Event-Triggered Parameterized Control of Nonlinear Systems
Anusree Rajan, Pavankumar Tallapragada
TL;DR
The paper addresses event-triggered parameterized control (ETPC) for nonlinear systems subjected to external disturbances by representing the input as a linear combination of basis functions within a finite set $\Phi$. Coefficients are updated at triggering instants determined by an event-triggering rule, and a finite-horizon convex quadratic program minimizes the deviation between the model-based reference control and the parameterized signal, yielding a unique solution. Theoretical guarantees show global uniform ultimate boundedness of trajectories and a uniform positive lower bound on inter-event times (non-Zeno behavior), with the analysis hinging on a Lyapunov function and ISS-type bounds for actuation error and disturbance. Numerical experiments on a disturbed Lorenz system and a forced Van der Pol oscillator illustrate reduced communication and robust performance under disturbances, compared to ZOH-based ETC and other dynamic triggering approaches.
Abstract
This paper deals with event-triggered parameterized control (ETPC) of nonlinear systems with external disturbances. In this control method, between two successive events, each control input to the plant is a linear combination of a set of linearly independent scalar functions. At each event, the controller updates the coefficients of the parameterized control input so as to minimize the error in approximating a continuous time control signal and communicates the same to the actuator. We design an event-triggering rule (ETR) that guarantees global uniform ultimate boundedness of trajectories of the closed loop system. We also ensure the absence of Zeno behavior by showing the existence of a uniform positive lower bound on the inter-event times (IETs). We illustrate our results through numerical examples.