Multiplier methods for nonlinear optimal control
SIAM Journal on Numerical Analysis
SIAM Journal on Control and Optimization
Computational optimal control
A cell-averaging Chebyshev spectral method for the controlled Duffing oscillator
Applied Numerical Mathematics
Computational Optimization and Applications
ACM Transactions on Mathematical Software (TOMS)
Computational Optimization and Applications
A numerical solution of the nonlinear controlled Duffing oscillator by radial basis functions
Computers & Mathematics with Applications
Convergence of the forward-backward sweep method in optimal control
Computational Optimization and Applications
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A pseudospectral method for generating optimal trajectoriesof linear and nonlinear constrained dynamic systems is proposed. Themethod consists of representing the solution of the optimal controlproblem by an mth degree interpolating polynomial, using Chebyshevnodes, and then discretizing the problem using a cell-averagingtechnique. The optimal control problem is thereby transformed into analgebraic nonlinear programming problem. Due to its dynamic nature,the proposed method avoids many of the numerical difficultiestypically encountered in solving standard optimal control problems.Furthermore, for discontinuous optimal control problems, we developand implement a Chebyshev smoothing procedure which extracts thepiecewise smooth solution from the oscillatory solution near thepoints of discontinuities. Numerical examples are provided, whichconfirm the convergence of the proposed method. Moreover, acomparison is made with optimal solutions obtained by closed-formanalysis and/or other numerical methods in the literature.