Analysis, Control and Optimization of Complex Dynamic by El-Kébir Boukas, Roland P. Malhamé

By El-Kébir Boukas, Roland P. Malhamé

Research, keep an eye on and Optimization of advanced Dynamic structures gathers in one quantity a spectrum of advanced dynamic platforms similar papers written by way of specialists of their fields, and strongly consultant of present study traits. complicated structures current very important demanding situations, in nice half because of their sheer dimension which makes it tricky to know their dynamic habit, optimize their operations, or examine their reliability. but, we are living in a global the place, as a result of expanding inter-dependencies and networking of platforms, complexity has turn into the norm. With this in brain, the amount includes elements. the 1st half is devoted to a spectrum of advanced difficulties of selection and regulate encountered within the region of construction and stock platforms. the second one half is devoted to massive scale or multi-agent procedure difficulties taking place in different parts of engineering akin to telecommunication and electrical strength networks, in addition to extra customary context.

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1972). Stochastic Differential Equations. Springer Verlag, Berlin, Germany. Karlin, S. and Fabens, A. (1960). The ( s , S ) inventory model under Markovian demand process. In: Mathematical Methods in the Social Sciences (K. Arrow, S. Karlin, and P. ), pp. 159-175, Stanford University Press, Stanford, CA. Ozekici, S. and Parlar, M. (1999). Inventory models with unreliable suppliers in random environment. Annals of Operations Research, 91:123136. Scarf, H. (1960). The Optimality of (s,S) Policies in the Dynamic Inventory Problem.

4 Assume (A1) -(A9). 7. The stationary feedback strategy U* = (u*,u*,. . ) defined bv is average optimal. 6. Concluding remarks In this paper we have carried out a rigorous analysis of the average cost stochastic inventory problem with Markovian demand, fixed ordering cost and lost sales. We have proved a verification theorem for the average cost optimality equation, which we have used to establish the existence of an optimal state-dependent ( s , S)-policy. Throughout the analysis, we have assumed that the inventory and shortage cost functions are of linear growth.

Therefore, 16 ANALYSIS, CONTROL, AND OPTIMIZATION This completes the proof. 2 Let Assumptions (A1)-(A9) hold. ) such that (1 - ak)vak(i,x) --+ A* and w,,(i, x) w*(i,x), locally uniformly in x and i as k goes to infinity. Moreover, (A*,w*) satisfies the average cost optimality equation w(i, x) + A = f ( i ,x) + 2120 inf {c(i, u) + Eq(i, x + u - 6') + F(w)(i,x + u)). 17) Proof. ) is locally equi-Lipschitzian for a 2 ao, and therefore it is uniformly continuous in any finite interval. 5, (1 a)v, (1,O) is uniformly bounded.

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