Connectivity-Preserving Consensus Control For Nonlinear Multi-Agent Systems With Limited Communication Ranges

The research on nonlinear multi-agent systems is of great significance whether from the perspective of theoretical research and practical applications.At present,the consensus control of nonlinear multi-agent system has become an important topic in control field.Note that most of the previous works rely on the assumption that the communication between agents is distance-independent.In many practical scenarios,the communication between agents is bound to be related to the distances and communication ranges between agents.A typical example is that the networked mobile robots can only interact with others within the ranges limited by the communication capability of the equipped wireless devices,and cannot interaction out of the ranges.Any connection interruption may cause the failure of the multiagent systems consensus control task.In order to ensure the implementation of consensus,a basic condition is usually that the communication network topology can be communicated frequently enough during the dynamic evolution of the system.Yet,for the given initial conditions and system dynamics,this condition is generally difficult to satisfy and verify,especially the connectivity of the initial communication network topology can not guarantee the connectivity in the whole evolution process.Therefore,the connectivity-preserving consensus control for nonlinear multi-agent systems subject to limited communication ranges is a unneglected and challenging problem.Based on Lyapunov stability theory and adaptive Backstepping recursive design,this dissertation studies the connectivity-preserving consensus control of nonlinear multi-agent systems with limited communication ranges.The specific works of this study are listed as follows:1.The fixed-time consensus control problem with preserved connectivity is considered for a class of strict-feedback nonlinear multi-agent systems.Firstly,Fourier series expansion is used to approximate the periodically time-varying disturbances,and then the approximation result is taken as a part of the inputs of radial basis function neural networks to describe the unknown disturbance-dependent nonlinear functions of the systems.A fixed-time filter is designed to avert the “explosion of calculation” problem caused by the repeatedly differentiation of virtual controllers in the conventional Backstepping recursive design procedure,and relax the requirement of filter time signal.In consideration of the limited communication ranges,a unified error transformation is utilized to preserve the initial connectivity of communication network topology determined by the initial location and communication ranges of the agents.Based on the Lyapunov stability theory and fixed-time theory,the proposed controller can ensure the distributed consensus errors converge to a small neighborhood around zero in fixed time.2.A connectivity-preserving dynamic event-driven control strategy is proposed for stochastic strict-feedback nonlinear multi-agent systems.By associating Fourier series expansion with fuzzy logic systems,a function approximator is constructed to describe the disturbancedependent nonlinear functions in the systems.A nonlinear filter is designed to avert the“explosion of calculation” problem and to estimate the upper bound of virtual controller to obtain reliable control capability.A nonlinear error transformation is incorporated to preserve the initial connectivity of communication network topology.Based on stochastic system stability theory and adaptive control method,dynamic event-driven control strategy is designed.It is proved that the proposed control strategies can ensure the connectivitypreserving consensus in the sense of fourth moment and the uniformly ultimately boundedness of other signals in the closed-loop systems in the sense of probability.In addition,the Zeno behavior is avoided by rigorous theoretical proof in the sense of probability.3.A connectivity-preserving predefined accuracy control scheme is studied for a class of switched nonlinear multi-agent systems.From the perspective of system dynamics,two typical practical factors,switched nonlinearities and aperiodic time-varying disturbances,are considered simultaneously.Firstly,the switched nonlinearities are tackled by the common Lyapunov function.The congelation of variables method is used to estimate aperiodically time-varying parameters,which are fast-varying in an unknown compact set.The structural characteristic of the radial basis function neural networks is devoted to address the nonstrictfeedback structure.Finally,two switching functions are incorporated into the common Lyapunov function to design the connectivity-preserving predefined accuracy controller.Based on Lyapunov stability theory and Barbalat lemma,the proposed control scheme guarantees that the distributed consensus errors converge with a predefined accuracy around the zero.4.The problem of connectivity-preserving fixed-time prescribed performance control for a class of switched nonlinear multi-agent systems with nonstrict-feedback structure is studied.The connectivity of the initial communication network topology is preserved by nonlinear error transformation.Regard prescribed performance as constraints,based on Lyapunov stability theory and asymmetric barrier Lyapunov function method,the proposed continuous and event-driven control strategies can ensure that the distributed consensus errors converge to the predefined ranges determined by the performance function within an arbitrarily preassigned fixed-time.That is,the fixed-time prescribed performance is achieved.In addition,the threshold of the proposed event-driven mechanism can be switched according to the amplitude of the control signal,which appropriately reduces the number of updates of the control signal.The positive lower bound of the event-driven interval is ensured by strictly theoretical proof.That is,the Zeno behavior is strictly avoided.5.For a class of stochastic nonstrict-feedback switched nonlinear multi-agent systems,the problem of connectivity-preserving fixed-time prescribed performance control is considered.The system model takes stochastic noises,actuator saturations,switched nonlinearities and periodic disturbances into account.So the system structure is general.Firstly,the auxiliary system is designed to dynamically compensate the actuator saturations.The nonlinear error transformation is used to preserve the connectivity of the initial communication network topology.The feasibility condition of virtual controllers need to be satisfied when barrier Lyapunov function method employed in previous chapter to deal with prescribed performance constraint problems is overcome by using fractional transformation.According to Lyapunov stability theory and stochastic system stability theory,it is proved that the proposed control scheme can ensure the fixed-time prescribed performance and the boundedness of all closed-loop signals in probability.