Some characterizations of optimal trajectories in control theory
- 1 January 1990
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 1646-1651 vol.3
- https://doi.org/10.1109/cdc.1990.203899
Abstract
Several characterizations of optimal trajectories for the classical Mayer problem in optimal control are presented. The regularity of directional derivatives of the value function is studied. For example, it is shown that for smooth control systems the value function V is continuously differentiable along an optimal trajectory x:(t/sub 0/, 1) to R/sup n/, provided V is differentiable at the initial point (t/sub 0/, x(t/sub 0/)). Then the upper semicontinuity of the optimal feedback map is deduced. The authors also address the problem of optimal design, obtaining sufficient conditions for optimality. Finally, it is shown that the optimal control problem can be reduced to a viability problem.Keywords
This publication has 8 references indexed in Scilit:
- A Survey of Viability TheorySIAM Journal on Control and Optimization, 1990
- Maximum principle, dynamic programming, and their connection in deterministic controlJournal of Optimization Theory and Applications, 1990
- Generalized one-sided estimates for solutions of Hamilton-Jacobi equations and applicationsNonlinear Analysis, 1989
- Optimal trajectories associated with a solution of the contingent Hamilton-Jacobi equationApplied Mathematics & Optimization, 1989
- Contingent Cones to Reachable Sets of Control SystemsSIAM Journal on Control and Optimization, 1989
- Some Properties of Viscosity Solutions of Hamilton-Jacobi EquationsTransactions of the American Mathematical Society, 1984
- Differential InclusionsPublished by Springer Nature ,1984
- Deterministic and Stochastic Optimal ControlPublished by Springer Nature ,1975