UC Berkeley

This dissertation is concerned with the distributed control of nonlinear multi-agent consensus problems. The main objective of the consensus study is to design distributed algorithms that rely on only local interaction to achieve global group behavior. We propose a distributed sliding mode control (DSMC) framework for nonlinear heterogeneous multi-agent systems under different information exchange topologies. The DSMC constructs the topological sliding surface and reaching law via a so-called "topological structured function". The control law obtained by matching the topological sliding surface and topological reaching law is naturally distributed. Under this framework, topological diversity is explicitly incorporated. Also, the consensus problem is significantly simplified by mapping N interconnected higher-order dynamics into an N-th order sliding variable. The DSMC framework supports both leaderless consensus and consensus with a leader. For both cases, we show asymptotic stability when the topology contains a spanning tree, and further prove finite-time convergence under the undirected topologies. We also extend the DSMC framework to MIMO systems.

To demonstrate the usage and show the effectiveness of DSMC, we discuss two major applications with simulation results. The first application is for heterogeneous platoon systems. The control objective is to regulate vehicles to travel at a common speed while maintaining desired inter-vehicle gaps. The information flow topology dictates the pattern of communication between vehicles in the platoon. The second application is for flocking of nonholonomic unicycle agents.