This book provides the core material for undergraduate courses on optimal control, the modern development that has grown out of the calculus of variations and classical optimization theory.
This book provides the core material for undergraduate courses on optimal control, the modern development that has grown out of the calculus of variations and classical optimization theory.
1: Introduction 1.1: The maxima and minima of functions 1.2: The calculus of variations 1.3: Optimal control Part 2: Optimization in 2.1: Functions of one variable 2.2: Critical points, end-points, and points of discontinuity 2.3: Functions of several variables 2.4: Minimization with constraints 2.5: A geometrical interpretation 2.6: Distinguishing maxima from minima Part 3: The calculus of variations 3.1: Problems in which the end-points are not fixed 3.2: Finding minimizing curves 3.3: Isoperimetric problems 3.4: Sufficiency conditions 3.5: Fields of extremals 3.6: Hilbert's invariant integral 3.7: Semi-fields and the Jacobi condition Part 4: Optimal Control I: Theory 4.1: Introduction 4.2: Control of a simple first-order system 4.3: Systems governed by ordinary differential equations 4.4: The optimal control problem 4.5: The Pontryagin maximum principle 4.6: Optimal control to target curves Part 5: Optimal Control II: Applications 5.1: Time-optimal control of linear systems 5.2: Optimal control to target curves 5.3: Singular controls 5.4: Fuel-optimal controls 5.5: Problems where the cost depends on X (t l) 5.6: Linear systems with quadratic cost 5.7: The steady-state Riccai equation 5.8: The calculus of variations revisited Part 6: Proof of the Maximum Principle of Pontryagin 6.1: Convex sets in 6.2: The linearized state equations 6.3: Behaviour of H on an optimal path 6.4: Sufficiency conditions for optimal control Appendix: Answers and hints for the exercises Bibliography Index
1: Introduction 1.1: The maxima and minima of functions 1.2: The calculus of variations 1.3: Optimal control Part 2: Optimization in 2.1: Functions of one variable 2.2: Critical points, end-points, and points of discontinuity 2.3: Functions of several variables 2.4: Minimization with constraints 2.5: A geometrical interpretation 2.6: Distinguishing maxima from minima Part 3: The calculus of variations 3.1: Problems in which the end-points are not fixed 3.2: Finding minimizing curves 3.3: Isoperimetric problems 3.4: Sufficiency conditions 3.5: Fields of extremals 3.6: Hilbert's invariant integral 3.7: Semi-fields and the Jacobi condition Part 4: Optimal Control I: Theory 4.1: Introduction 4.2: Control of a simple first-order system 4.3: Systems governed by ordinary differential equations 4.4: The optimal control problem 4.5: The Pontryagin maximum principle 4.6: Optimal control to target curves Part 5: Optimal Control II: Applications 5.1: Time-optimal control of linear systems 5.2: Optimal control to target curves 5.3: Singular controls 5.4: Fuel-optimal controls 5.5: Problems where the cost depends on X (t l) 5.6: Linear systems with quadratic cost 5.7: The steady-state Riccai equation 5.8: The calculus of variations revisited Part 6: Proof of the Maximum Principle of Pontryagin 6.1: Convex sets in 6.2: The linearized state equations 6.3: Behaviour of H on an optimal path 6.4: Sufficiency conditions for optimal control Appendix: Answers and hints for the exercises Bibliography Index
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