Locally optimal risk-sensitive controllers for strict-feedback nonlinear systems
type: Item
instance of: scholarly article
title: Locally optimal risk-sensitive controllers for strict-feedback nonlinear systems
zbMATH Open document ID: 0966.93111
DOI: 10.1023/A:1004684905658
published in: Journal of Optimization Theory and Applications
publication date: 2001-03-12T00:00:00Z
review text: This paper deals with risk-sensitive control of nonlinear stochastic systems whose dynamics are in strict feedback form. Using a backstepping procedure, the authors constructed the state-feedback control \(\mu^*\), which satisfies the following 3 conditions. 1. \(\mu^*\) is optimal for the linearized risk-sensitive design, which implies that the linear exponential quadratic Gaussian problem is solved. Namely, \(\mu^*\) is locally optimal. 2. For a given nonlinear systems there exists an appropriate cost function, according to which \(\mu^*\) is optimal. Namely, \(\mu^*\) is globally inverse optimal. 3. \(\mu^*\) leads to closed-loop system trajectories that are bounded in probability.
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93B18
zbMATH DE Number: 1533367
zbMATH Keywords: linearization
zbMATH Keywords: local optimality
zbMATH Keywords: inverse optimality
zbMATH Keywords: risk-sensitive control
zbMATH Keywords: nonlinear stochastic systems
zbMATH Keywords: strict feedback form
zbMATH Keywords: backstepping
zbMATH Keywords: linear exponential quadratic Gaussian problem
author: Tamer Başar
author: Cheng Tang
reviewed by: Makiko Nisio
MaRDI profile type: Publication
cites work: Q3997540
cites work: Q3140691
cites work: The risk-sensitive index and the \(H_ 2\) and \(H_ \infty\) norms for nonlinear systems
cites work: The equivalence between infinite-horizon optimal control of stochastic systems with exponential-of-integral performance index and stochastic differential games
cites work: Model Simplification and Optimal Control of Stochastic Singularly Perturbed Systems under Exponentiated Quadratic Cost
cites work: Backstepping Controller Design for Nonlinear Stochastic Systems Under a Risk-Sensitive Cost Criterion
full work available at URL: a:1004684905658
OpenAlex ID: W1915016325
description: scientific article; zbMATH DE number 1533367