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"Stochastic systems"
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A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria
We analyze a class of nonlinear partial differential equations (PDEs) defined on
eBook
Online Pareto optimal control of mean-field stochastic multi-player systems using policy iteration
In this study, the Pareto optimal strategy problem was investigated for multi-player mean-field stochastic systems governed by Itô differential equations using the reinforcement learning (RL) method. A partially model-free solution for Pareto-optimal control was derived. First, by applying the convexity of cost functions, the Pareto optimal control problem was solved using a weighted-sum optimal control problem. Subsequently, using on-policy RL, we present a novel policy iteration (PI) algorithm based on the
ℌ
-representation technique. In particular, by alternating between the policy evaluation and policy update steps, the Pareto optimal control policy is obtained when no further improvement occurs in system performance, which eliminates directly solving complicated cross-coupled generalized algebraic Riccati equations (GAREs). Practical numerical examples are presented to demonstrate the effectiveness of the proposed algorithm.
Journal Article
Sliding mode control for nonlinear stochastic systems with Markovian jumping parameters and mode-dependent time-varying delays
This paper reports on the sliding mode control (SMC) problem for nonlinear stochastic systems with one features: time-delays are not only varied with time but also characterized by random delays changed in line with a set of Markov chains (namely, time-delays are mode-dependent time-varying delays). Based on given systems, an integral switching surface is introduced. In particular, such a switching surface with an Itô process is given so that the traditional assumption imposed on systems is removed. And by applying the Itô formula, the linear matrix inequalities method and the lemma provided, more relaxed and indeed delay-dependent criteria for the second moment exponential stability are given. Then, the sliding mode controller is constructed to guarantee the reachability of the switching surface and the existence of the sliding mode. Finally, the validity and the application for the presented SMC method are illustrated by the DC motor system.
Journal Article
Fault estimation and fault-tolerant control for linear discrete time-varying stochastic systems
This paper presents a scheme for simultaneous fault estimation and fault-tolerant control of linear discrete time-varying stochastic systems. An observer is proposed to estimate the system state and the fault simultaneously. The estimation errors of both the system state and fault can achieve exponential stability in mean square sense even if the fault arbitrarily changes or is unbounded. The controllers of the drift term and diffusion term are designed separately, and then based on the estimated fault, the fault compensation is performed to realize fault tolerance. For the parameter design in the estimator and controllers, we provide two different algorithms via the cone complementarity linearization and the state transition matrix methods, respectively. As an extension, a class of quasi-linear systems is also discussed. A simulation example with two different fault types and an application in electromechanical servo systems are provided to illustrate the usefulness of the proposed scheme.
Journal Article
Event-triggered optimal control for nonlinear stochastic systems via adaptive dynamic programming
For nonlinear Itô-type stochastic systems, the problem of event-triggered optimal control (ETOC) is studied in this paper, and the adaptive dynamic programming (ADP) approach is explored to implement it. The value function of the Hamilton–Jacobi–Bellman(HJB) equation is approximated by applying critical neural network (CNN). Moreover, a new event-triggering scheme is proposed, which can be used to design ETOC directly via the solution of HJB equation. By utilizing the Lyapunov direct method, it can be proved that the ETOC based on ADP approach can ensure that the CNN weight errors and states of system are semi-globally uniformly ultimately bounded in probability. Furthermore, an upper bound is given on predetermined cost function. Specifically, there has been no published literature on the ETOC for nonlinear Itô-type stochastic systems via the ADP method. This work is the first attempt to fill the gap in this subject. Finally, the effectiveness of the proposed method is illustrated through two numerical examples.
Journal Article
Multistate systems reliability theory with applications
Most books in reliability theory are dealing with a description of component and system states as binary: functioning or failed. However, many systems are composed of multi-state components with different performance levels and several failure modes. There is a great need in a series of applications to have a more refined description of these states, for instance, the amount of power generated by an electrical power generation system or the amount of gas that can be delivered through an offshore gas pipeline network.
This book provides a descriptive account of various types of multistate system, bound-for multistate systems, probabilistic modeling of monitoring and maintenance of multistate systems with components along with examples of applications.
Key Features:
* Looks at modern multistate reliability theory with applications covering a refined description of components and system states.
* Presents new research, such as Bayesian assessment of system availabilities and measures of component importance.
* Complements the methodological description with two substantial case studies.
Reliability engineers and students involved in the field of reliability, applied mathematics and probability theory will benefit from this book.
eBook
Boundedness and stability of highly nonlinear hybrid neutral stochastic systems with multiple delays
This paper reports the boundedness and stability of highly nonlinear hybrid neutral stochastic differential delay equations (NSDDEs) with multiple delays. Without imposing linear growth condition, the boundedness and exponential stability of the exact solution are investigated by Lyapunov functional method. In particular, using the M-matrix technique, the mean square exponential stability is obtained. Finally, three examples are presented to verify our results.
Journal Article
Stochastic Maximum Principle for Square-Integrable Optimal Control of Linear Stochastic Systems
The authors give a stochastic maximum principle for square-integrable optimal control of linear stochastic systems. The control domain is not necessarily convex and the cost functional can have a quadratic growth. In particular, they give a stochastic maximum principle for the linear quadratic optimal control problem.
Journal Article