Abstract
Theorems 1 and 2 give general necessary conditions for optimality of the control policy. For optimality of a switching time it is necessary that hamiltonian is indifferent for the fluctuation in the optimal control value. We note that the maximum principle implies the indifference principle, but not vice versa. The indifference principle requires exploration of many more candidate optimal paths, but this does not make it unworkable. For optimality of a constant control value it is necessary to maximize an integral of hamiltonian over the interval between switchings.
The presented results could be generalized in many directions. For example concurrent minimization over switching points and the constant control values or a problem with the upper bounds the number of discontinuities imposed only on some control entries [5].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Blatt J.M., Optimal control with a cost of switching control, J. Austral. Math. Soc. vol. 20 ser. B, 1976, 316–332.
Cesari L., Optimization Theory and Applications, Springer Verlag, New York 1981.
Girsanov V. I., Lectures on Mathematical Theory of Extremum Problems, Springer Verlag, Berlin, 1972.
Ioffe A.D., Tichomirov M.W., Theory of Extremum Problems, Nauka, Moskwa, 1974
Kabziński J., Optimal control with a bounded number of switchings, Part I, II, Bull. Pol. Acad. Sci., Technical Sci., vol 32, 1984, 341–353.
Pontryagin L.s., Boltyanski R.V., Mischenko E.F., The Mathematical Theory of Optimal Processes, Interscience Publ. Inc., New York, 1962
Sargent R.W.H., Sullivan G.R., The development of an efficient optimal control package, in Optimization Techniques, edited by J. Stoer, Springer Verlag, Berlin, 1978, 158–168.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag
About this paper
Cite this paper
Kabziński, J. (1994). Optimal, piecewise constant control with bounded number of discontinuities. In: Henry, J., Yvon, JP. (eds) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035495
Download citation
DOI: https://doi.org/10.1007/BFb0035495
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-19893-2
Online ISBN: 978-3-540-39337-5
eBook Packages: Springer Book Archive