Cooperative Control Of Networked Nonlinear Systems

In recent years, due to the broad applications of multi-agent systems in many areas such as cooperative control of unmanned air vehicles (UAVs), formation control of multi-robots, flocking of multi-agents, distributed senior network, congestion control in communication networks, coop-erative control of networked system has attracted great attention of scientists in physics, biology, control science and computer science. The basic problems for cooperative control of networked system are consensus control, rendezvous control, flocking control and formation control, the latter three can be viewed as extensions or special cases of consensus control.In the framework of cooperative control, this thesis investigates the cooperative tracking problem of networked first-order nonlinear systems in the presence of uncertainty, virtual-agent-tracking based output synchronization control of networked strict-feedback systems with unknown parameters, actual-state based output synchronization control for networked strict-feedback sys-tems with unknown parameters, output synchronization of networked power integrators, consensus of networked agents with unknown control directions. Details are as follows:Considering the dynamics of agents are first-order integrators in the presence of uncertain-ty and disturbance, furthermore, the leader’s velocity is unmeasurable, we propose a cooperative tracking controller for each agent, such that the error between follower and the leader is bounded. Since the leader’s velocity is unmeasurable, each agent has to estimate the leader’s velocity by a distributed estimator. Combining adaptive parameter updater together with disturbance compen-sator, it is proved via Lyapunov theory that the tracking error between each agent and the leader is uniformly ultimately bounded (UUB) when the communication digraph has a spanning tree or strongly connected.When the dynamics of agents in the network are in strict-feedback forms with unknown pa-rameters, it is assumed that there is a virtual agent for each actual agent. The dynamic of the virtual agent is a linear integrator system with the same order as the actual agent’s model. Employing tra-ditional consensus controller, the outputs of all virtual agents can be synchronized. Meanwhile, we design a tracking controller for each actual agent via backstepping method such that its output can track the output of the virtual agent asymptotically. Therefore, output synchronization of the network is realized as long as there is a spanning tree in the communication digraph. Note that the above method may lead to large amount of computation and virtual state transmitting, i.e., the information transmitted throughout the network is the state of virtual agent which is obtained by calculation rather than by measuring, as an improvement, we propose an actual-state based con-troller for each agent. This distributed controller for each agent contains four parts:state-feedback of itself, neighborhood information, parameter updaters for the unknown parameters in its own dy-namic and parameter updaters for the unknown parameters in its neighbors’dynamics. It is proved that output synchronization of the network can be realized while other states in the overall system maintain bounded when the communication graph is connected. Note that the order of the parame-ter updater may increase significantly when the system order increases, tuning function is designed to minimize the order of the updater. Furthermore, it is also distributed.As a special case of nonlinear system, power integrator system has been well studied. For the first time, we investigate cooperative control of multiple power integrator systems. Combined Graph theory, a non-increasing and semi-positive definite function named Augmented Laplacian Potential is constructed and a distributed output synchronization controller is designed for each agent via adding power integrator method, such that all agents’outputs can be synchronized while other states in the overall system maintain bounded under the topology condition that the undirected graph is connected. Moreover, when agent’s input channel is perturbed by an unknown but bounded disturbance whose bounds are also unknown, a disturbance compensator is designed via sliding mode control and adaptive control such that output synchronization of the networked system can still be realized while other states maintain bounded.Stabilization or tracking control of systems with unknown control directions, i.e., the sign of high-frequency-gain is unknown, has been a hot topic in control community in recent years. For the first time, we investigate consensus of networked systems whose control directions are unknown. Employing the Nussbaum function to adjust control direction automatically, a distribut-ed consensus controller is designed for each agent. The Sub-Lyapunov function in analysis can avoid multiple Nussbaum functions coupling together, thus, the analysis is simplified significantly. Together with Graph theory and Barbalat Lemma, it is proved that consensus of the network can be realized when the undirected graph is connected or the balanced digraph is weakly connected. Furthermore, we propose a distributed regulator such that the networked system not only achieves consensus but also be regulated to the equilibrium.Finally, a summary has been done for all the discussions in the dissertation, then, application prospects and future work are presented.