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.

[1]  Gamal N. Elnagar,et al.  Pseudospectral Chebyshev Optimal Control of Constrained Nonlinear Dynamical Systems , 1998, Comput. Optim. Appl..

[2]  F. Callier.  Introduction to Mathematical Systems Theory: A Behavioural Approach, by Jan Willem Polderman and Jan C. Willems, Springer, New York, NY, 1998, Texts in Applied Mathematics Vol. 26, 424pp. , 2002 .

[3]  Gamal N. Elnagar.  State-control spectral Chebyshev parameterization for linearly constrained quadratic optimal control problems , 1997 .

[4]  Luca Consolini,et al.  Generalized bang-bang control for feedforward constrained regulation , 2006, CDC.

[5]  John McPhee,et al.  Determination of Minimum-Time Maneuvers for a Robotic Manipulator Using Numerical Optimization Methods∗ , 1999 .

[6]  Adolf Hermann Glattfelder,et al.  Control Systems with Input and Output Constraints , 2003 .

[7]  A. Quarteroni,et al.  Numerical Approximation of Partial Differential Equations , 2008 .

[8]  A. Piazzi,et al.  Minimum-time feedforward control with input and output constraints , 2006, 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control.

[9]  R. V. Dooren,et al.  A Chebyshev technique for solving nonlinear optimal control problems , 1988 .

[10]  Hussein Jaddu,et al.  Computation of optimal control trajectories using chebyshev polynomials : Parameterization, and quadratic programming , 1999 .

[11]  M. S. Salim,et al.  A Chebyshev approximation for solving optimal control problems , 1995 .

[12]  L. Fox,et al.  Chebyshev polynomials in numerical analysis , 1970 .