Formulation and applications of a variational feedback control technique

This work originates from the desire to produce innovative control for engineering applications in the field of Autonomous Vehicles (AVs). Nowadays, many controllers are present in the literature related to the AVs, from classical ones such as the Linear Quadratic Regulator to Model Predictive Controls techniques and Direct and Indirect methods based on Optimal Control Theories. Today used theories present some problems from an engineering point of view since they can be very demanding regarding the computational costs, or they may have some strict limitations in the mathematical form of the model. In this work, the goal was to find a reliable, robust and flexible control, which may be used with different dynamical systems providing an excellent fail-safe strategy. The flexibility requirement is due the versatility of Autonomous Vehicles regarding both models and applications. Anewmethodforcontrollingnonlineardynamicalsystemsishereintroduced, named FeedbackLocalOptimalityPrinciple–FLOP.TheFLOPcontrolisbasedonOptimal Control Theory and it tries to overcome some of the main difficulties of the classical theory and of its numerical method of solutions, i.e. directs and indirect methods. The FLOP control succeeds in providing a feedback control law for nonlinear dynamical systems, and its possible applications go from the control of ground vehicles, such as unicycles and autonomous cars to aerial and marine unmanned vehicles. In this thesis, the applicability of the FLOP control to Swarm Robotics applicationsisshown. Inparticular, thechancetocontrolahighnumberofnonlinear agents with different individual and collective tasks is explained deeply. The FLOP control, by the acceptance of a local optimum to a variational problem, is able to provide a feedback control law for a wide class of possible applications. It is a control that is easy to test since it does not require huge tuning-time, it has low computationalcostsandthereforeitcanbealsousedinreal-timeapplications. Inthis work it is tested on numerical examples and simulations, but further developments will show its applicability also in experimental situations