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

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By El-Kébir Boukas, Roland P. Malhamé

Research, regulate and Optimization of advanced Dynamic platforms gathers in one quantity a spectrum of advanced dynamic platforms comparable papers written through specialists of their fields, and strongly consultant of present learn developments. complicated platforms current very important demanding situations, in nice half because of their sheer measurement which makes it tricky to know their dynamic habit, optimize their operations, or research their reliability. but, we are living in a global the place, as a result of expanding inter-dependencies and networking of structures, complexity has develop into the norm. With this in brain, the amount contains components. the 1st half is devoted to a spectrum of advanced difficulties of choice and keep an eye on encountered within the quarter of construction and stock structures. the second one half is devoted to massive scale or multi-agent procedure difficulties taking place in different parts of engineering resembling telecommunication and electrical energy networks, in addition to extra universal context.

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This work develops asymptotically optimal production planning strategies for a class of discrete-time manufacturing systems. To reflect uncertainty, finite-state Markov chains are used in the formulation. The state space of the underlying Markov chain is decomposed into a number of recurrent classes and a group of transient states. Using a hierarchical control approach, by aggregating the states in each recurrent class into a single state, a continuous-time limit control problem in which the resulting limit Markov chain has much smaller state space is derived.

A. 8) where ( A 1 ,. . ,A') denotes a block diagonal matrix having matrix entries A 1 , . . , A 1 , and --- ( m l ,' . ,ml ) E I W ( ~ - ~ * ) ~ ~ . > It is easy to check that Q , is a generator. Let a ( . )= { a ( t ) :t 0 ) be a continuous-time Markov chain generated by Q,. The state space of a ( . ) is M = { I , . . , l } . Let 5 be a random variable uniformly distributed on [O, 11 that is independent of {a;). For each j = 1,.. )and a " ( . ) as aE(t)= a; and a" ( t )= a;, for t E [ne, n~ + E).

3 Let y be a positive constant. 24) with Ki = KX-', i = 1 , 2 is stable and moreover the closed-loop system satisfies the disturbance rejection level of y > 0. 5) that must always be satisfied. Extra constraints should then be added to the previous system of LMIs to force the control law to always satisfy the bounds. For this purpose, we note first that when the initial condition is known (which is the case in our problem), we can add the constraint x ~ X - ' x o 5 1, which using Schur complement leads to the LMI 2 Inventory Control of Switched Production Systems: LMI Approach 35 Since the Lyapunov function is V = xTx-'x, and the level sets of the Lyapunov function are invariant sets for the system trajectories, this LMI guarantees not only that the initial state is inside the set but also that x(t) E 9 , Vt 2 0.

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