Estimators Based on Non-squares Loss Functions to Approximate HJB-Riccati Equation Solution for DLQR Design via HDP

Author

Queiroz, Jonathan A. ; Rego, Patricia H. M. ; Neto, Joao V. F. ; Da Silva, Claudio ; Santana, Eder ; Kardec Barros, Allan

Author_Institution

Embedded Syst. & Intell. Control Lab., Fed. Univ. of Maranhao, Sao Luis, Brazil

fYear

2013

fDate

13-16 Oct. 2013

Firstpage

3238

Lastpage

3243

Abstract

This paper is concerned with the development of online algorithms for approximate solutions of the Hamilton-Jacobi-Bellman (HJB) equation. In the discrete linear quadratic regulator (DLQR) control system design, the HJB equation is the discrete algebraic Riccati (DARE) equation. Due to the problem of dimensionality curse, this equation is approximated via heuristic dynamic programming (HDP). The proposed methodology is based on a familiy of non-squares approximators for critic adaptive solution of the DARE associated to the DLQR problem, referred to in this work as HJB-Riccati equation, which is characterized as a parameterization of the HJB equation. The proposed method is evaluated in a multivariable dynamic system of 4th order with two inputs and it is compared with standard recursive least square algorithm.

Keywords

Jacobian matrices; Riccati equations; control system synthesis; discrete systems; dynamic programming; linear quadratic control; multivariable control systems; DARE equation; DLQR control system design; DLQR design; DLQR problem; HDP; HJB equation parameterization; HJB-Riccati equation solution; Hamilton-Jacobi-Bellman equation; dimensionality curse problem; discrete algebraic Riccati equation; discrete linear quadratic regulator control system design; heuristic dynamic programming; multivariable dynamic system; nonsquares approximators; nonsquares loss functions estimators; online algorithms; Algorithm design and analysis; Approximation algorithms; Convergence; Equations; Mathematical model; Standards; Vectors; Discrete Algebraic Riccati Equation; Discrete Linear Quadratic Regulator; Hamilton-Jacobi-Bellman Equation; Heuristic Dynamic Programming; Non-squares Approximators; Recursive Least-Squares;

fLanguage

English

Publisher

ieee

Conference_Titel

Systems, Man, and Cybernetics (SMC), 2013 IEEE International Conference on

Conference_Location

Manchester

Type

conf

DOI

10.1109/SMC.2013.552

Filename

6722305