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New Algorithms for the Solution
Stochastic Systems with DiscreteValued Disturbances
3 other sections not shown
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 f(xi first-order algorithm given by Equation given in Section Hence initial condition integration interval iteration number Lagrange multiplier Li(xi linear LQP problem McReynolds and Bryson minimize Mitter Monte-Carlo neighborhood nonlinear nonoptimal obtained open-loop control optimal control optimal control problems 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 Taylor series technique terminal error teſt tion Univ unspecified arguments xi+1 yields