Residual-driven non-causal tube-based stochastic model predictive control for wave energy converters with adaptive variance tightening and probabilistic safety

This paper proposes a residual-driven non-causal tube-based stochastic model predictive control (SMPC) framework for wave energy converters (WECs) to maximise absorbed energy while enforcing probabilistic safety under stochastic sea conditions. Short-horizon wave excitation force prediction is incorporated into a forward-looking receding-horizon controller, while disturbance uncertainty is calibrated online from wave-prediction residuals through a lightweight variance-update recursion. The resulting time-varying disturbance variance is used to drive adaptive tube tightening in the chance constraints, and the effective risk level is further calibrated online using tube-coverage information, enabling the controller to adjust its conservatism according to prediction quality and closed-loop uncertainty. An ancillary LQR feedback law and a steady-state Kalman filter are employed to improve robustness and implementability, while soft constraints are included to preserve feasibility under rare adverse realisations. The control action is obtained by solving a warm-started quadratic programme at each sampling instant. Simulation results using real wave data collected off the coast of Cornwall, UK, show that the proposed method maintains absorbed energy within 1% of a deterministic MPC benchmark, while achieving empirical tube-coverage rates of 92% for heave displacement and 90% for heave velocity. The results indicate improved tail-risk behaviour and a favourable performance-risk trade-off for prediction-enabled WEC control. • The proposed non-causal tube-based stochastic model predictive control is developed for wave energy converters. • The proposed algorithm updates disturbance variance online using wave-prediction residuals. • The proposed algorithm drives adaptive tube tightening using time-varying disturbance variance. • The proposed algorithm improves probabilistic safety under stochastic sea conditions. • The proposed algorithm preserves energy capture while reducing downside risk.