Game-theoretic approach for robust nonlinear Model Predictive Control on network dynamics

In this thesis, we explore the formation control of unmanned ground vehicles (UGVs) using a Nonlinear Model Predictive Control (NMPC) approach based on the Pontryagin Minimum (maximum, in the original form) Principle. The UGV model incorporates essential information about the involved agents dynamics, guiding our pursuit of optimal trajectories while concurrently establishing a dynamic network among them. The main goal of the thesis is to bridge the theoretical constructs with practical realities by introducing disturbances into the model. These disturbances, representing real-world uncertainties, contribute to the complexity of the control problem. To address the robust NMPC problem, we formulate the optimal control problem, in presence of exogeneous disturbance, as min-max optimization, wherein the goal is to minimize the trajectories for formation while maximizing the disturbances. To this end, we employ game theoretic approach, where the min-max optimal control problem can be viewed as a zero-sum game, with the aim of determining the minimum control inputs required for the formation while strategically maximizing the impact of disturbances. The incorporation of game theory introduces a strategic dimension to the control problem, seeking a Nash equilibrium point which coincides with a saddle node point of the Hamiltonian. By determining the parameters leading to this equilibrium, we establish the optimal control inputs necessary for formation under the influence of disturbances. Extending our focus beyond UGVs, we also propose the management of collision avoidance for drones within the formation. This is achieved through the implementation of the Artificial Potential Field (APF) method, enhancing the overall robustness and safety of the multi-agent system. The comprehensive approach outlined in this thesis combines advanced control techniques, disturbance modeling, and game theory, offering a nuanced perspective on the challenges associated with formation control in dynamic environments. The findings contribute to the growing body of knowledge in autonomous systems, paving the way for practical implementations in real-world scenarios.