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Unformatted text preview: MS&E 201 Dynamic Systems Handout #16, Page 1 of 5 Professor Edison Tse June 12th, 2006 Solutions to Quiz #3 1. (a) Rmin Ri (b) dR R dS B dR R dS R dP dR R dT ) ( ) ( ) ( ) ( +- = + = β There are three possibilities: (1) If ) ( > +- dR R dS B β for all R, there is no optimal R that maximizes T(R) because T is always increasing in R (or the optimal R is infinity); (2) If ) ( < +- dR R dS B β for all R, then the optimal R that maximizes T(R) is R min. (3) If ) ( = +- dR R dS B β for some R, then these Rs are the optimal solutions. (c) B β small Rmin Ri B β large R dS/dR R dT/dR MS&E 201 Dynamic Systems Handout #16, Page 2 of 5 Professor Edison Tse June 12th, 2006 (d) Rmin (e) Rmin As you see in the above graph, sudden appearance and disappearance happens even with only smooth variations of the environment. 2. a) The optimal control problem is γ δ δ γ δ γ < ≤ ≤ =-- = =- =- & ; 1 ) ( R R(0) ); ( ) ( )] ( 1 [ ) ( ) ( ); ( ) ( ) ( ) ( . ....
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- Spring '08
- Professor Edison Tse, Systems Professor Edison, Dynamic Systems Professor