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Solving optimal control problems by means of general Lagrange functionals. (English) Zbl 1049.49501

Summary: The method of Lagrange functionals is applied to the optimal control of systems with quadratic and implicit dynamics.

MSC:

49N10 Linear-quadratic optimal control problems
49K15 Optimality conditions for problems involving ordinary differential equations
49M37 Numerical methods based on nonlinear programming
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[1] Bender, D. J.; Laub, A. J., The linear-quadratic optimal regulator for descriptor systems, IEEE Transactions on Automatic Control, 32, 672-688 (1987) · Zbl 0624.93030
[2] Brockett, R. W. (1981). Control theory and singular Riemannian geometry. In P. J. Hilton and G. S. Young (Eds.), New directions in applied mathematics; Brockett, R. W. (1981). Control theory and singular Riemannian geometry. In P. J. Hilton and G. S. Young (Eds.), New directions in applied mathematics
[3] Campbell, S. L., Singular systems of differential equations, II (Research notes in mathematics, vol. 61) (1982), Pitman: Pitman San Francisco, CA · Zbl 0482.34008
[4] Caratheodory, C., Variationsrechnung und partielle differentialgleichungen erster Ordnung (1935), Teubner: Teubner Leipzig · JFM 61.0547.01
[5] D’Alessandro, D.; Ferrante, A., Optimal steering for an extended class of nonholonomic systems using Lagrange functionals, Automatica, 33, 1635-1646 (1997) · Zbl 1422.93025
[6] Fleming, W. H.; Rishel, R. W., Deterministic and Stochastic Optimal Control (1975), Springer: Springer New York · Zbl 0323.49001
[7] Goldstein, H., Classical mechanics (1980), Addison-Wesley: Addison-Wesley Reading, MA · Zbl 0491.70001
[8] Jonckheere, E., Variational calculus for descriptor problems, IEEE Transactions on Automatic Control, 33, 491-495 (1988) · Zbl 0644.49019
[9] Kosmol, P., Optimierung und Approximation (1991), De Gruyter Lehrbuch: De Gruyter Lehrbuch Berlin · Zbl 0749.49001
[10] Kosmol, P., & Pavon, M. (1992). Lagrange lemma and the optimal control of diffusions: Differentiable multipliers. Proceedings of the 31st CDC-IEEE conference IEEE control systems society; Kosmol, P., & Pavon, M. (1992). Lagrange lemma and the optimal control of diffusions: Differentiable multipliers. Proceedings of the 31st CDC-IEEE conference IEEE control systems society
[11] Kosmol, P.; Pavon, M., Lagrange approach to the optimal control of diffusions, Acta Applicandae Mathematicae, 32, 101-122 (1993) · Zbl 0794.93108
[12] Kosmol, P.; Pavon, M., Lagrange lemma and the optimal control of diffusions II: Nonlinear Lagrange functionals, Systems and Control Letters, 24, 215-221 (1995) · Zbl 1034.93561
[13] Krotov, V. F., Global methods in optimal control (1996), Marcel Dekker: Marcel Dekker New York · Zbl 0931.93046
[14] Lewis, F. L., A survey of linear singular systems, Circuits Systems and Signal Processing, 5, 3-36 (1986) · Zbl 0613.93029
[15] Murray, R. M.; Li, Z.; Sastry, S. S., Robotic manipulation (1994), CRC Press: CRC Press Boca Raton, FL · Zbl 0858.70001
[16] Murray, R. M.; Sastry, S. S., Nonholonomic motion planning: Steering using sinusoids, IEEE Transactions on Automatic Control, 38, 700-716 (1993) · Zbl 0800.93840
[17] Pavon, M., Hamilton’s principle in stochastic mechanics, Journal of Mathematical Physics, 36, 3804-3830 (1995)
[18] Pavon, M. (1998). Stochastic differential games in nonequilibrium thermodynamics. In A. Beghi, L. Finesso, & G. Picci (Eds.), Mathematical theory of networks and systems; Pavon, M. (1998). Stochastic differential games in nonequilibrium thermodynamics. In A. Beghi, L. Finesso, & G. Picci (Eds.), Mathematical theory of networks and systems
[19] Pavon, M., Derivation of the wave function collapse in the context of Nelson’s stochastic mechanics, Journal of Mathematical Physics, 40, 5565-5577 (1999) · Zbl 0968.81005
[20] Rockafeller, R. T.; Wets, R., Nonanticipativity and \(L^1\)-martingales in stochastic optimization problems, Mathematical Programming Study, 66, 170-180 (1976)
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