Linear Time-Varying Dynamic Systems Optimization via Higher-Order Method Using Shifted Chebyshev’s Polynomials

Abstract

For optimization of classes of linear time-varying dynamic systems with n states and m control inputs, a new higher-order procedure was presented by the authors 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 computation efficient, shifted Chebyshev’s polynomials are used in the paper to solve the higher-order differential equations. This further reduces the computations and makes this algorithm more appropriate for real-time implementation.