Computational Analysis of Control Systems Using Dynamic Optimization

TL;DR

This paper introduces a computational dynamic optimization approach to analyze key control system properties like observability, reachability, and robustness for both linear and nonlinear systems, including PDEs.

Contribution

It develops a unified computational framework for assessing observability, reachability, and robustness in complex control systems using dynamic optimization techniques.

Findings

Defined measures for observability and reachability applicable to complex systems

Computed $L^2$-gain for nonlinear control systems

Analyzed partial observability and strong vs. weak observability

Abstract

Several concepts on the measure of observability, reachability, and robustness are defined and illustrated for both linear and nonlinear control systems. Defined by using computational dynamic optimization, these concepts are applicable to a wide spectrum of problems. Some questions addressed include the observability based on user-information, the determination of strong observability vs. weak observability, partial observability of complex systems, the computation of $L^2$-gain for nonlinear control systems, and the measure of reachability in the presence of state constraints. Examples on dynamic systems defined by both ordinary and partial differential equations are shown.