Log-log convexity of an optimal control problem for positive linear systems

This paper investigates the finite-time optimal control problems for positive linear systems with a time-varying control input. Cost functional of the system state is constructed. Under some assumptions on the designed parameters and cost functionals, the optimization problem with piecewise-constant matrix functions is first proved to be log-log convex and can be solved via geometric programming. Then, the log-log convex result is further extended to the optimization problem with continuous functions. Finally, an optimal control problem is investigated to verify the effectiveness of the proposed optimization framework.(c) 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

This paper investigates the finite-time optimal control problems for positive linear systems with a time-varying control input. The optimization problem with piecewise-constant matrix functions is proven to be log-log convex and can be solved via geometric programming. The log-log convex result is further extended to the optimization problem with continuous functions. An optimal control problem is investigated to verify the effectiveness of the proposed optimization framework.