By R. Neck
This quantity comprises papers awarded on the IFAC symposium on Modeling and keep watch over of monetary platforms (SME 2001), which used to be held on the collage of Klagenfurt, Austria. The symposium introduced jointly scientists and clients to discover present theoretical advancements of modeling recommendations for financial platforms. It incorporates a portion of plenary, invited and contributed papers offered on the SME 2001 symposium. The papers awarded during this quantity replicate advances either in method and in purposes within the quarter of modeling and keep watch over of financial systems. Read more...
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Extra info for Modeling and Control of Economic Systems 2001. A Proceedings volume from the 10th IFAC Symposium, Klagenfurt, Austria, 6 – 8 September 2001
A symmetric solution XI - X T of the standard algebraic Rieeati equation (ARE(IE1)) The function A1 is independent of U 1 (if and) only if Q1 - 0, L1 - 0, but this is equivalent with ARE(E1) having a (stabilizing) solution. 4 Unique Nash equilibrium via the value function approach U* -- - t ~ I B T ( Ei z* "Jr-"~i ) and x*, Ai given by the solution of (19). It has to be considered that both players try to minimize their costs at the same time. Again one needs a stabilizing solution to ARE(Ei) to exist with Ri~ invertible.
Ba~ar, T. J. Olsder (1995). Dynamic Noncooperative Game Theory. 2 ed. Academic Press. London. A. M. Schumacher (2000). Feedback Nash equilibria in uncertain infinite time horizon differential games. In: Proceedings of MTNS 2000. W. (1989). Structure of Linear-Quadratic Control. PhD thesis. Eindhoven University of Technology. W. J. Hautus (1990). The outputstabilizable subspace and linear optimal control. In: Progress in Systems and Control Theory. Birkh~iuser. Boston. pp. 133-120. Nash, J. (1951).
2 -- Az /~1 - - Q l x ul - L~'x + B l U l + B 2 u 2 , x(0) - Xo -ATA1 -Llul - Mlu2 (16) +B~'Aj -k-R111t1 + NlU2 9 is called the Hamilton subsystem HSS(]E1) associated with the Popov triplet E a. 5. VALUE FUNCTION APPROACH 1... Now, introduce an equivalence relation for subsystems. To save indices this is representatively done for player 1. Proposition 17. Let E1 and E1 be two (X1, F 1)equivalent Popov triplets. And let HSS(21) and HSS (21) be the associated Hamilton subsystems, then ( u l , x , A1) annihilates the output of the HSS(21) if and only if (ul - F i x , x, "~1 -- X l z ) annihilates the output of H S S ( 2 1 ) , where u2 is the same in both systems.