When are selector control strategies optimal for constrained monotone systems?

TL;DR

This paper analyzes when selector control strategies are optimal for constrained monotone systems, demonstrating their effectiveness in simplifying control design for systems like battery charging.

Contribution

It identifies conditions under which selector control strategies are optimal for monotone systems with constraints, and shows their practical application in battery health management.

Findings

Optimal solutions are bang-ride, operating on constraint boundaries.

Optimal policies switch between a finite set of state feedback controllers.

Selector control can be designed without perfect models or full state measurements.

Abstract

This paper considers optimal control problems defined by a monotone dynamical system, a monotone cost, and monotone constraints. We identify families of such problems for which the optimal solution is bang-ride, i.e., always operates on the constraint boundaries, and prove that the optimal policy switches between a finite number of state feedback controllers. This motivates the use of simpler policies, such as selector control, that can be designed without perfect models and full state measurements. The approach is successfully applied to several variations of the health-aware fast charging problem for lithium-ion batteries.