A Numerical Investigation of Extremum-Seeking-Based Command Generation for Adaptively Controlled Systems

TL;DR

This paper presents a numerical study of an adaptive control framework combining extremum-seeking command generation with predictive adaptive control, enhancing system stabilization, command following, and disturbance rejection.

Contribution

It introduces a novel ECG/PCAC framework that integrates command optimization with system identification and online control in a unified approach.

Findings

ECG/PCAC effectively stabilizes systems and tracks commands.

The framework improves disturbance rejection capabilities.

Numerical results demonstrate the approach's robustness and adaptability.

Abstract

We develop an adaptive feedback control technique that combines an extremum-seeking-based command generator (ECG) with indirect adaptive control. In particular, ECG is used to generate commands that asymptotically optimize a cost function that is measured but whose functional form is unknown. For feedback control with command following and stabilization, the present paper combines ECG with predictive cost adaptive control (PCAC), which is an indirect adaptive control extension of model predictive control (MPC). PCAC extends generalized predictive control (GPC) by using quadratic programming to enforce output constraints and recursive least squares (RLS) with variable-rate forgetting (VRF) for system identification. The resulting ECG/PCAC framework combines command generation with closed-loop system identification and online optimization. The contribution of this paper is a numerical investigation of ECG/PCAC for adaptive stabilization, command following, and disturbance rejection