Enid R. Pinch
Optimal Control and the Calculus of Variations
Enid R. Pinch
Optimal Control and the Calculus of Variations
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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.
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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.
Produktdetails
- Produktdetails
- Verlag: OUP Oxford
- Seitenzahl: 244
- Erscheinungstermin: 7. September 1995
- Englisch
- Abmessung: 234mm x 156mm x 13mm
- Gewicht: 377g
- ISBN-13: 9780198514893
- ISBN-10: 0198514891
- Artikelnr.: 22099707
- Herstellerkennzeichnung
- Libri GmbH
- Europaallee 1
- 36244 Bad Hersfeld
- gpsr@libri.de
- Verlag: OUP Oxford
- Seitenzahl: 244
- Erscheinungstermin: 7. September 1995
- Englisch
- Abmessung: 234mm x 156mm x 13mm
- Gewicht: 377g
- ISBN-13: 9780198514893
- ISBN-10: 0198514891
- Artikelnr.: 22099707
- Herstellerkennzeichnung
- Libri GmbH
- Europaallee 1
- 36244 Bad Hersfeld
- gpsr@libri.de
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
1.1: 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
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