Enlarge your region of attraction using high-gain feedback

We can associate with the pseudo-linearization method of regulation a region of attraction, 𝒰₀, containing the equilibrium manifold of a nonlinear system. This paper discusses the use of high-gain feedback to force system trajectories into 𝒰₀ . The control strategy is to switch from the high-gain controller to the pseudolinear controller once the state enters an estimate of 𝒰₀. This controller structure can increase the size of the region of attraction when compared to pseudolinearization alone. Sufficient conditions for the existence of the controller are presented, as is an algorithm for controller construction. The peaking phenomenon, which can arise because of the high gain, is investigated. Finally, the acrobot is presented as an application of the high-gain switching control. Simulations indicate the region of attraction is significantly enlarged, while computational complexity of the overall control law, both in terms of off-line construction and real-time implementation, is reasonable