
Optimal Control and the Calculus of Variations (Revised)
by Pinch, Enid R-
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Summary
Table of Contents
Introduction | |
The maxima and minima of functions | |
The calculus of variations | |
Optimal control | |
Optimization in | |
Functions of one variable | |
Critical points, end-points, and points of discontinuity | |
Functions of several variables | |
Minimization with constraints | |
A geometrical interpretation | |
Distinguishing maxima from minima | |
The calculus of variations | |
Problems in which the end-points are not fixed | |
Finding minimizing curves | |
Isoperimetric problems | |
Sufficiency conditions | |
Fields of extremals | |
Hilbert's invariant integral | |
Semi-fields and the Jacobi condition | |
Optimal Control I: Theory | |
Introduction | |
Control of a simple first-order system | |
Systems governed by ordinary differential equations | |
The optimal control problem | |
The Pontryagin maximum principle | |
Optimal control to target curves | |
Optimal Control II: Applications | |
Time-optimal control of linear systems | |
Optimal control to target curves | |
Singular controls | |
Fuel-optimal controls | |
Problems where the cost depends on X (t l) | |
Linear systems with quadratic cost | |
The steady-state Riccai equation | |
The calculus of variations revisited | |
Proof of the Maximum Principle of Pontryagin | |
Convex sets in | |
The linearized state equations | |
Behaviour of H on an optimal path | |
Sufficiency conditions for optimal control | |
Table of Contents provided by Publisher. All Rights Reserved. |
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