Control theory for stochastic distributed parameter systems, an engineering perspective

Lü, Qi; Xu, Zuyan

doi:10.1016/j.arcontrol.2021.04.002

Cited by 13 publications

(4 citation statements)

References 86 publications

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“…We first recall the following well-posedness result for the equation (5.2). The proof can be found in [1,Chapter 6] and [14,Chapter 3].…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…Control theory for stochastic distributed parameter systems, is, in our opinion, still at its very beginning stage. This is actually a rather new branch of mathematical control theory, which is indeed the main concern of this course (See [14,15] for more material).…”

mentioning

confidence: 99%

“…For the proofs of the results presented in this section, we refer to [1,14]. In what follows, we shall denote by C a generic positive constant, which may change from one place to another.…”

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confidence: 99%

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A Mini-Course on Stochastic Control

Lü

2019

Series in Contemporary Applied Mathematics

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This course is addressed to giving a short introduction to control theory of stochastic systems, governed by stochastic differential equations in both finite and infinite dimensions. We will mainly explain the new phenomenon and difficulties in the study of controllability and optimal control problems for these sort of equations. In particular, we will show by some examples that both the formulation of stochastic control problems and the tools to solve them may differ considerably from their deterministic counterpart.3 Controllability of stochastic (ordinary) differential equations 13 4 Pontryagin-type maximum principle for controlled stochastic (ordinary) differential equations 21 * This is a lecture notes of a short introduction to stochastic control. It was written for the LIASFMA

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“…We first recall the following well-posedness result for the equation (5.2). The proof can be found in [1,Chapter 6] and [14,Chapter 3].…”

Section: Formulation Of the Problemmentioning

confidence: 99%

mentioning

confidence: 99%

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A Mini-Course on Stochastic Control

Lü

2019

Series in Contemporary Applied Mathematics

Self Cite

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“…(2) Different from the traditional control approaches for stochastic nonlinear systems in References 30,31 that only dealt with the bounded tracking control problem in probability, one advantage of the proposed method is that the asymptotic tracking control issue is realized in this work. (3) In order to prevent the violation of the full state constraints, the BLFs are used in the design process of backstepping algorithm.…”

Section: Introductionmentioning

confidence: 99%

Adaptive neural network asymptotic tracking control for a class of stochastic nonlinear systems with unknown control gains and full state constraints

Niu

Wang

et al. 2021

Adaptive Control & Signal

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This article addresses the issue of adaptive intelligent asymptotic tracking control for a class of stochastic nonlinear systems with unknown control gains and full state constraints. Unlike the existing systems in the literature in which the prior knowledge of the control gains is available for the controller design, the salient feature of our considered system is that the control gains are allowed to be unknown but have a positive sign. By introducing an auxiliary virtual controller and employing the new properties of Numbness functions, the major technique difficulty arising from the unknown control gains is overcome. At the same time, the log-type barrier Lyapunov functions are introduced to prevent the violation of the state constraints. What's more, neural networks' universal online approximation ability and gain suppression inequality technology are combined in the frame of adaptive backstepping design, so that a new control method is proposed, which cannot only realize the asymptotic tracking control in probability, but also meet the requirement of the full state constraints imposed on the system. In the end, the simulation results for a practical example demonstrate the effectiveness of the proposed control method.

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Increasing Objectivity in the System Analysis of Socio-Economic Objects

Lyabakh¹

2022

System Analysis in Engineering and Control

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Control theory for stochastic distributed parameter systems, an engineering perspective

Cited by 13 publications

References 86 publications

A Mini-Course on Stochastic Control

A Mini-Course on Stochastic Control

Adaptive neural network asymptotic tracking control for a class of stochastic nonlinear systems with unknown control gains and full state constraints

Increasing Objectivity in the System Analysis of Socio-Economic Objects

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