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Nonlinear optimal control (NOC) problem with complex dynamic constraints (CDC) is difficult to compute even with direct method. In this paper, a hybrid two-stage approach integrating an improved backtracking search optimization algorithm (IBSA) with the hp-adaptive Gauss pseudo-spectral methods (hpGPM) is proposed. Firstly, BSA is improved to enhance its convergent speed and the global search ability, by adopting the harmony search strategy and an adaptive amplitude control factor with individual optimum fitness feedback. Then, at the beginning stage of the hybrid search process, an initialization generator is constructed using IBSA to find a near optimum solution. When the change in fitness function approaches to a predefined value which is small enough, the search process is replaced by hpGPM to accelerate the search process and find an accurate solution. By this way, the hybrid algorithm is able to find a global optimum more quickly and accurately. Two NOC problems with CDC are examined using the proposed algorithm, and the corresponding Monte Carlo simulations are conducted. The comparison results show the hybrid algorithm achieves better performance in convergent speed, accuracy and robustness. [ABSTRACT FROM AUTHOR]

The approach and landing (A&L) trajectory optimization is a critical problem for secure flight of reusable launch vehicle (RLV). In this paper, the A&L is divided into two sub-phases, glide phase and flare phase respectively. The flare phase is designed firstly based on the desired touchdown (TD) states. Then, the glide phase is optimized using a proposed novel robust hybrid algorithm that combines advantages of the gravitational search algorithm (GSA) and gauss pseudospectral method (GPM). In the proposed hybrid algorithm, an improved GSA (IGSA) is presented to enhance the convergence speed and the global search ability, by adopting the elite memory reservation strategy and an adaptive gravitational constant adaption with individual optimum fitness feedback. At the beginning stage of search process, an initialization generator is constructed to find an optimum solution with IGSA, due to its strong global search ability and robustness to the initial values. When the change in fitness value satisfies the predefined value, the IGSA is replaced by the GPM to accelerate the search process and to get an accurate optimum solution. Finally, the Monte Carlo simulation results are analyzed in detail, which demonstrate the proposed method is practicable. The comparison with GSA and GPM shows that the hybrid algorithm has better performance in terms of convergence speed, robustness and accuracy for solving the RLV A&L trajectory optimization problem. [ABSTRACT FROM AUTHOR]