Using a Chebyshev technique for solving the generalized bang-bang control problem

In this paper we propose the use of the Chebyshev polynomials based approximation for the solution of the minimum-time rest-to-rest feedforward control problem with input and output constraints for continuous-time systems. It is shown that the optimal input can be determined, without discretizing the system, by suitably approximating the state variables and the input signal by means of Chebyshev series and by subsequently solving a constrained optimization problem. Simulation results confirm that the technique is effective.