Control and Dynamic Systems: Advances in Theory and by Cornelius T. Leondes

By Cornelius T. Leondes

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The set of admissible decentralized controls Ω is defined by Ω = { u ^ i , y 1 (Nk)], Uj[i, y_. (Nk) ] , . , u M [i, y M(Nk) ]} (1) r. 1 such that u, G R - for j = 1, ... , M and U j [i, ( N k ) ] = Cj(i)yj(Nk), yj i = Nk, Nk + 1, k = [N(k + 1 ) - 1 ] , (2) J^Qf kQ + 1, ···, where Ν _> 1 is a fixed integer that determines the frequency at which the output is sampled. (i) are allowed to vary at discrete instants of time between output measurements. Associated with each controller j is a quadratic cost function Jj[[u x, Uj, u M , i, x[N(k + 1)]], which is defined over the interval Nk £ i < N(k + 1 ) , for k = k n , k n + 1, ALBERT B.

The rest of the theorem follows from Theorem 3 and Lemma 2. Now, Theorem 4 characterizes the optimal strategy for agent 2 1 for any arbitrary strategy γ of agent 2. In particular. Theorem 4 holds for the optimal strategy of agent 2. Similarly, DISTRIBUTED E S T I M A T I O N FOR LARGE-SCALE EVENT-DRIVEN S Y S T E M S E{J(l,s2; I Fig. 6. 35 2) + c t 2 f ( T ) | s = 2 } a»(t) ßl(t) 1 Optimal strategy for agent 1. a reciprocal argument establishes that the optimal strategy for 2 2 agent 2 can be determined using thresholds α (t), $ (t) as in Theorem 4.

PATTIPATI and N. R. , "A Unified View of State Estimation in Switching Environments," American Control Conference, San Francisco, California, pp. 458-465, June 1983. 8. A. A. B. PRITSKER and C. D. PEGDEN, "Introduction to Simulations and SLAM," Halsted, New York, 1979. 9. A. N. SHIRYAYEV, "Statistical Sequential Analysis," Translations of Mathematical Monographs, American Mathematical Society, 38, 1973. 10. D. T. MAGILL, "Optimal Adaptive Estimation of Sampled Processes," IEEE Trans. Autom. Control AC-10 (1965).

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