Optimization: algorithms and consistent approximations
Optimization: algorithms and consistent approximations
On the Time-Discretization of Control Systems
SIAM Journal on Control and Optimization
Pseudospectral Chebyshev Optimal Control of Constrained Nonlinear Dynamical Systems
Computational Optimization and Applications
Spectral methods in MatLab
The Euler approximation in state constrained optimal control
Mathematics of Computation
Practical methods for optimal control using nonlinear programming
Practical methods for optimal control using nonlinear programming
Second-Order Runge--Kutta Approximations in Control Constrained Optimal Control
SIAM Journal on Numerical Analysis
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
SIAM Journal on Optimization
Discretization methods for optimal control problems with state constraints
Journal of Computational and Applied Mathematics
Smooth proximity computation for collision-free optimal control of multiple robotic manipulators
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
Automatica (Journal of IFAC)
Sequential virtual motion camouflage method for nonlinear constrained optimal trajectory control
Automatica (Journal of IFAC)
Journal of Computational and Applied Mathematics
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In recent years, many practical nonlinear optimal control problems have been solved by pseudospectral (PS) methods. In particular, the Legendre PS method offers a Covector Mapping Theorem that blurs the distinction between traditional direct and indirect methods for optimal control. In an effort to better understand the PS approach for solving control problems, we present consistency results for nonlinear optimal control problems with mixed state and control constraints. A set of sufficient conditions is proved under which a solution of the discretized optimal control problem converges to the continuous solution. Convergence of the primal variables does not necessarily imply the convergence of the duals. This leads to a clarification of the Covector Mapping Theorem in its relationship to the convergence properties of PS methods and its connections to constraint qualifications. Conditions for the convergence of the duals are described and illustrated. An application of the ideas to the optimal attitude control of NPSAT1, a highly nonlinear spacecraft, shows that the method performs well for real-world problems.