A numerically tractable Stochastic Model Predictive Control (SMPC) strategy using Conditional Value at Risk (CVaR) optimization for discrete-time linear time-invariant systems, with state and input constraints, subject to additive uncertainty, is presented. SMPC strategies make use of the probabilistic description of uncertainty to define chance constraints which allow a certain admissible level of constraint violation. SMPC strategies require the initial state of a system to be within a particular set, referred to as feasibility set, probabilistically, such that the derived control input, when applied to the system, gives rise to states that are also within the feasibility set satisfying all chance constraints on the system. This leads to recursive feasibility of the SMPC strategy. Such strategies are restrictive in nature when the uncertainty in the system is unbounded, as in the case of White Gaussian noise. In such a case, the feasibility set is very small and leads to a strategy that is very conservative. To reduce this conservatism, some constraint violations are permitted. However, such violations affect the closed-loop behaviour of the system leading to performance degradation. This performance degradation can be quantified as a penalty on the system for violating constraints, and intuitively, it can be thought of as a risk taken by the system in that undesirable state. An approach following the exact penalty method is proposed using the CVaR function to determine the penalty cost. The same optimal solution as the original constrained problem is obtained from a single unconstrained minimization. Since accurate computation of the expected value of risk using the CVaR function is not possible, a scenario-based approximation of the CVaR is used to obtain an overall tractable and computationally efficient SMPC strategy. An extensive simulation study of the double integrator system is provided to present the functionality of the proposed method.

The Ampelmann system offers a safe and reliable solution for offshore access. As safety is a key factor, an extensive safety and warning management system is employed which accommodates for different fault types that may occur. Accommodation of sensor failure in the Ampelmann system is currently done through switching to a redundant component. However, there are several faults that are left undetected in the system. Detection only occurs when the faults exceed a critical threshold. Exceeding this threshold immediately results in shut-down of the system as safety is no longer guaranteed. For sensor equipment critical to the motion compensation, this leads to a code black in the system. The occurrences of code blacks should be limited where possible due to the fact that these lead to downtime. A critical sensor for the motion control is the position transducer in the hydraulic cylinders. The measured lengths are used for feedback purposes in the control system. The position transducer is redundant in each cylinder. The redundant sensor is mainly utilized for checking the main sensor. However, when the measurements from both sensors deviate too much from one another the system will shut down. Therefore, in this thesis, the possibility of a model-based fault detection method for the position transducer in the hydraulic cylinder is explored. Firstly, an accurate model of the hydraulic cylinder is derived and identified. Then, the model is combined with an observer to generate accurate estimates of the cylinder lengths. Furthermore, the estimates are compared with the actual measured cylinder lengths from the position transducer to generate residuals. Finally, the residuals are evaluated in order to make a decision about the health of the sensor. Three different fault types have been defined, which are expected to cause sensor degradation/failure. For each fault type, the residuals are evaluated. Prior to this a threshold has been defined based on a fault-free case. The threshold determines whether the system is healthy or not. Ideally, when there is no fault in the system, the residual is close to zero. Whereas, when there is a fault present the residual will be much larger. Whenever the threshold is exceeded, the detection system knows that there is a fault present, which allows it to sent out a warning. There are three model-based fault detection estimators which generate three different residuals. These three estimators are combined into one fault detection architecture. The results developed throughout this thesis have provided new insights for the fault monitoring system in the Ampelmann system. Currently it has only been applied for the position transducer. However, it can be extended to other critical components in the system. Furthermore, the work presented in this thesis is valuable for predictive maintenance purposes. Finally, the detection estimators can be used for the implementation of fault tolerant control in the system.