Generalizations of singular optimal control theory

Authors:
P. J. Moylan;J. B. Moore
Affiliations:
Department of Electrical Engineering, University of Newcastle, New South Wales 2308, Australia;Department of Electrical Engineering, University of Newcastle, New South Wales 2308, Australia
Venue:
Automatica (Journal of IFAC)
Year:
1971

Citing 2
Cited 4

Correspondence item: A note on a singular optimal control problem

Automatica (Journal of IFAC)
Correspondence item: Tolerance of non-linearities in relay systems

Automatica (Journal of IFAC)

Correspondence: Comments on "Optimally switched linear systems"

Automatica (Journal of IFAC)
Singular perturbations and order reduction in control theory - An overview

Automatica (Journal of IFAC)
Optimal stochastic fault detection filter

Automatica (Journal of IFAC)
Original article: A numerical framework for optimal control of switched input affine nonlinear systems subject to path constraint

Mathematics and Computers in Simulation

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Abstract

This paper considers a new approach to the optimization of the linear, possibly time-varying, system x@? = Fx + Gu |u"i| @? 1 with respect to the performance index V = @!^t^"^1"t"""0x'Qxdt. The new approach applies standard regulator theory using appropriate transformations and thereby enables the problem to be solved more completely than has hitherto been possible. For example we consider the cases which arise when Q is singular. Particular attention is given to the limiting case as t"1 becomes infinite. For this case, conditions are presented for the asymptotic stability of the singular optimal trajectories. Some stability results concerning the ''bang-bang'' solutions are also considered.