Multiprogram Stabilization Problem for the Mathematical Pendulum

In this paper, the model of mathematical pendulum is formulated as a non-linear dynamic system. The equilibrium positions of the dynamic system are obtained as a solution of corresponding problem of multiprogram stabilization. This solution is eventually formalized in a form of Hermit's polynomial

Multiprogram Stabilization of Equilibrium Positions for a Nonlinear Dynamic System

ABSTRACT In this paper, we consider the problem of multiprogram stable controls synthesis for dynamic systems. We solve the problem for nonlinear systems based on Zubov's approach (a multiprogram control as Hermite's interpolative polynomial) that provides constraining of multiprogram controls. The theorem of a sufficient condition for control synthesis in a nonlinear system is formulated. Control synthesis for a model of the mathematical pendulum is presented as an example. Equilibrium positions of the system are considered in a capacity of a program motion set