Short communication: A collocation-type method for linear quadratic optimal control problems

This communication presents a spectral method for solving time-varying linear quadratic optimal control problems. Legendre–Gauss–Lobatto nodes are used to construct the mth-degree polynomial approximation of the state and control variables. The derivative x ·(t) of the state vector x (t) is approximaed by the analytic derivative of the corresponding interpolating polynomial. The performance index approximation is based on Gauss–Lobatto integration. The optimal control problem is then transformed into a linear programming problem. The proposed technique is easy to implement, efficient and yields accurate results. Numerical examples are included and a comparison is made with an existing result.