On continuoustime constrained stochastic linearxe2x80x93quadratic control Abstract   This paper studies a class of continuoustime scalarstate stochastic Linearxe2x80x93Quadratic (LQ) optimal control problems with the linear control constraints. Using the state separation theorem induced from its special structure, we derive the analytical solution for this class of problems. The revealed optimal control policy is a piecewise affine function of system state. This control policy can be computed efficiently by solving two Riccati equations offline. Under some mild conditions, the stationary optimal control policy can be also achieved for this class of problems over an infinite horizon. Examples are presented to shed light on the theoretical results established.

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.