On Continuous-Time Infinite Horizon Optimal Control -- Dissipativity, Stability and Transversality

This paper analyzes the interplay between dissipativity and stability properties in continuous-time infinite-horizon Optimal Control Problems (OCPs). We establish several relations between these properties, which culminate in a set of equivalence conditions. Moreover, we investigate the stability of the infinite-horizon optimal adjoint trajectories. The workhorse for our investigations is a notion of strict dissipativity in OCPs, which has been coined in context of economic model predictive control. Furthermore, we show that strict dissipativity provides a conclusive answer to the question of adjoint transversality conditions in infinite-horizon optimal control which has been raised by Halkin in 1974. Put differently, we establish conditions under which the adjoints converge to their optimal steady state value. We draw upon several examples to illustrate our findings. Moreover, we discuss the relation of our findings to existing approaches.