Control of a Multi-link Inverted Pendulum by a Single Torque

The paper concerns a control problem for a multi-link inverted pendulum with fixed suspension point. The pendulum moves in a vertical plane actuated by a bounded control torque applied to the first link with the other links being passive. We construct a feedback control law steering the pendulum from a neighbourhood of the upright equilibrium point to this point in a finite time. To this end, we consider an auxiliary control problem for the linearized system. Then, the control algorithm designed for the linear system is applied to the nonlinear multi-link pendulum. The proposed approach uses linear matrix inequalities techniques and enables one to construct bounded feedback controls that steers multi-link inverted pendulums with an arbitrary number of links to the upright equilibrium point in a finite time. The results of computer simulation of the three-links pendulum motion are presented.