By Tamer Basar, Pierre Bernhard
This e-book is dedicated to 1 of the quickest constructing fields in smooth keep an eye on idea - the so-called H-infinity optimum regulate idea. The ebook can be utilized for a moment or 3rd 12 months graduate point path within the topic, and researchers operating within the zone will locate the ebook priceless as a customary reference. primarily based on contemporary paintings of the authors, the publication is written on an exceptional mathematical point. Many leads to it are unique, attention-grabbing, and inspirational. the subject is primary to trendy keep watch over and therefore this definitive e-book is very instructed to a person who needs to meet up with vital theoretical advancements in utilized arithmetic and control.
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Additional info for H-infinity Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach (Systems & Control)
Then, necessarily, they are representations of each other. Proof. It follows from the ordered interchangeability property of multi- ple saddle points (cf. 1) that (jJ, II") is also a saddle-point pair. e. J(J-I,II*)) over M, and hence are representations of each other. A symmetrical argument shows that II" and iI are also representations of each other, thus completing the proof. o Faced with the possibility of existence of multiple saddle-point equilibria in dynamic games when (at least one of) the players have access to Chapter 2 22 dynamic (such as CLPS, or CLlS) information,2 a natural question to ask is whether one can refine the notion of a saddle-point soiution further, so as to ensure unicity of equilibria.
If 6We will shortly see that this is true also for the infinite-horizon case. 48 Chapter 3 a "mixed" [2 policy for the disturbance, which features a discrete distribution. 1). 4. 31) k=l and with the initial state taken to be Xl = O. 34) This, of course, in itself is meaningless since for the problem at hand Xl = O. 887651. 35). This is unique up to a normalization constant, which is determined by the energy bound b. 27),. with P = 0) ILr = O. 39) where ~ is as defined above. For a different (more direct) method to obtain the solution above, see .
1): P2 < (r - 1)(2r2 - 4r + 1) (2r -1)2 . 2 indeed provides the least stringent condition on the parameter r. 98218 . Note the degradation in the concavity condition due to loss in the informa- • tion available to the players (particularly, Player 1). For comparison purposes, let us also compute the bound on r under the simpler (no-memory) sThis boWld is the largest root of the polynomial 13s 3 - 1952 + 8s - 1. 31768 which is (as expected) the most stringent of the three. 2. 26a) where 'Y. 2a).
H-infinity Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach (Systems & Control) by Tamer Basar, Pierre Bernhard