Gauss Pseudospectral Method for Solving Infinite-Horizon Optimal Control Problems

The previously developed Gauss pseudospectral method is extended to the case of nonlinear infinite-horizon optimal control problems. First, the semi-infinite domain t ∈ [0,+∞) is transformed to the domain τ = [−1,+1). The first-order optimality conditions of NLP obtained from the pseudospectral discretization are then presented. These optimality conditions are related to the KKT multipliers of the nonlinear programming problem, leading to an approximation for the costate of the continuous optimal control problem. A key result is that the state and costate are obtained on the entire horizon (including the solution at t = +∞). Numerical results show that the method of this paper lead to the ability to determine accurate primal and dual solutions for infinite-horizon optimal control problems.