Tracking Model Predictive Control Paradigm for Underwater Optical Communication

High-precision positioning of two underwater mobile robots is investigated in this work. To achieve good performance in underwater communication, control algorithms are implemented to maintain the position of the receiver robot aligned with that of the transmitter in the presence of measurement noise and process uncertainty. Although recent research works have successfully integrated control algorithms with Extended Kalman Filter (EKF) estimator to track the desired position of the transmitter, other aspects besides the convergence to the equilibrium point such as operational constraints and input constraints were not taken into account within these controllers. Such inability of these control algorithms may degrade the performance of the controlled process. Motivated by the above considerations, a tracking Model Predictive Control (MPC) with an EKF-based estimator is developed to both estimate the process states online and drive the actual system to the desired equilibrium point while meeting input and state constraints. The closed-loop stability and the recursive feasibility of the proposed tracking MPC scheme are rigorously proved. To demonstrate the applicability of the proposed control design, the performance of the tracking MPC with that of the conventional Proportional (P), Proportional Integral Derivative (PID), and Linear Quadratic Regulator (LQR) controllers are compared.