Decentralized / Distributed Control and Dynamic Systems by Cornelius T. Leondes

By Cornelius T. Leondes

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U. dtl, is is is is -I' i = 1, 2. (107) Let ai s (t) = { zi s (t)f z 0 0 ' Ν Οθ} (108) and ^i s (t) denote the sigma-algebra generated by the informa­ tion set aij3 (t). Further,let Hig denote the classof second- order stochastic processes {u. (t) , t >_ 0 } which are σ. 1 S measurable. I S (·,a . J , j = 11,, 2 J, \, i = 1, 2 , (109) where R. is = I + (a7*b . ) ’q . ( \ 11 1 1 / a T^b . ) . i\ 1 1 1 1 / The decision makers are required to select the matrices * * * F. , Η. , L. , the initial conditions z.

N} are standard Wiener processes inde­ pendent of each other. Each fast subsystem has its own singular perturbation parameter € subsystems through and is weakly coupled to other fast The fast subsystem i is affected by its own control input ui (t) and disturbance input w ^ t ) . The slow subsystem, being the common "core," is affected, in gen­ eral, by all the subsystem controls and disturbances. " For the i-th controller "to neglect all other subsystems" simply means to set all 26 VIKRÄM R. SAKSENA AND TAMER BA§AR € parameters equal to zero, except for at its true value.

T, τ), ri]s ' \ 00 Oi is Oi is/Ti]s ' ' s ( t , fg(j) = τ) = A 0 0 Φs ( t , E η s (t:T ) = τ) , [ z Qs ( t j ) φδ ( τ , I 6j _ 1 ] τ) and = I, n s (t) (138c) s a t is fie s 2 *s = A 00n s + Σ B0 iVi s ( t ' ai>' i= l n s ( 0) = te z 00, 11 j_1 , tj), j + M s (3 )[ys (j) - = l , . . c:. i = 1, 2, where satisfies n , (139) c 0 ns(tj)], + v ±j] j G Θ \ (140) (124) 's(tj ) = E [(z0 s (tj) - T's(tj))(z0 s (tj) - ^ ( S ) ) ’] and Σ (t) s satisfies Σ s = Α λλΣ 00 s + Σ s:A 0 0 + Σ G 0 iG 0 i' i=l Zs (0) = N 0 0 ' W G [tj-l' tj)' j = 1' '·" N ' = ls{^) ~ V ^ V s ^ j ) and M (j) = Σ (t~)c' C nl (t~)cl + S \ J / 0 0 s\ J / 0 > y jL , i=l ys (j) = [yl s (^ C 0 = [C10 Ül l = [ CI l G22 = [ ° y 2 s ( *>] C2o] ' C .

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