Explicit stochastic model predictive control for anti-pitching a high-speed multihull

Abstract

Heave and pitch motion control of a high-speed multihull is important for restraining its large heave and pitch motions and improving its seaworthiness. However, stochastic ocean wave disturbances and strict input constraints on the T-foil and the flap highly increase difficulties in heave and pitch motion control. This paper proposes a explicit stochastic model predictive control (ESMPC) approach for anti-pitching the multihull without the violation of the control input constraints. A quadratic cost function is designed for the stochastic receding-horizon optimization of MPC under control input constraints, by considering the stochastic control model for the multihull as the predictive model. Then, the stochastic optimization is converted into deterministic optimization based on a Kalman-filter-based estimator and state mean prediction, and the ESMPC law is obtained by a combination of offline design and online search, which reduces the complexity of online optimization and enhances real-time control performance. The mean-square boundedness of stochastic system state is theoretically analyzed using the Lyapunov theory. The control effectiveness is illustrated by simulations and experiments, from which the pitch motion and the heave motion are reduced by 30% and 40%, respectively.