Investigation On Consensus For Multi-Agent Systems With Saturation Constraints

Distributed consensus coordination of multi-agent systems has been received many attractions due to its applications in such areas as distributed sensor networks, formation control, UAVs (unmanned aerial vehicles) in aerospace, astronautics and industrial pro-cess. However, the algorithms designed by control theory and applied on physical systems generally cannot satisfy expected performance, and sometimes cannot guarantee consen-sus. On the one hand, the reason is the difference between the theoretical model and the practical model. On the other hand, the important reason is that saturation constraints are not fully investigated when designing the consensus algorithms for the practical model of multi-agent systems. As a result, consensus algorithms designed by theoretical models are limited to apply on the practical plant. Therefore, according to the fact that physi-cal actuator is always subject to saturation constraints, consensus analysis and design in multi-agent systems have attracted many researchers, and a lot of works have been done in this cutting-edge research topics in the field of multi-agent systems in recent years.Based on the study of previous works, this thesis systematically and deeply inves-tigates consensus for continuous-and discrete-time multi-agent systems with saturation constraints in a unified leader-follower framework. A new design and analysis method to deal with first-order, high-order and linear agents with saturation constraints is proposed under undirected and directed topologies, and part of the developed theories is applied to the attitude coordinated tracking of multiple spacecraft with control input saturation.According to the analysis and summary of background and existing results on top-ics in this thesis, we establish a basic leader-follower frame to solve consensus problems after in-deep study on first-order single-integrator agents. As the first application of this frame, the effect of neighbours’saturated input for single-integrator agents is firstly con-sidered. Then, global consensus of continuous-and discrete-time single-integrator agents is solved under undirected topologies. Both input saturation and actuator saturation are considered in this chapter. Furthermore, different from existing consensus algorithms, a new consensus algorithm is proposed, which can significantly improve the convergence speed. The results show that global consensus for single-integrator agents can be achieved even when saturation constraints are involved. This thesis also investigates global consensus and coordinated tracking of marginal-ly stable agents with saturation constraints. At first, global consensus of marginally stable agents with actuator saturation is studied under undirected and detailed balanced directed topologies. Then, global coordinated tracking of continuous-and discrete-time marginal-ly stable agents with input saturation is investigated. The results further show that global consensus for high-order agents with saturation constraints can be achieved.Global consensus problems of non-stable dynamic agents with saturation constraints are solved in this thesis, including multi-oscillators and multi-integrator agents with satu-ration constraints. More specifically, the sufficient condition of global consensus for non-stable dynamic agents is having a directed spanning tree. Both undirected and detailed balanced directed topologies are considered. This result give an example of the important theoretic view that nonlinear feedback control algorithms are needed to achieve global consensus problems of non-stable dynamic agents with saturation constraints.As for the semi-global consensus problems, the semi-global consensus of linear multi-agent systems is firstly considered under undirected topologies. As a special case of linear agents, the global consensus problem of double-integrator dynamic agents is solved. Then, this chapter studies the same problem under directed topologies, and the parametric Lyapunov method is proposed to design consensus algorithms. This indicate that linear feedback control algorithms are capable of semi-global consensus for linear multi-agent systems.Based on the previous analysis, attitude coordinated controllers for multiple space-craft are designed with control input saturation. At first, based on the introduction of the nonlinear saturation function, a bounded attitude coordinated control law is proposed to deal with input saturation. Then, different from existing results, an attitude coordinated tracking algorithm with input saturation and without angular velocity measurements is p-resented. Specifically, controller designed method in this chanter can not only accomplish the attitude coordinated tracking but also reduce control complex in performance. These results provide a tentative design example in practical projects.