New algorithms for unconstrained nonlinear optimal control problems
- 1 August 1981
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 26 (4) , 868-884
- https://doi.org/10.1109/tac.1981.1102732
Abstract
A family of new first-order algorithms for solving continuous time optimal control problems is presented. The algorithms make use of the Riccati matrix differential equation and are capable of solving the linear quadratic problem in one step. The paper includes an analysis of the convergence of the proposed algorithms in the space of relaxed controls, as well as the proof of the reduction of the cost functional at each iteration and numerical examples.Keywords
This publication has 9 references indexed in Scilit:
- Fréchet differentiability and optimal controlInternational Journal of Control, 1978
- A feasible directions algorithm for optimal control problems with control and terminal inequality constraintsIEEE Transactions on Automatic Control, 1977
- Relaxed Controls and the Convergence of Optimal Control AlgorithmsSIAM Journal on Control and Optimization, 1976
- Variable metric methods in Hilbert space with applications to control problemsJournal of Optimization Theory and Applications, 1976
- First-order strong variation algorithms for optimal controlJournal of Optimization Theory and Applications, 1975
- Suboptimal control for the nonlinear quadratic regulator problemAutomatica, 1975
- Computation of optimal controls using a piecewise polynomial parameterizationIEEE Transactions on Automatic Control, 1973
- Introdction to Measure and ProbabilityPublished by Cambridge University Press (CUP) ,1966
- Minimizing variational curves restricted to a preassigned setTransactions of the American Mathematical Society, 1964