Generating a robustly stabilizable class of nonlinear systems for the converse optimality problem

TL;DR

This paper extends converse optimality theory to affine nonlinear systems with disturbances, providing conditions for robust stabilizability and a design method for systems that are both stabilizable and globally asymptotically stable.

Contribution

It introduces a robust stabilizability condition using inverse optimality and develops a design framework for a class of nonlinear systems with disturbances.

Findings

Established a robust stabilizability condition for affine systems with disturbances.

Designed a nonlinear system class that is both robustly stabilizable and globally asymptotically stable.

Validated the theory with a case study.

Abstract

Converse optimality theory addresses an optimal control problem conversely where the system is unknown and the value function is chosen. Previous work treated this problem both in continuous and discrete time and non-extensively considered disturbances. In this paper, the converse optimality theory is extended to the class of affine systems with disturbances in continuous time while considering norm constraints on both control inputs and disturbances. The admissibility theorem and the design of the internal dynamics model are generalized in this context. A robust stabilizability condition is added for the initial converse optimality probelm using inverse optimality tool: the robust control Lyapunov function. A design for nonlinear class of systems that are both robustly stabilizable and globally asymptotically stable in open loop is obtained. A case study illustrates the presented theory.