Relaxed dynamic programming in switching systems
- 1 September 2006
- journal article
- Published by Institution of Engineering and Technology (IET) in IEE Proceedings - Control Theory and Applications
- Vol. 153 (5), 567-574
- https://doi.org/10.1049/ip-cta:20050094
Abstract
In order to simplify computational methods based on dynamic programming, a relaxed procedure based on upper and lower bounds of the optimal cost was recently introduced. The convergence properties of this procedure are analysed here. In particular, it is shown that the computational effort in finding an approximately optimal control law by relaxed value iteration is related to the polynomial degree that is needed to approximate the optimal cost. This gives a rigorous foundation for the claim that the search for optimal control laws requires complex computations only if the optimal cost function is complex. A computational example is given for switching control on a graph with 60 nodes, 120 edges and 30 continuous states.Keywords
This publication has 13 references indexed in Scilit:
- Convergence Properties of Policy IterationSIAM Journal on Control and Optimization, 2004
- The Linear Programming Approach to Approximate Dynamic ProgrammingOperations Research, 2003
- Neuro-Dynamic ProgrammingPublished by Springer Science and Business Media LLC ,2001
- Constrained model predictive control: Stability and optimalityAutomatica, 2000
- Piecewise linear quadratic optimal controlIEEE Transactions on Automatic Control, 2000
- Controllers for reachability specifications for hybrid systemsAutomatica, 1999
- Robustness analysis and synthesis for nonlinear uncertain systemsIEEE Transactions on Automatic Control, 1997
- Convex Duality and Nonlinear Optimal ControlSIAM Journal on Control and Optimization, 1993
- A numerical approach to the infinite horizon problem of deterministic control theoryApplied Mathematics & Optimization, 1987
- On the Convergence of Policy Iteration in Stationary Dynamic ProgrammingMathematics of Operations Research, 1979