This work presents a new method of stabilization for unstable periodic orbits of continuous-time dynamical systems. The principle of this method is to use feedback term based on the difference between the actual state value and the future state value computed along the trajectories of the uncontrolled system. To compute the value of the latter, an implicit Runge-Kutta ODE integration method is used, giving rise to a time-varying dynamical controller. The stability of the control method is defined in terms of the Floquet theory and the conditions for calculation of the monodromy matrix are presented. Numerical results are obtained using the forced van der Pol oscillator as case study and the orthogonal collocation method as implicit Runge-Kutta method.
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机译：这项工作提出了一种新的连续动态系统的不稳定周期轨道稳定方法。 该方法的原理是基于实际状态值与沿着不受控制系统的轨迹计算的未来状态值之间的差异使用反馈期。 为了计算后者的值，使用隐式runge-Kutta ode集成方法，从而产生时变动态控制器。 在浮子理论方面定义了控制方法的稳定性，并提出了单曲线矩阵的计算条件。 使用强制van der POL振荡器获得数值结果作为案例研究和正交搭配方法作为隐式跳动-Kutta方法。
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