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Lectur27 - Lecture XXVII Application of Optimal Control to...

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Lecture XXVII Application of Optimal Control to Fisheries I. One application of deterministic optimal control is the optimal harvest problem found in Clark, Collin W. Mathematical Bioeconomics (New York: John Wiley & Sons, Inc. 1990). A. Writing the basic resource problem as: ( 29 max ( ) ( ) max e pqx c E dt st d x d t F x q E x E t E t - - = - δ 0 0 The Hamiltonian can then be written as: ( 29 [ ] ( 29 [ ] H e pqx c E F x q E x e pqx c qx E F x t = - + - = - - + - - δ δ λ λ λ ( ) ( ) This yields a control problem with a single control variable, E (effort). B. The Pontryagin conditions then become: 1. The optimality condition: ( 29 0 2 = = - - = - = - -
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  • Fall '08
  • Moss
  • dt, deterministic optimal control, Optimal Control to Fisheries, optimal harvest problem, W. Mathematical Bioeconomics

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