Stabilisation and tracking for swarm-based UAV missions subject to time-delay

Abstract

It is well known that time-delay is often inherent in dynamic systems, which can be an important source of instability and degradation in the control performance. In particular, when safety is concerned for Unmanned Aerial Vehicle (UAV) applications, neglecting the presence of time-delay in the measurable states may jeopardise or result in catastrophic failures for operations. In this letter sufficient conditions for the existence of fuzzy state feedback gain are proposed for the stabilisation/tracking problem of swarm-based UAV missions subject to time-delays. The nonlinear model of the dynamics are represented by Takagi-Sugeno (TS) fuzzy models which offer a systematic analysis for stabilisation/tracking problems. Through a special property motivated by the Razumikhin theorem it allows the design of the distributed control law to be performed using tools from Lyapunov theory. The control law is composed of both node and network-level information. The design follows a two-step procedure. Firstly feedback gains are synthesised for the isolated UAVs ignoring interconnections among UAVs. The resulting common Lyapunov matrix is utilised at network level, to incorporate into the control law the relative differences in the states of the agents, to induce cooperative behaviour. Eventually stability is guaranteed for the entire swarm. The corresponding design criteria, proposed, are posed as Linear Matrix Inequalities (LMIs) where performance for the entire swarm is also stressed. The benefits of this analysis is that the design of the controller is decoupled from the size and topology of the network, and it allows a convenient choice of feedback gains for the term that is based on the relative state information. An illustrative example based on a UAV tracking scenario is included to outline the potential of the analysis.