Abstract

This dissertation presents five main contributions to the field of distance-based formation control
and target tracking for multi-agent systems.

The first contribution proposes a neural network-based backstepping controller for distancebased formation control in the presence of disturbance. Agents are modeled as second-order nonlinear systems, and a rigid graph theory is used to develop the controller. The radial basis function neural network (RBFNN) is used to compensate for unknown nonlinearities in the system dynamics, and the neural network (NN) weights tuning law is derived using the Lyapunov stability theory. The uniform ultimate boundedness of the formation distance error and NN weights norm estimation error is proven, and simulation results demonstrate the proposed method’s performance on nonlinear multi-agent systems.

The second contribution establishes the properties of the normalized rigidity matrix in two- and three-dimensional spaces. The upper bounds of the normalized rigidity matrix singular values are derived for minimally and infinitesimally rigid frameworks, and it is proven that transformations of a framework do not affect the normalized rigidity matrix properties. The maximum smallest singular value for a three-agent rigid framework in two-dimensional space is derived, along with the necessary and sufficient conditions to reach that value. The results are applied to stability analysis and control design of distance-based formation control, and numerical simulations are provided to illustrate the theoretical results.

The third contribution proposes an adaptive neural network-based backstepping controller for distance-based formation control and target tracking in the presence of bounded time delay and disturbance. The RBFNN is used to overcome unknown nonlinearities and disturbances, and the control signal is designed based on a Lyapunov function and Young’s inequality to alleviate the effect of state time delay. The adaptive NN weights tuning law is derived using the Lyapunov function, and the uniform ultimate boundedness of the formation distance error is proven. The performance of the proposed method is validated through simulation results and comparisons with an existing displacement-based method.

The fourth contribution addresses the leader-following formation control problem for heterogeneous, uncertain, input-affine, nonlinear multi-agent systems modeled by a directed graph. A tunable three-layer NN is proposed to approximate unknown nonlinearities, and the NN weights tuning laws are derived using the Lyapunov theory. The leader-following and formation control problems are addressed using a robust integral of the sign of the error feedback and NN-based control. The results are rigorously proven using the Lyapunov stability theory, and the performance of the proposed method is compared with two other results.

The fifth contribution is the study of formation control with constant communication delays for second-order, uncertain, nonlinear multi-agent systems with asymmetric control gain matrix and unknown control direction. A three-layer NN is proposed to approximate unknown nonlinearities, and the NN weights tuning law is derived using the Lyapunov stability theory. The leader-following formation control problem with communication delay is addressed using a delayed integral of error variables, NN-based control, and a robustifying term. The semi-globally uniformly ultimately bounded solution of closed-loop signals is rigorously proven using a barrier Lyapunov function, and simulation results are provided to evaluate the efficiency and performance of the proposed method.

The thesis concludes with a summary of the contributions, limitations of the proposed methods, and suggestions for future work.