Abstract
A hybrid double-loop optimization algorithm combing particle swarm optimization (PSO) and nonintrusive polynomial chaos (NIPC) is proposed for solving the robust trajectory optimization of hypersonic glide vehicle (HGV) under uncertainties. In the outer loop, the PSO method searches globally for the robust optimal control law according to a penalized fitness function that contains the system robustness considerations. In the inner loop, uncertainty propagation of the stochastic system is performed using the NIPC method, to provide statistical moments for the iterative scheme of the PSO method in the outer loop. Only control variables are discretized, and the state constraints are satisfied implicitly through the numerical integration process, which reduces the number of decision variables as well as the huge amount of computation increased by NIPC. In the end, the robust optimal control law is achieved conveniently. Numerical simulations are carried out considering a classical time-optimal trajectory optimization problem of HGV with uncertainties in both initial states and aerodynamic coefficients. The results demonstrate the feasibility and effectiveness of the proposed method.
Highlights
Hypersonic glide vehicle (HGV) is generally released from solid rocket boosters and reentry glides through the atmosphere at hypersonic speed without power
The reentry region of HGV is quite narrow and always suffers from complex uncertainties, due to large space span, long flight time, changeable aerodynamic environment, and shortage of flight experience [4]. erefore, the reentry trajectory design, as a core problem of the guidance and control, has become a challenge and hotspot for HGV [5, 6]. e performance of trajectory design is the essential section of a flight. e trajectory design framework of offline trajectory optimization and online tracking guidance is usually adopted in engineering, because of the limitation of the current vehicle-borne computing capacity and the high real-time calculation requirements [6, 7]
According to the above double-loop optimization framework, the particle swarm optimization (PSO) iterates for the global optimal solution in the outer loop, while the corresponding fitness functions with robustness considerations are calculated in the inner loop by the nonintrusive polynomial chaos (NIPC) method and numerical integrations
Summary
Hypersonic glide vehicle (HGV) is generally released from solid rocket boosters and reentry glides through the atmosphere at hypersonic speed without power. The deterministic optimization methods lack robustness considerations for uncertainties and, will increase the design burden of the online tracking guidance system for the case of unpredictable fluctuations or deviations from the original reference trajectory [14]. This is achieved by adding appropriate statistical information (such as the mean and the standard deviation) of the user-defined qualities to the original objective function as well as the constraints To this end, the efficient and accurate uncertainty propagation (UP) techniques [17] are necessary, which usually include Monte Carlo (MC) simulation, linear methods, and nonlinear methods. Cottrill and Harmon [22] proved that the gPC algorithm displayed improved calculation efficiency while it maintained the same accuracy with Monte Carlo simulation They proposed a robust trajectory optimization model that used the polynomial chaos method and the Gaussian pseudospectral method to transform the stochastic optimization problem into a set of similar deterministic optimization problems. When this model is performed for trajectory planning problems of HGV, it is necessary to solve the complex stochastic ODEs as well as system robustness considerations
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