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New Algorithms for the Solution of a Class
New Algorithms for the Solution
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antithetic variate method applied assume bang-bang control problems Bellman boundary conditions calculate Calculus of Variations change in cost Chapter consider continuous-time system control function control law cost function D. H. Jacobson D. Q. Mayne defined denote determining deterministic difference equations differential dynamic programming differential equations discrete-time discrete-time system Equa error estimate first-order algorithm given by Equation given in Section Hence integration interval t0 iteration number Lagrange multiplier linear LQP problem McReynolds and Bryson minimize Mitter Monte-Carlo neighborhood nominal trajectory nonlinear nonoptimal obtained open-loop control optimal control optimal control problems optimal cost optimal trajectory parameters partial derivatives positive-definite random variables realizations reduction in cost respect Riccati equation satisfied second-order algorithm second-variation sequence side of Equation Sufficient conditions sufficiently small switch point t e t0 Taylor series technique terminal error tion Univ unspecified arguments Vx;t xi+1 yields