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

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.