A Refined Algorithm for the Adaptive Optimal Output Regulation Problem

TL;DR

This paper introduces a refined algorithm for the adaptive optimal output regulation problem in linear unknown systems, which simplifies the solution process by decoupling complex equations into lower-dimensional ones, thereby easing solvability conditions.

Contribution

The paper's main contribution is the decoupling of complex linear equations into two simpler, lower-dimensional equations, improving the solvability and computational efficiency of the adaptive regulation algorithm.

Findings

Decoupling reduces the number of unknowns in each equation.

Weakened solvability conditions facilitate easier solution.

Enhanced algorithm efficiency for adaptive output regulation.

Abstract

Given a linear unknown system with $m$ inputs, $p$ outputs, $n$ dimensional state vector, and $q$ dimensional ecosystem, the problem of the adaptive optimal output regulation of this system boils down to iteratively solving a set of linear equations and each of these equations contains $\frac{n (n+1)}{2} + (m+q)n$ unknown variables. In this paper, we refine the existing algorithm by decoupling each of these linear equations into two lower-dimensional linear equations. The first one contains $nq$ unknown variables, and the second one contains $\frac{n (n+1)}{2} + mn$ unknown variables. As a result, the solvability conditions for these equations are also significantly weakened.