We consider a particular model predictive control (MPC) problem involving a nonlinear constrained submarine in order to explore the specific features of this genre. A considerable amount of the extant theoretical literature is deliberately very general in its formulation and, by considering this physically comprehensible example, we are able to identify and develop generalisable results concerning the solution and behaviour of such problems in a way which is not available from the abstract viewpoint. The MPC which we consider is designed using a discretised nonlinear model with online constrained finite-horizon optimisation accompanied by an extended Kalman filter state estimator. This control is implemented on the continuous time submarine system. These observations are simulation-based, but use deliberately imperfect models in the MPC.
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