Decentralised adaptive control of a class of hidden leader–follower non-linearly parameterised coupled MASs

In this study, decentralised adaptive control is investigated for a class of discrete-time non-linear hidden leader–follower multi-agent systems (MASs). Different from the conventional leader–follower MAS, among all the agents, there exists a hidden leader that knows the desired reference trajectory, while the follower agents know neither the desired reference signal nor which is a leader agent. Each agent is affected from the history information of its own neighbours. The dynamics of each agent is described by the non-linear discrete-time auto-regressive model with unknown parameters. In order to deal with the uncertainties and non-linearity, a projection algorithm is applied to estimate the unknown parameters. Based on the certainty equivalence principle in adaptive control theory, the control for the hidden leader agent is designed by the desired reference signal, and the local control for each follower agent is designed using neighbourhood history information. Under the decentralised adaptive control, rigorous mathematical proofs are provided to show that the hidden leader agent tracks the desired reference signal, all the follower agents follow the hidden leader agent, and the closed-loop system eventually achieves strong synchronisation in the presence of strong couplings. In the end, the simulation results show the validity of this scheme

Adaptive Synchronization of Nonlinearly Parameterized Complex Dynamical Networks with Unknown Time-Varying Parameters

A new adaptive learning control approach is proposed for a class of nonlinearly parameterized complex dynamical networks with unknown time-varying parameters. By using the parameter separation and reparameterization technique, the adaptive learning laws of periodically time-varying and constant parameters and an adaptive control strategy are designed to ensure the asymptotic convergence of the synchronization error in the sense of square error norm. Then, a sufficient condition of the synchronization is given by constructing a composite energy function. Finally, an example of the complex network is used to verify the effectiveness of proposed approach

Distributed adaptive control for nonlinear multi-agent systems with nonlinear parametric uncertainties

This paper considers the distributed tracking control problem for a class of nonlinear multi-agent systems with nonlinearly parameterized control coefficients and inherent nonlinearities. The essential of multi-agent systems makes it difficult to directly generalize the existing works for single nonlinearly parameterized systems with uncontrollable unstable linearization to the case in this paper. To dominate the inherent nonlinearities and nonlinear parametric uncertainties, a powerful distributed adaptive tracking control is presented by combing the algebra graph theory with the distributed backstepping method, which guarantees that all the closed-loop system signals are global bounded while the range of the tracking error between the follower's output and the leader's output can be tuned arbitrarily small. Finally, a numerical example is provided to verify the validity of the developed methods

Adaptive Consensus and Parameter Estimation of Multi-Agent Systems with An Uncertain Leader

In this note, the problem of simultaneous leader-following consensus and parameter estimation is studied for a class of multi-agent systems subject to an uncertain leader system. The leader system is described by a sum of sinusoids with unknown amplitudes, frequencies and phases. A distributed adaptive observer is established for each agent to estimate the unknown frequencies of the leader. It is shown that if the signal of the leader is sufficiently rich, the estimation errors of the unknown frequencies converge to zero asymptotically for all the agents. Based on the designed distributed adaptive observer, a distributed adaptive control law is synthesized for each agent to solve the leader-following consensus problem.Comment: 8 pag

Time-Energy Optimal Cluster Space Motion Planning for Mobile Robot Formations

The motions of a formation of mobile robots along predetermined paths are optimized according to a tunable time-energy cost function using the cluster space approach to multiagent system specification and control. Upon path-parameterizing cluster state variables describing the geometry and pose of a multirobot group, an optimal control problem is formulated that incorporates formation dynamics and state constraints. The optimal trajectory is derived numerically via a gradient search, iterating over the initial value of one costate. A multirobot formation control simulation is then used to demonstrate the effectiveness of the technique. Results indicate that a substantial tradeoff is made between energy expenditure and motion time when considered as minimization criteria in varying proportions, allowing the operator to tailor mission trajectories according to desired levels of each

Distributed Robust Synchronization Control of Multiple Heterogeneous Quadcopters with An Active Virtual Leader*

This paper studies leader-following synchronization control of a group of multiple quadrotor unmanned aerial systems (UASs). A robust distributed scheme is developed to maintain the attitude motions of UASs with an active virtual leader. Complicated settings are considered in the design, where the topology is in a directed graph, and only one or some agents are connected to the leader. UASs can have different dynamic parameters. Also, some time-varying disturbances are added to the closed-loop system. A control protocol containing a robust term is proposed to each UAS to achieve asymptotic consensus. A rigorous mathematical proof and numerical example are presented to demonstrate the effectiveness of our scheme

Adaptive fuzzy prescribed-time connectivity-preserving consensus of stochastic nonstrict-feedback switched multiagent systems

An adaptive fuzzy prescribed-time connectivity-preserving consensus protocol is designed for a class of stochastic nonstrict-feedback multiagent systems, in which periodic disturbances, switched nonlinearities, input saturation, and limited communication ranges are taken into consideration simultaneously. The connectivity, determined by the limited communication ranges and initial positions of agents, is preserved by incorporating an error transformation. Further, a common Lyapunov function is considered to deal with the switching modes. By combining a reduced fuzzy logic system with Fourier series expansion, a novel approximator is constructed to deal with periodically disturbed nonlinearities and to surmount the difficulty brought by the nonstrict-feedback structure. More importantly, distinctly from the existing finite/fixed-time control strategies where the settling time is heavily dependent on the accurate value of the initial states and control parameters, the settling time of the proposed prescribed-time consensus is completely independent of the initialization and control parameters and can be given a priori only according to actual demands. Based on the Lyapunov stability theory, the designed controller ensures that the connectivity-preserving consensus is achieved in prescribed time and all the signals remain bounded in probability. To the end, the feasibility of the proposed consensus protocol is demonstrated by simulation