Nozomu Araki

This paper considered a new implementation method for the stable manifold method, which is one of the nonlinear optimal control methods, using the state-dependent Riccati equation (SDRE) method. In the conventional stable manifold method, the optimal trajectory of the control object was generated by integrating the Euler-Lagrange equations corresponding to the Hamiltonian in the inverse time direction, and the state feedback control law was obtained by a polynomial approximation of the obtained solution. However, implementing this method using polynomial approximation is difficult due to problems such as determining the degree of the approximation formula, the computational cost of the approximation calculation itself, and the inability to perform polynomial approximation for complex trajectories. In contrast, the proposed method in this study aimed to achieve pseudo-nonlinear optimal control by using the SDRE method to track the optimal trajectory obtained by the stable manifold method. This method is easier to implement than the conventional stable manifold method because it does not use polynomial approximation, which is a barrier to applying it to actual systems, and instead uses a linear optimal control framework to track the optimal trajectory. The effectiveness of this method was demonstrated by swing-up and stabilization control experiments of a rotary inverted pendulum.