This master thesis studies the implementation of a Robust MPC controllerin marine vessels on different tasks. A tube based MPC is designed based onsystem linearization around the target point guaranteeing local input to statestability of the respective linearized version of the original nonlinear system.The method is then applied to three different tasks: Dynamic positioningon which recursive feasibility of the nominal MPC is also guaranteed, Speed-Heading control and trajectory tracking with the Line of sight algorithm.Numerical simulation is then provided to show technique’s effectiveness. / Detta examensarbete studerar design och implementering av en robustmodellprediktiv regulator (MPC) för marina fartyg. En tub-baserad MPCär designad baserad på linjärisering av systemdynamiken runt en målpunkt,vilket garanterar local insignal-till-tillstånds stabilitet av det linjäriserade systemet.Metoden är sedan applicerad på tre olika uppgifter: dynamisk positionering,för vilken vi även kan garantera rekursiv lösbarhet för den nominellaregulatorn; riktningsstyrning; och banfötljning med en siktlinje-algoritm. Numeriskasimuleringsstudier bekräftar metodens effektivitet.

The work in this thesis focuses on the development of a Stochastic Model Predictive Control (SMPC) algorithm for linear systems with additive and multiplicative stochastic uncertainty subjected to linear input/state constraints. Constraints can be in the form of hard constraints, which must be satisfied at all times, or soft constraints, which can be violated up to a pre-defined limit on the frequency of violation or the expected number of violations in a given period. When constraints are included in the SMPC algorithm, the difficulty arising from stochastic model parameters manifests itself in the online optimization in two ways. Namely, the difficulty lies in predicting the probability distribution of future states and imposing constraints on closed loop responses through constraints on predictions. This problem is overcome through the introduction of layered tubes around a centre trajectory. These tubes are optimized online in order to produce a systematic and less conservative approach of handling constraints. The layered tubes centered around a nominal trajectory achieve soft constraint satisfaction through the imposition of constraints on the probabilities of one-step-ahead transition of the predicted state between the layered tubes and constraints on the probability of one-step-ahead constraint violations. An application in the field of Sustainable Development policy is used as an example. With some adaptation, the algorithm is extended the case where the uncertainty is not identically and independently distributed. Also, by including linearization errors, it is extended to non-linear systems with additive uncertainty.

Constraint handling is difficult in model predictive control (MPC) of linear differential inclusions (LDIs) and linear parameter varying (LPV) systems. The designer is faced with a choice of using conservative bounds that may give poor performance, or accurate ones that require heavy online computation. This thesis presents a framework to achieve a more flexible trade-off between these two extremes by using a state tube, a sequence of parametrised polyhedra that is guaranteed to contain the future state. To define controllers using a tube, one must ensure that the polyhedra are a sub-set of the region defined by constraints. Necessary and sufficient conditions for these subset relations follow from duality theory, and it is possible to apply these conditions to constrain predicted system states and inputs with only a little conservatism. This leads to a general method of MPC design for uncertain-parameter systems. The resulting controllers have strong theoretical properties, can be implemented using standard algorithms and outperform existing techniques. Crucially, the online optimisation used in the controller is a convex problem with a number of constraints and variables that increases only linearly with the length of the prediction horizon. This holds true for both LDI and LPV systems. For the latter it is possible to optimise over a class of gain-scheduled control policies to improve performance, with a similar linear increase in problem size. The framework extends to stochastic LDIs with chance constraints, for which there are efficient suboptimal methods using online sampling. Sample approximations of chance constraint-admissible sets are generally not positively invariant, which motivates the novel concept of ‘sample-admissible' sets with this property to ensure recursive feasibility when using sampling methods. The thesis concludes by introducing a simple, convex alternative to chance-constrained MPC that applies a robust bound to the time average of constraint violations in closed-loop.