Model Predictive Control with State Dependent Input Weight: An Application to Underwater Vehicles

Model predictive control (MPC) is an excellent approach for controlling systems with constraints. For nonlinear systems, nonlinear model predictive control (NMPC) is a natural solution, but it seems to be not suitable for system with relative fast dynamics. The main disadvantage is the time needed for solving the corresponding optimisation problem. Different approaches are used to simplify the optimisation problem and most of them yield an approximated optimal solution. It may happen that the best plant performances are obtained on the constraint borders. Thus, a controller that is able to handle and to work as close as possible to constraints without violating them, is desired. A faster computational power availability and improvements on the algorithms, make both the academic community and the industry to work intensively on the feasibility of using MPC on faster dynamics systems. In this work a model predictive control approach for controlling the depth of an underwater vehicle, with relatively fast nonlinear dynamics, is presented. Three different approaches are considered. For the internal model both a linear time invariant (LTI) and a linear time varying (LTV) model are implemented. A constant input weight is used for the LTI model, while for the LTV model also a state dependent input weight is utilised. The latter shows improvement on the control performance. An Extended Kalman Filter is used for state estimation.