Sequential Action Control for Tracking of Free Invariant Manifolds

This paper presents a hybrid control method that controls to unstable equilibria of nonlinear systems by taking advantage of systems’ stable manifold of free dynamics. Resulting nonlinear controllers are closed-loop and can be computed in real-time. Thus, we present a computationally efficient approach to optimization-based switching control design using a manifold tracking objective. Our method is validated for the cart-pendulum and the pendubot inversion problems. Results show the proposed approach conserves control effort compared to tracking the desired equilibrium directly. Moreover, the method avoids parameter tuning and reduces sensitivity to initial conditions. Finally, when compared to existing energy based swing-up strategies, our approach does not rely on pre-derived, system-specific switching controllers. We use hybrid optimization to automate switching control synthesis on-line for nonlinear systems.