Dissipativity in Infinite-Horizon Optimal Control: Willems' 1971 Paper Revisited

Jan Willems introduced the system-theoretic notion of dissipativity in his foundational two-part paper which appeared in the Archive of Rational Mechanics and Analysis in 1972. Even earlier, in a likewise pivotal 1971 IEEE Transactions on Automatic Control paper, he investigated infinite-horizon least-squares optimal control and the algebraic Riccati equation from a dissipativity point of view. This note revisits infinite-horizon optimal control leveraging strict dissipativity. We discuss the interplay between dissipativity and stability properties in continuous-time infinite-horizon problems without assuming linear dynamics or quadratic cost functions. Finally, we compare our recent results from Faulwasser and Kellett (2021) to the original findings of Willems (1971). Copyright (C) 2022 The Authors.

Automated summary

This paper revisits the problem of continuous-time infinite-horizon optimal control and investigates the interplay between dissipativity and stability properties. By comparing the original findings of Jan Willems in 1972 with recent research results, further investigation is conducted.