Sub-Optimality of a Dyadic Adaptive Control Architecture

TL;DR

This paper investigates the limitations of a dyadic adaptive control architecture when using LQG-based control laws, providing bounds on its sub-optimality compared to standard control methods.

Contribution

It introduces a framework for analyzing the sub-optimality of dyadic adaptive control with LQG laws and derives analytical bounds for its performance.

Findings

Bounds on sub-optimality of the control law are analytically derived.

The control law's performance is benchmarked against standard LQ and state-dependent Riccati control.

The analysis highlights the conditions under which the control law is near-optimal or sub-optimal.

Abstract

The dyadic adaptive control architecture evolved as a solution to the problem of designing control laws for nonlinear systems with unmatched nonlinearities, disturbances and uncertainties. A salient feature of this framework is its ability to work with infinite as well as finite dimensional systems, and with a wide range of control and adaptive laws. In this paper, we consider the case where a control law based on the linear quadratic regulator theory is employed for designing the control law. We benchmark the closed-loop system against standard linear quadratic control laws as well as those based on the state-dependent Riccati equation. We pose the problem of designing a part of the control law as a Nehari problem. We obtain analytical expressions for the bounds on the sub-optimality of the control law.