Optimal Steady-State Control for Linear Time-Invariant Systems

TL;DR

This paper presents a feedback control design for linear systems that ensures steady-state optimality of input and output variables with respect to a convex optimization problem, even under unknown disturbances.

Contribution

It introduces a novel control approach that enforces KKT conditions at steady-state without using dual variables, providing stability and optimality guarantees.

Findings

The proposed controller achieves optimal steady-state input and output.

The method stabilizes the system while satisfying optimality conditions.

Simulations demonstrate effectiveness in simple examples.

Abstract

We consider the problem of designing a feedback controller that guides the input and output of a linear time-invariant system to a minimizer of a convex optimization problem. The system is subject to an unknown disturbance that determines the feasible set defined by the system equilibrium constraints. Our proposed design enforces the Karush-Kuhn-Tucker optimality conditions in steady-state without incorporating dual variables into the controller. We prove that the input and output variables achieve optimality in equilibrium and outline two procedures for designing controllers that stabilize the closed-loop system. We explore key ideas through simple examples and simulations.