Optimal control of stochastic hybrid system with jumps: A numerical approximation

The generalized class of stochastic hybrid systems consists of models with regime changes including the occurrence of impulsive behavior. In this paper, the stochastic hybrid processes with jumps are approximated by locally consistent Markov decision processes that preserve local mean and covariance. We further apply a randomized switching policy for approximating the dynamics on the switching boundaries. To investigate the validity of the approximation, we study a stochastic optimal control problem. On the basis of the discrete approximation, we solve the optimal control problem and show that the solution obtained from the discretized problem converges to the solution of the original optimal control problem.

Lyapunov conditions certifying stability and recurrence for a class of stochastic hybrid systems

Lyapunov-based conditions for stability and recurrence are presented for a class of stochastic hybrid systems where solutions are not necessarily unique, either due to nontrivial overlap of the flow and jump sets, a set-valued jump map, or a set-valued flow map. Randomness enters exclusively through the jump map, yet the framework covers systems with spontaneous transitions. Regularity conditions are given that guarantee the existence of random solutions and robustness of the Lyapunov conditions.

Probabilistic-constrained optimal control of a class of stochastic hybrid systems

Stochastic hybrid systems have several applications such as biological systems and communication networks, but it is difficult to consider control of general stochastic hybrid systems. In this paper, a class of discrete-time stochastic hybrid systems, in which only discrete dynamics are stochastic, is considered. For this system, a solution method for the optimal control problem with probabilistic constraints is proposed. Probabilistic constraints guarantee that the probability that the continuous state reaches a given unsafe region is less than a given constant. In the propose method, first, continuous state regions, from which the state reaches a given unsafe region, are computed by a backward-reachability graph. Next, mixed integer quadratic programming problems with constraints derived from the backward-reachability graph are solved. The proposed method can be applied to model predictive control.

Hybrid Possibilistic Systems with Nondeterministic Continuous Evolutions and Switchings

We propose a new class of hybrid (discrete-continuous) dynamical system models with nondeterministic continuous evolutions and switching between discrete modes. Formally, this class is rather similar to the class of stochastic hybrid systems, but it is based on possibility theory. This approach has an advantage over stochastic models when available statistical information is not sufficient for constructing a reliable stochastic model. For example, it may be useful for modeling human-machine-environment systems, because, as it has been argued in the literature, possibility theory describes many aspects of human behavior better than probability theory. In this work we present a motivating example, give a definition and semantics of our systems, consider reachability problems for large subclasses of them, and propose methods to tackle these problems.

New stochastic stability criteria for Markovian jump systems with mode‐dependent time‐varying‐delays

Purpose – As a class of stochastic hybrid systems, Markovian jump systems have been extensively studied in the past decades. In light of some results obtained on this topic. The purpose of this paper is to investigate the stability problems for delayed Markovian jump systems.Design/methodology/approach – The time‐varying‐delays considered in this paper are switched synchronously with system mode. Based on stochastic Lyapunov theory, the delay‐dependent stability conditions are developed by using some linear matrix inequality techniques. To obtain better stability criteria, the different Lyapunov‐Krasovskii functional is chosen and an important inequality is introduced.Findings – Numerical examples show that the resulting criteria in this paper have advantages over some previous ones in that they involve fewer matrix variables, but have less conservatism. Furthermore, they only involve the matrix variables appeared in the Lyapunov functional. Therefore, there are no additional matrix variables coupled with...

Fluid limit theorems for stochastic hybrid systems with application to neuron models

In this paper we establish limit theorems for a class of stochastic hybrid systems (continuous deterministic dynamics coupled with jump Markov processes) in the fluid limit (small jumps at high frequency), thus extending known results for jump Markov processes. We prove a functional law of large numbers with exponential convergence speed, derive a diffusion approximation, and establish a functional central limit theorem. We apply these results to neuron models with stochastic ion channels, as the number of channels goes to infinity, estimating the convergence to the deterministic model. In terms of neural coding, we apply our central limit theorems to numerically estimate the impact of channel noise both on frequency and spike timing coding.

Fluid limit theorems for stochastic hybrid systems with application to neuron models

In this paper we establish limit theorems for a class of stochastic hybrid systems (continuous deterministic dynamics coupled with jump Markov processes) in the fluid limit (small jumps at high frequency), thus extending known results for jump Markov processes. We prove a functional law of large numbers with exponential convergence speed, derive a diffusion approximation, and establish a functional central limit theorem. We apply these results to neuron models with stochastic ion channels, as the number of channels goes to infinity, estimating the convergence to the deterministic model. In terms of neural coding, we apply our central limit theorems to numerically estimate the impact of channel noise both on frequency and spike timing coding.

Near optimal control for a class of stochastic hybrid systems

To address a computationally intractable optimal control problem for a class of stochastic hybrid systems, this paper proposes a near optimal state feedback control scheme, which is constructed by using a statistical prediction method based on approximate numerical solution that samples over the entire state space. A numerical example illustrates the potential of the approach.

Robust Variance-constrained Control of a Class of Stochastic Hybrid Systems

摘要: 对一类结构参数不完全已知的Markov跳变参数系统, 研究使得闭环系统的稳态状态方差小于某个给定的上界, 同时满足一定H∞性能的状态反馈鲁棒方差控制器设计问题. 运用线性矩阵不等式(Linear matrix inequality, LMI)方法, 对系统进行了方差分析, 给出并证明了控制器存在的条件, 进而用一组线性矩阵不等式的可行解给出了控制器的一个参数化表示. 通过建立一个具有LMI约束的凸优化问题, 给出了最小方差鲁棒控制器的设计方法. 最后仿真结果表明了该方法的有效性. 关键词: 方差约束 / H∞性能 / 容错控制系统 / Markov跳变系统 / 乘性噪声

Stability and dissipative analysis for a class of stochastic system with time-delay

Abstract This paper deals with the stability and dissipative problem of a class of stochastic hybrid system. The system under study involves Markovian jump, impulsive effects and time delay, which are often encountered in practice and are the sources of instability. Our attention is focused on analysis of whether the stochastic hybrid system with time-delay is stochastically asymptotically stable and strictly (Q, S, R) dissipative. By introducing an extra artificial time instance, the equivalent system is obtained and the sufficient conditions are derived by using linear matrix inequality (LMI) techniques. The main results of this paper unify the existing results on H ∞ control.

Approximations of Stochastic Hybrid Systems

This paper develops a notion of approximation for a class of stochastic hybrid systems that includes, as special cases, both jump linear stochastic systems and linear stochastic hybrid automata. Our approximation framework is based on the recently developed notion of the so-called stochastic simulation functions. These Lyapunov-like functions can be used to rigorously quantify the distance or error between a system and its approximate abstraction. For the class of jump linear stochastic systems and linear stochastic hybrid automata, we show that the computation of stochastic simulation functions can be cast as a tractable linear matrix inequality problem. This enables us to compute the modeling error incurred by abstracting some of the continuous dynamics, or by neglecting the influence of stochastic noise, or even the influence of stochastic discrete jumps.

Output Feedback H2/H∞ Control of a Class of Discrete-time Reconfigurable Control Systems

In this paper, static output feedback control of a class of discrete-time reconfigurable systems with Markovian parameters is addressed. The main contribution is to formulate conditions for multi-performance design related to this class of systems. The specifications and objectives under consideration include stochastic stability, H2 and H∞ performances. Another problematic related to a more general class of stochastic hybrid systems, known as Markovian Jump Linear Systems (MJLS), is also considered. This problematic concerns the mode-independent output feedback control of discrete-time MJLS. Results are formulated as nonlinear matrix inequalities. A numerical algorithm is provided and its running is illustrated on a classical example from literature.

Stability analysis on uncertain stochastic impulsive systems with time-delay

This Letter deals with the problem of stochastic robust stability analysis and control on a class of stochastic hybrid system. The system under study involves Markovian jump, norm-bounded uncertainties, time delay and impulsive effects. Sufficient conditions for the stochastic hybrid system stochastically robustly stable are obtained, we also give some criteria on how to design a memoryless feedback controller and an impulsive controller to stabilize such stochastic hybrid system.

Perfect Simulation of a Class of Stochastic Hybrid Systems with an Application to Peer to Peer Systems

In this paper we present a class of hybrid systems made of deterministic differential equations and random discrete jumps. We then show how to construct a simulation of such a stochastic hybrid system that provides perfect samples of its asymptotic behavior based on the extension to continuous state-space of coupling-from-the-past techniques introduced by Foss and Tweedie (Stoch Models 14:187–204, 1998) and using suitable envelope trajectories to tackle non-monotonicity. The applicability of the method is illustrated by showing how this framework can be used to model the Squirrel peer to peer system and by reporting a simulation study based on this approach. This paper provides both a framework on how to carry simulation based experimental studies of large and complex hybrid systems and its application in the Squirrel model demonstrating how versatile and powerful this approach can be over a typical example.

Output feedback control of a class of stochastic hybrid systems

This paper deals with static output feedback control of a class of reconfigurable systems with Markovian Parameters and state-dependent noise. The main contribution is to formulate conditions for multi-performance design related to this class of stochastic hybrid systems. The specifications and objectives under consideration include stochastic stability, H 2 and H ∞ performances. Another problem related to a more general class of stochastic hybrid systems, known as Markovian Jump Linear Systems (MJLS), is also addressed. This problem concerns the mode-independent output feedback control of MJLS. The obtained results are illustrated on a numerical example.

Reliable dissipative control for stochastic impulsive systems

This paper deals with the problem of reliable dissipative control for a class of stochastic hybrid systems. The systems under study are subject to Markovian jump, parameter uncertainties, possible actuator failure and impulsive effects, which are often encountered in practice and the sources of instability. Our attention is focused on the design of linear state feedback controllers and impulsive controllers such that, for all admissible uncertainties as well as actuator failure occurring among a prespecified subset of actuators, the stochastic hybrid system is stochastically robustly stable and strictly (Q,S,R)-dissipative. The sufficient conditions are obtained by using linear matrix inequality (LMI) techniques. The main results of this paper extend the existing results on H∞ control.

Output‐feedback ℋ︁2/ℋ︁∞ control of a class of networked fault tolerant control systems

AbstractThis paper deals with static output feedback control of a class of discrete‐time networked control systems (NCS) subject to random failures and random delays. The different random processes are modeled as Markovian chains, and the resulting closed‐loop system belongs to the class of discrete‐time Markovian jump linear systems (MJLS). The main contribution is to formulate conditions for multi‐performance design related to this class of stochastic hybrid systems. The specifications and objectives under consideration include stochastic stability, ℋ︁2 and ℋ︁∞ performances. Results are formulated as matrix inequalities. A numerical algorithm is provided and its running is illustrated on a numerical example. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Multiobjective Output Feedback Control of a Class of Stochastic Hybrid Systems with State-Dependent Noise

This paper deals with dynamic output feedback control of continuous-time active fault tolerant control systems with Markovian parameters (AFTCSMP) and state-dependent noise. The main contribution is to formulate conditions for multiperformance design, related to this class of stochastic hybrid systems, that take into account the problematic resulting from the fact that the controller only depends on the fault detection and isolation (FDI) process. The specifications and objectives under consideration include stochastic stability,ℋ2andℋ∞(or more generally,stochastic integral quadratic constraints) performances. Results are formulated as matrix inequalities. The theoretical results are illustrated using a classical example from literature.

Asymptotic Stability and Boundedness of Delay Switching Diffusions

Multiple Lyapunov functions are used to establish sufficient conditions for locating the limit sets of switching diffusions. The conditions lead to a number of useful results on stochastic asymptotic stability and boundedness for this class of stochastic hybrid systems.

Composite stabilization of singularly perturbed stochastic hybrid systems

This paper studies stability conditions and composite stabilization schemes for a class of stochastic hybrid systems. Such systems switch among a finite number of linear singularly perturbed system models, with switched behaviour governed by a nearly completely decomposable finite state Markov chain. The stability properties of a decoupled slow mode subsystem, a decoupled fast mode subsystem and an overall system are also investigated. Linear switching stabilization schemes with perfect as well as imperfect Markov chain detectors are developed to stabilize the overall system. Two examples are provided to illustrate the stabilization schemes.