Research On Distributed Consensus Problems For Multi-Agent Systems With Nonconvex Constraints

Researchers across diverse fields have been focusing on the consensus problem for multiagent systems for more than two decades.Groups of agents with simple functions can achieve complex and ordered functions through a distributed consensus protocol.There are many applications for consensus problems in multi-agent systems such as formation control for UAVs,attitude alignment of clusters of satellites,et cetera.Therefore,we can put a high value on consensus problems naturally in the sense of both theory and application.Physical limitations(e.g.,saturation and dead zone)exist in almost every practical system,and thus the saturation consensus is a frontier topic in multi-agent systems.After consulting and analyzing a great many existing works,we discuss consensus problems for discrete-time multi-agent systems whose states have nonconvex constraints in this thesis.Primary works are as follows:a)We propose a consensus protocol for a class of discrete-time double-integral multi-agent systems in directed networks with fixed topology and provide a method to analyze the consensus based on SIA transition matrix.Firstly,we analyze the communication topology of multi-agent systems and consider graph theory to analyze the consensus and converge rate for a continuous-time first-order multi-agent system.Furthermore,we present a control algorithm based on its own and neighbor's information for the discrete-time doubleintegral multi-agent system and utilize the convergence property of column vector in SIA matrix to analyze the consensus of the multi-agent system.Lastly,we give a sufficient condition for the consensus of the position state.Simulation analysis verifies the effectiveness of the control algorithm.b)We propose a class of distributed control algorithm on account of a novel restriction operator and the design of velocity damping gain for a discrete-time double-integral multiagent system with communication delays in a directed network with switching topology whose velocity has a nonconvex constraint.Firstly,we provide a restriction operator with restriction parameter under consideration of the nonconvex saturation constraint for agent's velocity.Secondly,we design a distributed state-feedback controller with velocity damping gain and transform the close loop multi-agent system into transition function with a rawstochastic matrix.Lastly,a sufficient condition utilizes the convexity of the stochastic matrix is provided to judge the consensus of the multi-agent system.System simulation illustrates the validity and effectiveness of the theory and control algorithm.c)We propose a class of distributed control algorithm based on a brand new state-feedback controller and the design of damping gains and conversion parameters for a discrete-time triple-integral multi-agent system with communication delays in a directed network with switching topology whose both velocity and acceleration have nonconvex constraints.In the first place,we consider the constitutional change of the agent' s dynamic caused by the nonconvex constraint of the system acceleration and propose a triple-integral agent dynamic.Furthermore,we present a state-feedback controller with both velocity damping gain and acceleration damping gain and introduce some conversion parameters to take a nonsingular conversion of coordinates.At last,we provide the design method for conversion parameters and damping gains by analyzing the convexity of the transition matrix and give a sufficient condition for the consensus of the position state of the multiagent system.System simulation shows the convergence process of velocities and accelerations with nonconvex constraints and verifies the effectiveness of the distributed control algorithm with multi-state under nonconvex constraints.