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Lecture on the Calculus of Variations and Optimal Control Theory
Laurence Chisholm Young
Limited preview - 1980
Integration of the EulerLagrange Equation
An Inverse Problem
The Weierstrass Necessary Condition
Jacobis Necessary Condition
Regular Optimal Trajectories
Examples of Extremal Control
adjoint equations admissible control bang-bang bang-bang control belongs calculus of variations class C1 conditions of Theorem consequence Consider the integral continuous function control constraint set corresponding cost function deduce an extremal defined denote derivative desired to transfer Dido's problem differential equation discontinuous Discuss extremal control discussed in Section end conditions end points Euler Euler-Lagrange equation example Exercise exists feasible functions of class furnishes Furthermore given initial global minimum hence illustrated in Figure implies instance interval Jacobi's equation Lagrange equation Lemma linear linearly independent mass flow rate maximize maximum principle minimizing function namely necessary conditions obtain optimal control optimal feedback control optimal trajectory Pareto-optimal piecewise continuous piecewise smooth functions prescribed problem of Section proof regular interior point respect rocket satisfied subinterval sufficiency theorem sufficient conditions suppose switching function switching sequence tangent plane target set terminal transversality condition terminal values time.optimal tions unique vector weak local minimum Weierstrass zero
Page 307 - PONTRYAGIN, LS, BOLTYANSKII, VG, GAMKRELIDZE, RV and MlSHCHENKO, EF, The Mathematical Theory of Optimal Processes...
Page 302 - On a Class of Variational Problems in Rocket Flight, " Journal of the Aerospace Sciences, Vol.
Page 302 - LS Pontryagin's maximum principle and optimal programming of rocket thrust.
Page 307 - Tabak, D., and Kuo, BC, Optimal Control by Mathematical Programming, Prentice-Hall, Englewood Cliffs, NJ, 1971.
Page 304 - Stadler, W. , Natural structural shapes of shallow arches, J. Appl. Mech. Trans. ASME, 44, 2 (1977) 291-298.
Page 305 - Bryson, AE, Jr. and Ho, YC, Applied Optimal Control. Blaisdell Publishing Company, Waltham, Massachusetts, 1969.