cw562194_Numerical solutions to infinite time control problem_upload

Cw562194_Numerical solutions to infinite time control problem_upload

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Numerical solutions to an infinite time control problem May 25, 2007 Prof. Edison Tse Kihoon Kim - Do Not Distribute
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Agenda ± Discounted, infinite-horizon optimal control problem ± Numerical Approach (using bvp4c of Matlab) ± Example: public knowledge-sharing network (i.e. Yahoo Answers!)
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Infinite horizon, discounted optimal control problem ± Problem formulation Max J = subject to ± Current-value Hamiltonian: ± Optimality Conditions 1) Control variables should maximize a Hamiltonian: u*(t) =argmax H 2) Differential equations: 3) Boundary conditions: (,, ) (,) (,) T H xu lxu f xu λλ =+ T rt dt u x l e 0 ) , ( 0 ) 0 ( ); , ( x x u x f dt dx = = () ; ( , ) dt H d x rt f x u dt x t dt λ =− = 0 (0) ; lim ( ) 0 rt t xx e t −>∞ = = Question: What is the meaning of lambda(t)?
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Numerical Solutions: Preparation 1) Find u* that maximizes H: 2) Derive differential equations for costate variables ( ) 3) Substitute u* into state and costate differential equations 4) Write down two m-files that describes differential equations and boundary conditions 0 H u = λ () dt H rt x t
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Cw562194_Numerical solutions to infinite time control problem_upload

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