Impulsive optimal control with finite or infinite time horizon
- 203 Downloads
We consider a dynamical system subjected to feedback optimal control in such a way that the evolution of the state exhibits both sudden jumps and continuous changes. Previously obtained necessary conditions (Ref. 1) for such impulsive optimal feedback controls are generalized to admit the case of infinite time horizon; this generalization permits application to a wider class of problems. The results are illustrated by application to a version of the innkeeper's problem.
Key WordsState-variable discontinuities minimum principle optimal control impulsive control optimal maintenance
Unable to display preview. Download preview PDF.
- 1.Blaquière, A.,Differential Games with Piecewise Continuous Trajectories, Differential Games and Applications, Edited by P. Hagedorn, H. W. Knobloch, and G. J. Olsder, Springer-Verlag, Berlin, Germany, 1977.Google Scholar
- 2.Case, J. H.,Economics and the Competitive Process, New York University Press, New York, New York, 1979.Google Scholar
- 3.Vincent, T. L., andMason, J. D.,Disconnected Optimal Trajectories, Journal of Optimization Theory and Applications, Vol. 3, pp. 263–281, 1969.Google Scholar
- 4.Case, J. H.,Impulsively Controlled D. G., The Theory and Application of Differential Games, Edited by J. D. Grote, D. Reidel Publishing Company, Dordrecht, The Netherlands, 1975.Google Scholar
- 5.Blaquière, A.,Jeux Differentiels à Deux Joueurs, Somme Nulle, avec Trajectoires Discontinues, Comptes Rendus de l'Académie des Sciences, Série A, Vol. 282, pp. 1047–1049, 1976.Google Scholar
- 6.Geering, H. P.,Continuous-Time Optimal Control Theory for Cost Functionals Including Discrete State Penalty Terms, IEEE Transactions on Automatic Control, Vol. AC-21, pp. 866–869, 1976.Google Scholar
- 7.Blaquière, A.,Necessary and Sufficiency Conditions for Optimal Strategies in Impulsive Control, Differential Games and Control Theory, III, Edited by P. T. Liu and E. Roxin, Marcel Dekker, New York, New York, 1979.Google Scholar
- 8.Blaquière, A.,Necessary and Sufficient Conditions for Optimal Strategies in Impulsive Control and Applications, New Trends in Dynamic System Theory and Economics, Edited by M. Aoki and A. Marzollo, Academic Press, New York, New York, 1979.Google Scholar
- 9.Getz, W. M., andMartin, D. H.,Optimal Control Systems with State Variable Jump Discontinuities, Journal of Optimization Theory and Applications, Vol. 31, pp. 195–205, 1980.Google Scholar
- 10.Blaquière, A., andLeitmann, G.,On the Geometry of Optimal Processes, Parts I, II, III, University of California, Berkeley, IER Reports Nos. AM-64-10, 1964; AM-65-11, 1965; and AM-66-1, 1966.Google Scholar
- 11.Blaquière, A., andLeitmann, G.,On the Geometry of Optimal Processes, Topics in Optimization, Edited by G. Leitmann, Academic Press, New York, New York, 1967.Google Scholar