The plant mode will be assumed Perfectly measurable throughout the note and for the plant state, a noisy observation channel is introduced as M. MARITON
dy=C(r(t))xdt+G(x(t), r(t))dw,+H(r(t))dos (3)Abs@acf-Jump linear systems are considered in a random environment where y E RP is the observation vector. Again matrices C, G , and H where they are subject to additive and multiplicative noises. Stochastic have appropriate dimensions and w4, u5 are independent Wiener processes notions of stabilizability and detectability are introduced to characterize in Rn4 and Rns which are also independent of wI, w 2 , and og. the asymptotic behavior of the optimal jump linear quadratic Gaussian Investigations are limited to the case where D, E, and G have the regulator and a dual Kalman fiiter. following form:
SUMMARYMany applications of optimization theory require the solution of a set of coupled Riccati equations. In multi-person-games problems, the players' decision for the Nash equilibrium depend on Riccati equations coupled through their quadratic terms. Another example is provided by linear-quadratic control. When the system is subject to sudden and random changes in parameter values, the optimal feedback is computed from the solution of Riccati equations coupled through their weighting terms. After recalling the principle of homotopy methods, it is shown how it generates a new and efficient algorithm for this class of problem. An illustrative example is given.
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