By Cornelius T. Leondes
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Additional resources for Decentralized / Distributed Control and Dynamic Systems
Sample text
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 ' '