Fixed-time consensus based cooperative control for multi-agent systems

Multi-agent systems have received intense research interest, offering advantages such as robustness and energy saving due to the capability to cooperate, namely, cooperative control of agents to collectively fulfill complex tasks. One fundamental research topic of cooperative control is consensus, which focuses on designing distributed controllers to drive agents to achieve state agreement. Most of the current work can achieve consensus over an infinite time horizon or in a finite time that depends on initial states, which fails to meet specific convergence requirement in an unknown environment. To address this issue, in this thesis, we solve the consensus problem in a fixed-time framework. A distinctive feature is that an estimated upper bound of settling time is obtained without dependence on initial states of agents once system parameters are determined. The fixed-time consensus for first-order multi-agent systems is investigated, including leaderless consensus, leader-following consensus, and containment control. Since second-order dynamics can better describe robot dynamics, fixed-time consensus is further investigated for second-order multi-agent systems. Then collective behaviours of dispersion and flocking are explored for second-order multi-agent systems by applying a fixed-time consensus based interaction rule. The resulting dispersion and flocking hold the advantages of scalability, connectivity, robustness, and effective area coverage. To further elaborate the interaction rule, in wireless robotic networks, a two-stage robot deployment strategy is proposed to build reliable and robust connections among distant stations. The main contributions of this thesis are summarized as follows: Firstly, the fixed-time consensus problem for multi-robot systems with single-integrator dynamics is investigated in the presence of discontinuous nonlinear inherent dynamics. Over a fixed topology, a distributed nonlinear protocol is proposed based on fixed-time stability analysis to achieve the state agreement in a fixed time without dependence on initial conditions. Over a switching topology, a common Lyapunov function is constructed and the fixed-time consensus is still guaranteed as long as the controller parameters are properly selected. Secondly, in the presence of single/multiple leaders, the fixed-time coordinated tracking probiii lem of nonlinear multi-agent systems over a directed graph is investigated. An upper bound of settling time is directly estimated once the system parameters are determined. Such an approach is able to provide system information in advance, i.e., the estimated settling time, when designing controllers in practical scenarios where the knowledge of initial conditions is unavailable. Thirdly, collective behaviours of dispersion and flocking are investigated for a team of mobile robots with double-integrator dynamics when interacting with each other by an acute angle test (AAT)-based interaction rule. For the dispersion, a spring-like collision-free controller is proposed, and system stability is analyzed with both fixed and switching topologies by using a new fixed-time consensus based energy function. For the flocking, the velocity matching is achieved by a class of generalized potential functions, and is analyzed using some non-smooth techniques. Finally, a two-stage robot deployment strategy is proposed to build reliable and robust connections between distant control stations while optimizing the communication quality of specific flows in wireless robotic networks. In the first stage, robots from distant groups are merged into one group that covers a desirable area. In the second stage, the flow between any two stations is further optimized in terms of ETX (expected number of transmissions per successfully delivered packet). In both stages, a proposed collision-free controller together with an AAT interaction model is implemented to guide robots to achieve the goal. In essential, the fixed-time consensus based strategies in this thesis are able to provide the state convergence information without dependence on initial conditions and therefore enable the design of controllers in an unknown environment.