Stochastic constrained control: Trading performance for state constraint feasibility

Abstract

In this paper, we address finite-horizon control for a stochastic linear system subject to constraints on the control and state variables. A control design methodology is proposed where the appropriate trade-off between the minimization of the control cost (performance) and the satisfaction of the state constraints (safety) can be decided by introducing appropriate chance-constrained problems depending on some parameter to be tuned. From an algorithmic viewpoint, a computationally tractable randomized approach to find approximate solutions which are guaranteed to be feasible for the original chanceconstrained problem is proposed. A numerical example concludes the paper.

Scenario MPC for linear time-varying systems with individual chance constraints

“…The basic idea of Scenario MPC is to approximate the state distributions by particles, or 'scenarios'. This idea has been explored in several recent contributions [11]- [15], however not in the light of [16], [17]. The presented results build heavily on the latter work.…”

“…The sampling approach also allows for the inclusion of nonlinear disturbance feedback laws over the prediction horizon [11], [15], [22], without affecting the convexity of the resulting optimization problem.…”

A set based probabilistic approach to threshold design for optimal fault detection

“…As it has been shown in [5,Lemma 4.3], the set of the solutions of (13b) is equivalent to the union of the solution sets of ξ different convex programs, where we recall that 2ξ is the degree of I T (r, θ). The following remark highlights some issues to be addressed in order to extend the theoretical results in [31] and the experimental two-step solution of [32] to the cascade structure of the optimization formulation (13).…”

Energy management of a building cooling system with thermal storage: a randomized solution with feedforward disturbance compensation

“…where T z and s are parameterized in terms ofT z , C z ,s, and C s as in (3) and (4). Let us collect the optimization variables in vector ϑ =…”

“…This rules out "bad" situations adversely affecting the robust approach. Moreover, probabilistic constraints are the only way to avoid unfeasibility of state constraints when the disturbance has unbounded support (see [4] and the references therein). The dark side of the coin is that probabilistic constraints are in general non-convex and more difficult to treat than standard deterministic constraints.…”