State-control spectral Chebyshev parameterization for linearly constrained quadratic optimal control problems

In this paper we propose a computationally attractive numerical method for determining the optimal control of constrained linear dynamic systems with a quadratic performance. The method is based upon constructing the mth degree interpolating polynomials, using Chebyshev nodes, to approximate the control and the state vectors. The system dynamics are collocated at Chebyshev nodes. The performance index is discretized by a cell averaging method. The state and control inequality constraints are converted into algebraic inequalities through collocation at the nodes. The linear quadratic optimal control problem is thereby transformed into a quadratic programming one. Simulation studies demonstrate computational advantages relative to a standard Riccati method, a classical Chebyshev-based method, Fourier-based method and other methods in the literature.