PSEUDOSPECTRAL CHEBYSHEV OPTIMAL-CONTROL OF CONSTRAINED NONLINEAR DYNAMICAL-SYSTEMS

A pseudospectral method for generating optimal trajectories of linear and nonlinear constrained dynamic systems is proposed. The method cons ists of representing the solution of the optimal control problem by an mth degree interpolating polynomial, using Chebyshev nodes, and then discretizing the problem using a cell-averaging technique. The optimal control problem is thereby transformed into an algebraic nonlinear pr ogramming problem. Due to its dynamic nature, the proposed method avoi ds many of the numerical difficulties typically encountered in solving standard optimal control problems. Furthermore, for discontinuous opt imal control problems, we develop and implement a Chebyshev smoothing procedure which extracts the piecewise smooth solution from the oscill atory solution near the points of discontinuities. Numerical examples are provided, which confirm the convergence of the proposed method. Mo reover, a comparison is made with optimal solutions obtained by closed -form analysis and/or other numerical methods in the literature.