Dissipativity properties in constrained optimal control: A computational approach Abstract   In this paper, we consider discretetime nonlinear optimal control problems with possibly nonconvex cost subject to constraints on states and inputs. For these problems, we present a computational approach for the verification of strict dissipativity properties, which have recently been employed to study optimal system operation, turnpike phenomena, and closedloop properties of economic model predictive control schemes. Based on a nonstrict dissipation inequality, we provide necessary and sufficient conditions for strict dissipativity by explicitly computing the set w.r.t. which the system is strictly dissipative as well as the corresponding storage function. We focus on strict dissipativity w.r.t. periodic orbits and steadystates, being the most relevant cases of strict dissipativity, although our approach can be directly extended to strict dissipativity w.r.t. more general sets. For polynomial optimal control problems, the presented approach leads to a polynomial optimization problem, which is solved via sumofsquares programming. The optimal periodic orbit can then be constructed, without a priori knowledge of its period length, as the set of points for which a suitable nonstrict dissipation inequality holds with equality. In addition, we consider the important special case of indefinite linear quadratic optimal control problems subject to quadratic constraints, for which an optimal periodic orbit resulting from our construction is always located on the boundary of the constraint set.

Optimality conditions for optimal impulsive control problems with multipoint state constraints This paper addresses an optimal impulsive control problem whose trajectories are functions of bounded variation and impulsive controls are regular vector measures. This problem is characterized by two main features. First, the dynamical control system to be considered may not possess the socalled wellposedness property. Second, the constraints on the onesided limits of states are presented. Such constraints are interpreted as multipoint state constraints. For this problem, we derive global optimality conditions based on using of compound Lyapunov type functions which possess strongly monotone properties with respect to the control system. As a motivating case, a model of advertising expenses optimization for mutually complementary products is considered. For this model, we propose four variants of resolving sets of Lyapunov type functions and explain the technique of applying the optimality conditions.