Equilibrium-Independent Control of Continuous-Time Nonlinear Systems via the LPV Framework -- Extended Version (2308.08335v1)

Abstract: In this paper, we consider the analysis and control of continuous-time nonlinear systems to ensure universal shifted stability and performance, i.e., stability and performance w.r.t. each forced equilibrium point of the system. This "equilibrium-free" concept is especially beneficial for control problems that require the tracking of setpoints and rejection of persistent disturbances, such as input loads. In this paper, we show how the velocity form, i.e., the time-differentiated dynamics of the system, plays a crucial role in characterizing these properties and how the analysis of it can be solved by the application of Linear Parameter-Varying (LPV) methods in a computationally efficient manner. Furthermore, by leveraging the properties of the velocity form and the LPV framework, a novel controller synthesis method is presented which ensures closed-loop universal shifted stability and performance. The proposed controller design is verified in a simulation study and also experimentally on a real system. Additionally, we compare the proposed method to a standard LPV control design, demonstrating the improved stability and performance guarantees of the new approach.