Abstract
Nonlinear dynamic systems are considered that are described by the Lagrangian equations and subjected to uncertain disturbances and bounded control forces. Under certain assumptions, feedback control laws are obtained that satisfy the imposed constraints and drive the systems to the prescribed terminal states in finite time. The approaches developed in the paper are based on the decomposition of the given system into subsystems with one degree of freedom each. Methods of optimal control and differential games are then applied to the subsystems. As a result, explicit formulae for the closed-loop control forces and for the time of motion are derived. The obtained feedback controls are time-suboptimal and robust, they can cope with small disturbances and parameter variations. Applications to control of robots are discussed.
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References
Leitmann, G., Deterministic control of uncertain systems. Acta Astronautica, 7, 1457–1461, 1980.
Corless, M., and Leitmann, G., Adaptive control of systems containing uncertain functions and unknown functions with uncertain bounds. J. Optimization Theory Appl., 41, 155–168, 1983.
Corless, M., and Leitmann, G., Adaptive controllers for a class of uncertain systems. Annales Fond. de Broglie., 9, 65–95, 1984.
Pontryagin, L.S., Boltyansky, V.G., Gamkrelidze, R.V., and Mishchenko, E.F., Mathematical Theory of Optimal Processes, Wiley-Inter-science, 1972.
Krasovskii, N.N., Game Problems of the Encounter of Motions, Nauka, Moscow, 1970 (in Russian).
Chernousko F.L., Decomposition and suboptimal control in dynamical systems, J.Appl. Maths Mechs (PMM), 54, 6, 727-734, 1990.
Chernousko, F.L., Decomposition and synthesis of control in dynamical systems, Soviet J. Computer and Systems Sciences, 29, 5, 126-144, 1990.
Chernousko, F.L., Control synthesis in a system with a non-linear damping, J. Appl. Maths Mechs (PMM), 55, 6, 1991.
Chernousko, F.L., Decomposition and suboptimal control in dynamic systems, Optimal Control Appl. and Methods, 1993, to appear.
Chernousko, F.L., Control synthesis in a non-linear dynamical system, J. Appl. Maths Mechs (PMM), 56, 2, 157-166, 1992.
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Chernousko, F.L. (1993). The Decomposition of Controlled Dynamic Systems. In: Kurzhanski, A.B. (eds) Advances in Nonlinear Dynamics and Control: A Report from Russia . Progress in Systems and Control Theory, vol 17. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0349-0_1
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DOI: https://doi.org/10.1007/978-1-4612-0349-0_1
Publisher Name: Birkhäuser, Boston, MA
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