Output Feedback Design for Parameter Varying Systems subject to Persistent Disturbances and Control Rate Constraints

TL;DR

This paper develops a robust output feedback control method for constrained parameter-varying systems with persistent disturbances, ensuring bounded trajectories and satisfying control and state constraints through invariant sets.

Contribution

It introduces an incremental control law using algebraic conditions and bilinear optimization to handle constraints and disturbances in parameter-varying systems.

Findings

Ensures trajectories remain bounded despite disturbances.

Provides a systematic way to design controllers satisfying multiple constraints.

Demonstrates effectiveness through numerical examples.

Abstract

This paper presents a technique for designing output feedback controllers for constrained linear parameter-varying systems that are subject to persistent disturbances. Specifically, we develop an incremental parameter-varying output feedback control law to address control rate constraints, as well as state and control amplitude constraints. The proposal is based on the concept of robust positively invariant sets and applies the extended Farkas' lemma to derive a set of algebraic conditions that define both the control gains and a robust positively invariant polyhedron that satisfies the control and state constraints. These algebraic conditions are formulated into a bilinear optimization problem aimed at determining the output feedback gains and the associated polyedral robust positively invariant region. The obtained controller ensures that any closed-loop trajectory originating from the polyhedron converges to another smaller inner polyhedral set around the origin in finite time, where the trajectory remains ultimately bounded regardless of the persistent disturbances and variations in system parameters. Furthermore, by including the sizes of the two polyhedral sets inside the objective function, the proposed optimization can also jointly enlarge the outer set while minimizing the inner one. Numerical examples are presented to demonstrate the effectiveness of our proposal in managing the specified constraints, disturbances, and parameter variations.