An Introduction to Optimal Control Theory, Tema 3Mathematics Research Center, United States Army, University of Wisconsin, 1968 - 153 páginas The report presents an introduction to some of the concepts and results currently popular in optimal control theory. The introduction is intended for someone acquainted with ordinary differential equations and real variables, but with no prior knowledge of control theory. The material covered includes the problems of controllability, controllability using special (e.g., bang-bang) controls, the geometry of linear time optimal processes, general existence of optimal controls, and the Pontryagin maximum principle. (Author). |
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4 | 21 |
matrix | 33 |
CONTROLLABILITY USING SPECIAL CONTROLS | 47 |
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admissible class assume bang-bang controls bang-bang principle bounded C(uk calculus of variations closed set compact set component Consider contains a neighborhood contains an optimal continuous function contradiction control region control steering controllability matrix controllable set convex hull cost functional defined eigenvalues equicontinuous Filippov finite fixed given grad HALKIN Hausdorff metric hence holds hyperplane implies initial point interior interval LEE and MARKUS linear system maximum principle necessary condition NEUSTADT non-zero nonlinear systems optimal control exists optimal control problem optimal half-parabola ordinary differential equations piecewise constant PONTRYAGIN Pontryagin maximum principle Principle of Optimality proof of Theorem prove railroad train example reachable cone reachable set REMARK response ROXIN satisfy SIAM solutions Suppose switch synthesis t₁ t₂ target G Theorem 7.1 u₂ unit cube vector x(t₁ x₁ y²(t zero target