Linear time-varying dynamic systems optimization via higher-order method using shifted Chevyshev's polynomials

摘要

For optimization of classes of linear time-varying dynamic systems with n states and m control inputs, a new higher-order procedure is presented that does not use Lagrange multipliers. ^In this new procedure, the optimal solution was shown to satisfy m 2p-order differential equations with time-varying coefficients. ^These differential equations were solved using weighted residual methods. ^Even though solution of the optimization problem using this procedure was demonstrated to be quite computationally efficient, the shifted Chebyshev polynomials are used in a novel way to solve the higher-order differential equations. ^This further reduces the computations and makes this algorithm more appropriate for real-time implementation. ^The procedure is illustrated by an example. ^(Author)