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

By El-Kébir Boukas, Roland P. Malhamé

Research, regulate and Optimization of advanced Dynamic structures gathers in one quantity a spectrum of advanced dynamic platforms similar papers written by means of specialists of their fields, and strongly consultant of present study tendencies. advanced platforms current very important demanding situations, in nice half because of their sheer dimension which makes it tough to know their dynamic habit, optimize their operations, or research their reliability. but, we are living in an international the place, because of expanding inter-dependencies and networking of structures, complexity has turn into the norm. With this in brain, the quantity contains components. the 1st half is devoted to a spectrum of complicated difficulties of determination and keep watch over encountered within the region of creation and stock structures. the second one half is devoted to giant scale or multi-agent approach difficulties happening in different parts of engineering comparable to telecommunication and electrical strength networks, in addition to extra customary context.

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3). Then u*(x, a ) is optimal; see Bertsekas (1987). 3). It is therefore difficult to solve these equations. In the rest of the paper, we study an approximate optimal scheme that requires solving simpler problems and yields near 46 ANALYSIS, CONTROL, AND OPTIMIZATION optimal controls. Let us give two examples as special cases to the general model. 1 (SINGLE-MACHINE SYSTEM)Consider a production system with one machine producing one part type. Let ck E {0,1) denote the machine state where 1 means the machine is up with maximum capacity 1 and 0 means that the machine is down.

In these references, both stochastic and deterministic models have been proposed to handle the production planning and/or maintenance. Different approaches have been used t o tackle production planning, such as,dynamic programming, linear programming, queuing theory, Petri nets, etc. In this paper we will deal only with deterministic production systems and we will depart considerably from previous research by showing how piecewise-affine control theory can be used to handle production planning of switched production systems.

Uo,ul, . ) denote the control sequence. We consider the cost function where y > 0 is a constant and G(x, a , u ) is bounded and Lipschitz in (x, u) for each a E M . The objective is to choose u. to minimize J E . We use the DP approach to solve the problem. ). 3). Then u*(x, a ) is optimal; see Bertsekas (1987). 3). It is therefore difficult to solve these equations. In the rest of the paper, we study an approximate optimal scheme that requires solving simpler problems and yields near 46 ANALYSIS, CONTROL, AND OPTIMIZATION optimal controls.

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