Convergence of pseudospectral discretizations of optimal control problems
- Resource Type
- Conference
- Authors
- Ross, I.M.; Fahroo, F.
- Source
- Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228) Decision and control Decision and Control, 2001. Proceedings of the 40th IEEE Conference on. 4:3175-3177 vol.4 2001
- Subject
- Robotics and Control Systems
Computing and Processing
Convergence
Optimal control
Polynomials
Cost function
Postal services
Approximation methods
Educational institutions
Government
Protection
Lagrangian functions
- Language
A generic nonlinear optimal control problem with a Bolza cost functional is discretized by a Legendre pseudospectral method. According to the covector mapping theorem, the Karush-Kuhn-Tucker multipliers of the discrete problem map linearly to the spectrally discretized covectors of the Bolza problem. Using this result, it is shown that the nonlinear programming problem converges to the continuous Bolza problem at a spectral rate assuming regularity of appropriate functions.