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"stochastic system"
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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
Computational Analysis of stochastic arithmetic computing and stochastic activation function
Stochastic Number Generators (SNG) plays a significant role in designing a stochastic computing system. SNGs make the stochastic system comfortable for computing in the stochastic domain. The challenges in developing the stochastic computing system are correlation and hardware area occupancy. By considering these phenomena, we have considered Linear Feedback Shift Register (LFSR) based SNG and S-box based SNG in this work. Our contributions to this paper are stochastic computation for activation functions using the SNGs mentioned above and stochastic computation for arithmetic components in the stochastic domain. By considering the two SNG methods, the difference in the computation for accuracy has been analyzed for stochastic activation function and stochastic arithmetic computation. The better SNG method will be used as SNG for stochastic convolutional neural network design using this analysis.
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
Optimal Controllability for Multi-Term Time-Fractional Stochastic Systems with Non-Instantaneous Impulses
In the present paper, we study the existence and optimal controllability of a multi-term time-fractional stochastic system with non-instantaneous impulses. Using semigroup theory, stochastic techniques, and Krasnoselskii’s fixed point theorem, we first establish the existence of a mild solution. Further, we obtain that there exists an optimal state-control pair for the system under certain assumptions. Some examples are given to illustrate the abstract results.
Journal Article
Stabilization of the Linear Controlled Output of an Autonomous Stochastic Differential System on an Infinite Horizon
The control problem of the linear output of an autonomous nonlinear stochastic differential system is considered. The infinite horizon and the quadratic functional make it possible to interpret the control goal as stabilization of the output near the position determined by the state, which is described by a nonlinear stochastic differential equation. The solution is obtained for two variants of the model: with accurate measurements and under the assumption that the linear output represents indirect observations of the state. In the case of indirect observations, a continuous Markov chain is used as a state model, which makes it possible to separate the control and filtering tasks and apply the Wonham filter. In both variants, sufficient conditions for the existence of the optimal solution consist of typical requirements for linear systems that ensure the existence of a limiting solution of the Riccati equation. The ergodicity of the nonlinear dynamics and the existence of a limit in the Feynman–Kac formula for the coefficients of the nonlinear part of the control are additional requirements due to the nonlinear elements. The results of the numerical experiment are presented and analyzed.
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
Gradient-Based Iterative Parameter Estimation Algorithms for Dynamical Systems from Observation Data
It is well-known that mathematical models are the basis for system analysis and controller design. This paper considers the parameter identification problems of stochastic systems by the controlled autoregressive model. A gradient-based iterative algorithm is derived from observation data by using the gradient search. By using the multi-innovation identification theory, we propose a multi-innovation gradient-based iterative algorithm to improve the performance of the algorithm. Finally, a numerical simulation example is given to demonstrate the effectiveness of the proposed algorithms.
Journal Article