Time-varying optimal control under measurement errors

TL;DR

This paper develops a robust, measurement-error-aware time-varying optimal control method that guarantees stability and accurate tracking, demonstrated on a train model and predator-prey system.

Contribution

It introduces a control algorithm that accounts for measurement errors, providing stability guarantees and a measurement triggering condition.

Findings

The method ensures convergence to zero from a vicinity of the true state.

It derives a measurement accuracy requirement for stability.

The approach is validated on a train acceleration and predator-prey models.

Abstract

Solving optimal control problems to determine a stabilizing controller involves a significant computational effort. Time-varying optimal control provides a remedy by designing a tracking system, given as an ordinary differential equation, to track the solution of the optimal control problem. To improve the applicability of the method, measurement errors are considered in this paper and it is described how these errors influence a control Lyapunov function-based decay condition. As a result of these investigations, input-affine constraints that meet the standard formulation and that describe the set of admissible controls are obtained. The paper also derives a requirement on the necessary measurement accuracy as well as a triggering condition for taking a new measurement. The main theorem combines these results into a robustly stabilizing control algorithm, meaning that all closed-loop trajectories starting in a vicinity around the true state converge to zero. Additionally, the tracking system ensures that the optimal control is tracked at the end of each sampling period. The effectiveness of this approach is demonstrated using a train acceleration model and the well-known predator-prey model.