Fixed-Order H2-Conic Control

TL;DR

This paper introduces a new iterative convex approximation method for fixed-order H2-conic control design, enabling more flexible controller synthesis for nonlinear systems with uncertain parameters.

Contribution

It reformulates the fixed-order H2-conic control problem as a series of convex problems and proposes a synthesis algorithm with multiple initializations.

Findings

Successfully applied to a passivity-violated system with uncertainties

Achieved improved control performance compared to benchmark designs

Demonstrated convergence of the proposed iterative method

Abstract

H2-conic controller design seeks to minimize the closed-loop H2-norm for a nominal linear system while satisfying the Conic Sector Theorem for nonlinear stability. This problem has only been posed with limited design freedom, as opposed to fixed-order design where all controller parameters except the number of state estimates are free variables. Here, the fixed-order H2-conic design problem is reformulated as a convergent series of convex approximations using iterative convex overbounding. A synthesis algorithm and various initializations are proposed. The synthesis is applied to a passivity-violated system with uncertain parameters and compared to benchmark controller designs.