Inverse optimal design of input-to-state stabilizing homogeneous controllers for nonlinear homogeneous systems

TL;DR

This paper develops a method to design controllers for nonlinear homogeneous systems that are both input-to-state and input-output stable by solving an inverse optimal control problem with a novel cost functional.

Contribution

It introduces a new inverse optimal control formulation incorporating output penalties and provides conditions for solving the inverse gain assignment problem in homogeneous systems.

Findings

Homogeneous stabilizability ensures solvability of the inverse gain assignment.

The proposed method guarantees input-to-state and input-output stability.

A technique using homogeneity properties constructs the cost functional.

Abstract

This work studies the inverse optimality of input-to-state stabilizing controllers with input-output stability guarantees for nonlinear homogeneous systems. We formulate a new inverse optimal control problem, where the cost functional incorporates penalties on the output, in addition to the state, control and disturbance as in current related works. One benefit of penalizing the output is that the resulting inverse optimal controllers can ensure both input-to-state stability and input-output stability. We propose a technique for constructing the corresponding meaningful cost functional by using homogeneity properties, and provide sufficient conditions on solving the inverse optimal gain assignment problem. We show that homogeneous stabilizability of homogeneous systems in the case without disturbance is sufficient for the solvability of inverse optimal gain assignment problem for homogeneous systems.