This paper is a tutorial introduction to pseudospectral optimal control. With pseudospectral methods, a function is approximated as a linear combination of smooth basis functions, which are often chosen to be Legendre or Chebyshev polynomials. Collocation of the differential-algebraic equations is performed at orthogonal collocation points, which are selected to yield interpolation of high accuracy. Pseudospectral methods directly discretize the original optimal control problem to recast it into a nonlinear programming format. A numerical optimizer is then employed to find approximate local optimal solutions. The paper also briefly describes the functionality and implementation of PSOPT, an open source software package written in C++ that employs pseudospectral discretization methods to solve multi-phase optimal control problems. The software implements the Legendre and Chebyshev pseudospectral methods, and it has useful features such as automatic differentiation, sparsity detection, and automatic scaling. The use of pseudo-spectral methods is illustrated in two problems taken from the literature on computational optimal control.
Optimal Control; Pseudospectral Methods; Nonlinear Programming; Trajectory Planning
