Emulated controller design for networked control systems implemented on FlexRay

Abstract

Abstract-We design stabilizing controllers for nonlinear networked control systems (NCS) whose transmissions are scheduled by FlexRay. FlexRay protocol has been developed by the automotive industry to provide high bandwidth and deterministic communications. It works with communication cycles which consist of a static segment and a dynamic segment during which different scheduling rules are employed. We generalize existing emulated controller designs to be applicable to NCS with FlexRay. We start from a feedback law which stabilizes the origin of the plant when there is no network. We then present a novel hybrid model of the closed-loop system when the controller is implemented over a network scheduled by FlexRay. Afterwards, we provide conditions on the network under which the stability of the NCS is ensured. In particular, we consider segments of arbitrary lengths and we provide segment-dependent maximal allowable transmission interval bounds. The analysis relies on the construction of a new hybrid Lyapunov function. We believe that this work demonstrates the flexibility of the emulation approach and that it can be used to investigate other control problems for NCS with switched protocols. I. INTRODUCTIONNetworked control systems (NCS) are systems which integrate computer networks into the control loops. The communication constraints induced by the network must be carefully taken into account when designing the controller for NCS. A common approach for the stabilization of NCS is emulation. The idea is to design a controller that stabilizes the plant in the absence of communication constraints, to implement the controller over the network and then to give conditions on the communication channel under which the stability of the NCS is preserved, see [1], [9], [13] for example. The emulation approach provides great freedom in the choice of continuous-time design tools and pertains to a large class of nonlinear NCS. On the other hand, the mathematical models of NCS are sometimes hard to relate to real physical networks. In this paper, we address this gap by tailoring emulation results so that they are applicable to NCS with FlexRay [3]. We need for that purpose to solve non-trivial technical issues notably in terms of modeling and Lyapunov analysis.