A computationally efficient sequential convex programming using Chebyshev collocation method

Abstract

This paper aims to develop a computationally efficient sequential convex programming algorithm for a class of nonlinear systems. A Chebyshev collocation discretization (CCD) technique is proposed that transforms the continuous convex optimization problem into a finite-dimensional discrete optimization problem. The CCD technique uses Chebyshev polynomials to construct a closed-form approximate solution to the convex dynamic equation. Moreover, it establishes a linear mapping between the control inputs and the system states. This enables the constraints of the dynamics equations to be externalized from the optimization problem and computed using efficient linear equation solving algorithms. On the one hand, this strategy significantly reduces the number of constraint equations and optimization variables, improving the speed of the optimizer. On the other hand, it preserves the path constraints on the system states in the optimization problem. A numerical simulation example of the perching maneuver for a fixed-wing unmanned aerial vehicle is presented to validate the efficiency of the algorithm. The result shows significant improvements in both speed and accuracy compared to the Euler discretization, and greatly improves the solution speed while maintaining almost the same solution accuracy compared to the Gauss pseudospectral optimization method.