Constrained infinite-time quadratic optimal control: the linear stochastic and nonlinear deterministic cases

In this work, we study the infinite-time quadratic optimal control problem for linear stochastic and nonlinear deterministic systems with input constraints (CITLSQOC, CITNDQOC). First, we develop conditions under which separability and certainty equivalence hold for the CITLSQOC problem. Necessary and sufficient conditions are presented for the existence of optimal solutions, and global closed-loop stability is shown to be guaranteed for both the full state information and the partial state information cases. Finally, the CITNDQOC problem is shown to be equivalent to a finite-time problem for all constrained stabilizable initial conditions and to yield a stabilizing feedback law.