Nonlinear optimal control: approximations via moments and LMI-relaxations
- 4 October 2006
- conference paper
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 1648-1653
- https://doi.org/10.1109/cdc.2005.1582395
Abstract
We consider the class of nonlinear optimal control problems with all data (differentail equation, state and control constraints, cost) being polynomials. We provide a simple hierarchy of LMI-relaxations whose optimal values form a nondecreasing sequence of lower bounds on the optimal value. Preliminary results show that good approximations are obtained with few moments.Keywords
This publication has 11 references indexed in Scilit:
- Robust optimal stabilization of the Brockett integrator via a hybrid feedbackMathematics of Control, Signals, and Systems, 2005
- Solving nonconvex optimization problemsIEEE Control Systems, 2004
- Bounds on measures satisfying moment conditionsThe Annals of Applied Probability, 2002
- Introduction to Numerical AnalysisTexts in Applied Mathematics, 2002
- Global Optimization with Polynomials and the Problem of MomentsSIAM Journal on Optimization, 2001
- Hamilton–Jacobi theory and the heat kernel on Heisenberg groupsJournal de Mathématiques Pures et Appliquées, 2000
- Approximation Schemes for Infinite Linear ProgramsSIAM Journal on Optimization, 1998
- Adjoint Estimation from a Direct Multiple Shooting MethodJournal of Optimization Theory and Applications, 1997
- Discrete-Time Markov Control ProcessesPublished by Springer Science and Business Media LLC ,1996
- Direct and indirect methods for trajectory optimizationAnnals of Operations Research, 1992