×

zbMATH — the first resource for mathematics

Optimal control problems over large time intervals. (English) Zbl 0623.49010
Consider a linear quadratic optimal control problem with prescribed initial and final states, in which the time interval T is large - it does not appear that a criterion is given to determine when this condition actually occurs. The authors show that most of the transient activity occurs near \(t=0\) and \(t=T\), that the state vector remains small away from these points, and that the optimal trajectory and control for the original problem can be approximately obtained by piecing together the optimal trajectories and controls for two infinite-time problems.
Reviewer: J.Rubio

MSC:
49K15 Optimality conditions for problems involving ordinary differential equations
49M99 Numerical methods in optimal control
93C05 Linear systems in control theory
93B40 Computational methods in systems theory (MSC2010)
93C15 Control/observation systems governed by ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Anderson, B.D.O., Stability results for optimal systems, Electronics lett., 5, (1969)
[2] Asseo, S.J., Optimal control of a servo derived from nonquadratic performance criteria, IEEE trans aut. control, AC-14, 404, (1969)
[3] Bass, R.W.; Weber, R.F., Optimal nonlinear feedback control derived from quartic and higher-order performance criteria, IEEE trans aut. control, AC-11, 448, (1966)
[4] Glad, S.T., On the gain margin of nonlinear and optimal regulators, IEEE trans aut. control, AC-29, 615, (1984) · Zbl 0547.93017
[5] Kokotovic, P.V., Applications of singular perturbation techniques to control problems, SIAM rev., 26, 501, (1984) · Zbl 0548.93001
[6] Kokotovic, P.V.; Khalil, H.K.; O’Reilly, J., ()
[7] Kokotovic, P.V.; O’Malley, R.E.; Sannuti, P., Singular perturbations and order reduction in control theory—an overview, Automatica, 12, 123, (1976) · Zbl 0323.93020
[8] Moylan, P.J.; Anderson, B.D.O., Nonlinear regulator theory and an inverse optimal control problem, IEEE trans. aut. control, AC-18, 460, (1973) · Zbl 0283.49007
[9] Rekasius, Z.V., Suboptimal design of intentionally nonlinear controllers, IEEE trans aut. control, AC-9, 380, (1964)
[10] Tsitsiklis, J.N.; Athans, M., Guaranteed robustness properties of multivariable nonlinear stochastic optimal regulators, IEEE trans aut. control, AC-29, 690, (1984) · Zbl 0544.93079
[11] Wilde, R.R.; Kokotovic, P.V., A dichotomy in linear control theory, IEEE trans aut. control, AC-17, 382, (1972) · Zbl 0261.93014
[12] Wilde, R.R.; Kokotovic, P.V., Optimal open- and closed-loop control of singularly perturbed linear systems, IEEE trans aut. control, AC-18, 616, (1973) · Zbl 0273.49053
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.