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 complicated dynamic platforms similar papers written by means of specialists of their fields, and strongly consultant of present learn tendencies. complicated structures current vital demanding situations, in nice half as a result of their sheer dimension which makes it tricky to understand their dynamic habit, optimize their operations, or examine their reliability. but, we are living in an international the place, as a result of expanding inter-dependencies and networking of platforms, complexity has turn into the norm. With this in brain, the quantity contains components. the 1st half is devoted to a spectrum of advanced difficulties of determination and keep watch over encountered within the quarter of creation and stock structures. the second one half is devoted to massive scale or multi-agent method difficulties taking place in different parts of engineering corresponding to telecommunication and electrical energy networks, in addition to extra standard context.

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5). From a practical point of view, the controller that quadratically stabilizes the system and at the same time guarantees the maximum disturbance rejection is of great interest. 36). 23) and simultaneously guarantees the smallest disturbance rejection level. 1 Let v > 0, X > 0, Yl, and Y2 be the solution of the optimization problem P . 24) with Ki= Y , X - ' , i = 1 , 2 quadratically stabilizes the class of production systems we are considering and moreover the closed-loop system satisfies a disturbance rejection level of fi.

5 (JOHANSSON (2003)) Let x ( t ) E X be an absolutely continuous function. 21) on [to,tf] if,for almost all t E [to,tf] and Lebesgue measurable u ( t ) , w(t), the equation ~ ( t=)A i x ( t ) bi Biu(t) BWiw(t)holds for ~ ( tE )Ri. + + + Finally, the following result establishes global uniform (where uniform means for any switching) exponential stability of a homogeneous switched linear system (therefore, including piecewise-linear systems) when a globally quadratic Lyapunov function can be found.

2 that ( 1 - ak)v,, ( i ,x ) 4 A* on a subsequence {ak}& converging to one. Thus, there exists an a < 1 such that which contradicts the definition of the value function v,(i, x ) . 5. 17). A n admissible strategy U = (uo,u l , . . I E I , 2 0 and for each initial 1 lim -E ( w ( i k ,zk))= 0 , k -k ~ ~ 18 ANALYSIS, CONTROL, AND OPTIMIZATION where xk is the inventory level in period k corresponding to the initial state (i,x) and the strategy U. 7 Assume (A1)-(A9). 2. Furthermore, the stationary feedback strategy U* = (u*,u*, .

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