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An adaptive neural control method is proposed in this paper for the flexible air-breathing hypersonic vehicle (AHV) with constraints on actuators. This scheme firstly converts the original control problem with input constraints into a new control problem without input constraints based on the control input saturation function. Secondly, on the basis of the implicit function theorem, the radial basis function neural network (RBFNN) is introduced to approximate the uncertain items of the model. And the minimal-learning-parameter (MLP) technique is adopted to design the adaptive law for the norm of network weight vector, which significantly reduces calculations. Meanwhile, the finite-time convergence differentiator (FD) is introduced, through which the model state variables and their derivatives are accurately estimated to ensure the control effect. Finally, it is theoretically proved that the closed-loop control system is stable. And the effectiveness of the designed controller is verified by simulation.

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The adaptive hp pseudospectral method is an effective choice in solving the optimal control problem. In order to improve the computing efficiency of the adaptive hp method, an improved adaptive hp mesh refinement method is proposed in this paper. There are two main cores in this method. The first is to refine the mesh in advance based on the change rate of the control, so that the algorithm can more efficiently deal with the optimal control problem with discontinuous control. And the second is to based on the accumulation of curvature values to ensure that those positions that need to be refined more can be quickly allocated to more mesh points. These two are combined with each other to improve the solving efficiency of the algorithm proposed in this paper, which shortens the required computing time. In addition, the convergence of the algorithm is proved in this paper. The simulation results show the effectiveness and superiority of the algorithm proposed in this paper.

The adaptive hp pseudospectral method is an effective choice in solving the optimal control problem. In order to improve the computing efficiency of the adaptive hp method, an improved adaptive hp mesh refinement method is proposed in this paper. There are two main cores in this method. The first is to refine the mesh in advance based on the change rate of the control, so that the algorithm can more efficiently deal with the optimal control problem with discontinuous control. And the second is to based on the accumulation of curvature values to ensure that those positions that need to be refined more can be quickly allocated to more mesh points. These two are combined with each other to improve the solving efficiency of the algorithm proposed in this paper, which shortens the required computing time. In addition, the convergence of the algorithm is proved in this paper. The simulation results show the effectiveness and superiority of the algorithm proposed in this paper.