Work

Convergence Rate for a Gauss Collocation Method Applied to Constrained Optimal Control

Year: 2018

Type: article

Abstract: A local convergence rate is established for a Gauss orthogonal collocation method applied to optimal control problems with control constraints. If the Hamiltonian possesses a strong convexity property, then the theory yields convergence for problems whose optimal state and costate possess two square integrable derivatives. The convergence theory is based on a stability result for the sup-norm change in the solution of a variational inequality relative to a 2-norm perturbation, and on a Sobolev space bound for the error in interpolation at the Gauss quadrature points and the additional point -1. The tightness of the convergence theory is examined using a numerical example.

Source: SIAM Journal on Control and Optimization

DOI: 10.1137/16m1096761

Authors: William W. Hager, Jun Liu, Subhashree Mohapatra, Anil V. Rao, Xiang-Sheng Wang

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, U.S. Air Force, Office of Naval Research, Air Force Research Laboratory

Awards: G2170114997, G2193832229, Fast Sparse Nonlinear Optimization and Its Application to Optimal Control, G3645034541, G4065003692, G6057435024, G8876996369

OpenAlex ID: W2500347040

FWCI: 6.234

Cites: 30

Cited by: 47

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