Hybrid functions approach for nonlinear constrained optimal control problems

In this paper, a new numerical method for solving the nonlinear constrained optimal control with quadratic performance index is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrix of integration is introduced. This matrix is then utilized to reduce the solution of the nonlinear constrained optimal control to a nonlinear programming one to which existing well-developed algorithms may be applied. Illustrative examples are included to demonstrate the validity and applicability of the technique.

► Hybrid functions consisting of the combination of block-pulse with polynomial series have been shown to be a powerful tool. ► The hybrid of block-pulse and Bernoulli polynomials is introduced. We then solve the constrained optimal control problems. ► The operational matrices of integration P and the integration of the cross product of two hybrid functions D are given. ► The matrices P and D for this hybrid functions have many zero elements. This reduces the CPU time and computer memory.