Adaptive formation control for second-order heterogeneous multi-agent systems with states nonidentical dimensions

An adaptive formation control is proposed for a specific class of second-order heterogeneous multi-agent systems (MASs) with state nonidentical dimensions. Each agent with nonidentical dimensions is introduced. A novel definition of a similar combination structure for heterogeneous MAS with nonidentical dimensions is presented. By calculating the similar attributes within this structure, similarity vectors or matrices that referred to as similar parameters between the leader and follower agents can be obtained. Based on the defined mapping transformation using these similar parameters, the dimensions of the followers can be aligned with those of the leader. A time-varying transformation equation incorporating exponential signals is designed to ensure that the physical states of the agents remains within predetermined bounds, thereby avoiding inter-agent collisions. The traditional radial basis function neural network is replaced with a novel structure in which the input of radial basis function neural network is loaded within a non-zero adaptive parameter. This new structure enables the online update of the radial basis function neural network’s approximation capability through the proposed adaptive laws. Furthermore, by employing the designed sliding mode control technique, the expanded state can be driven back into the finite domain of the radial basis function neural network when it exceeds the limits. Finally, two simulation examples are provided: one involving agents with identical dimensions and another with agents of non-identical dimensions in a nonlinear heterogeneous MAS. The effectiveness of the proposed control technique is demonstrated through simulation results and comparative analysis.