Event-based controller design for a class of nolinear systems via convex optimization

In this paper, an event-based controller design scheme is proposed for a class of Lipschitz nonlinear systems. Using a delay system approach, the event-based system is modelled in a continuous time form. Then, the controller and event generator design methodology is formulated as a convex multi-objective optimization problem with LMI constraints, where the admissible Lipschitz constant of the system is maximized and data communication between plant and controller is minimized simultaneously. Finally, the proposed system is evaluated via simulations.

I. Introduction

In recent years there has been an explosion of interest in event-triggered control systems (or event-based systems). Event-triggered systems provide an alternative to well established (periodic) sampled-data systems and present the advantage that require lower data exchange between plant and controller, without significant performance degradation. In an event-triggered system a new control signal is processed and transmitted to the plant only when a pre-designed triggering condition is violated. Early works on event-based systems dates back to the 1990's [1], motivated by the advent of distributed and networked control systems, where limited channel capacity makes it desirable to investigate mechanisms to reduce unnecessary transfer of information between plant and controller. In [2], Tabuada proposed an event triggering strategy for a class of input-to-state (ISS) systems that retains the ISS properties of the original design. In [3], Lunze and Lehmann introduced a new method for event-based state feedback of LTI systems in which a control input generator is used to mimic a continuous feedback between two consecutive event times. In [4], Donkers and Heemels used an impulsive model to study the and stability of an output feedback control system in the presence of event-based mechanism. In the works cited before, it is assumed that the triggering condition is verified continuously which demands a high level of computational resources. To cope with this drawback, periodic event-triggered control (PETC) was proposed, where the event triggering condition is checked periodically [5], [6]. In [5], Heemels et. al. consider PETC for LTI systems and take different approaches such as impulsive systems and piecewise linear systems to analyze the stability of the proposed system. In [6] Hu et. al. proposed a novel periodic, event triggering sampling scheme, and using delay system approach, studied the control for state feedback linear systems.