LMI-Based Model Predictive Control for Underactuated Surface Vessels with Input Constraints

A nonlinear model predictive control (MPC) is proposed for underactuated surface vessel (USV) with constrained inputs. Aimed at the special structure of USV, a state-dependent coefficient (SDC) under the given USV is constructed in terms of diffeomorphism and state-dependent Riccati equation (SDRE) theory. Based on linear matrix inequalities (LMIs), the states of the USV are steered into an operating region around zero. When the states reach the region, the control law is switched to stabilize the system. And the constrained control input of the considered systemis solved by convex optimization based on MPC involving LMIs. The simulation results verified the effectiveness of the proposed method. It is shown that, based on LMIs, it is easy to get the MPC for the USV with input constraints.