This thesis investigates optimization-based control allocation methods designed for fault-tolerant and scalable application in multi-stage rockets. It is particularly focused on rockets with Thrust Vector Control (TVC), aerodynamic fins and Reaction Control Systems (RCS). The aim is to minimize the error between control commands and actuator output, besides actuator effort. Both in nominal and faulty conditions. Three convex optimization formulations are proposed: an Angle-Deflection (AD) problem, a linearized problem and a Second-Order Cone Programming (SOCP) problem. The AD problem includes actuator deflections and the linearized and SOCP formulations jointly consider actuator deflections and engine throttling. This work allows integration of faulty scenarios by constraint tightening, allowing reconfiguration of control allocation without changing the problem structure. Simulation data is used to validate the effectiveness of the formulations in satisfying control commands and fault handling. The work contributes to fault-tolerant and scalable control allocation frameworks.

Quantile regression is a useful method to analyse data such that the estimates are more robust to outliers and the conditional distributions are more reliable for asymmetric distributions with respect to the commonly used ordinary least squares regression. Besides this, the quantile regression analysis might also include extra information on the conditional relations between the response variable and the explanatory variables. Therefore, it is previously used in educational sciences, among many other research areas. Bayesian statistics is an upcoming approach for computing estimates, as it allows prior knowledge modelling. The Bayesian quantile regression approach produces accurate parameter estimates by specifying prior distributions, likelihood estimators and MCMC methods to model an informative posterior distribution. In this research, the theory behind the quantile regression and the Bayesian quantile regression approach are considered. Especially Bayesian quantile regression for ordinal longitudinal data. This theory is then used on data of academic emotions to analyse its effect on attained grades of engineering students. Multiple aspects of quantile regression are included to analyse this effect, regarding gender, time and correlations between academic emotions. It was found that the quantile regression produced insights that were ignored by ordinary least squares regression, as the effects of anxiety altered over different quantiles. Especially when seperating genders, the effect of anxiety seemed to differ a lot between genders and different fractions of the response variable. Furthermore, an assumption for Bayesian quantile regression is made by specifying an exponentially distributed prior and by seperating the gender distributions, as was found by the estimates of the quantile regression approach.