Closed-form H-infinity optimal control for a class of infinite-dimensional systems

Abstract

We address a class of systems for which the solution to an H-infinity optimal control problem can be given on a very simple closed form. In fact, both the control law and optimal performance value are explicitly given. The class of systems include models for large-scale systems such as temperature dynamics in buildings, buffer networks and transportations systems. Furthermore, the structure of the control law is suitable for distributed control of such large-scale systems, which is illustrated through examples. * C. Bergeling, R. Pates and A. Rantzer are with the

On the Optimal Control of Relaxation Systems

“…Therefore given any stabilisingK 0, the worst case disturbance is of the form in eq. (8). Therefore the controller in 1) is not only optimal over all disturbances in W ∞ Q , but also over all in W Q , and therefore solves Problem 1.…”

“…Our main contribution is to show that the same inherent structure in the realisations of relaxations systems can be exploited to solve two optimal control problems analytically. In particular we build on the techniques in [8] to show that if the system with dynamics ŷ (s) = G (s) û (s) is of the relaxation type, then the control law…”

H-Infinity Optimal Control for Systems With a Bottleneck Frequency

“…Remark 3: It holds that F l (G, K) T ∞ = F l (G, K) ∞ , where F l (G, K) T is the dual system to F l (G, K), see [2, p. 34]. Hence, the synthesis for the dual to ( 13) is also covered by Theorem 2, see [30] for an interpretation of this problem. Moreover, it is possible to add alternative weight matrices on the regulated output z and still be able to explicitly solve the minimization problem, see [26,Rem.…”

“…Moreover, it is possible to add alternative weight matrices on the regulated output z and still be able to explicitly solve the minimization problem, see [26,Rem. 1] as well as [30].…”