Using Modified IPSO-SQP Algorithm to Solve Nonlinear Time Optimal Bang-bang Control Problem

In this paper, an intelligent-gradient based algorithm is proposed to solve time optimal bang-bang control problem. The proposed algorithm is a combination of an intelligent algorithm called improved particle swarm optimization algorithm (IPSO) in the first stage of optimization process together with a gradient-based algorithm called successive quadratic programming method (SQP) in the second stage. The proposed algorithm is called MIPSO-SQP algorithm which in essence is a modification of the previous IPSO-SQP algorithm (PIPSO-SQP). New steps in optimization process of the proposed MIPSO-SQP algorithm causes the algorithm to reach to global optimal solution regardless of any guess of the initial control input and/or the number of switching. Validity of results is verified through adding some arcs to present arcs. The proposed algorithm is successfully applied in time optimal bang-bang control of the Van Der Pol equations, Rayleigh system and F8 aircraft model. A comparison study is also performed to assess the performance of MIPSO-SQP with respect to Switching Time Optimal method (TOS), mathematical programming method and PIPSO-SQP algorithm. It is shown that MIPSO-SQP algorithm is more effective than these algorithms due to ability to find global optimum solution in less iteration and in a more systematic way