Optimal synthesis for a class of L $\infty$ optimal control problems in the plane with L 1 constraint on the input

TL;DR

This paper derives optimal control strategies for linear planar systems with L1 input constraints, generalizing previous epidemiological results to broader biological models using novel mathematical techniques.

Contribution

It introduces a new optimal synthesis method for L-infinity control problems with L1 constraints in planar systems, expanding previous epidemiological findings.

Findings

Feedback strategy 'null-singular null' is optimal under L1 constraints.

Optimal cost as a function of the control budget is characterized.

Results apply to various biological models beyond epidemiology.

Abstract

For a particular class of planar dynamics that are linear with respect to the control variable, we show that the feedback strategy ''null-singular null'' is minimizing the maximum of a coordinate over infinite horizon, under a L 1 budget constraint on the control. Moreover, we characterize the optimal cost as a function of the budget. The proof is based on an unusual use of the clock form. This result generalizes the one obtained formerly for the SIR epidemiological model to more general Kolmogorov dynamics, that we illustrate on other biological models.