Morten Hagdrup: In daily life we are surrounded by an increasing number of devices that each involve some element of automatic control. Drones and self-driving cars are just the most recent examples.
In case a model is available for the dynamics of the system to be controlled, an optimization-based predictive control technique may well be an attractive option. However, the faster the systems dynamics, the more stringent requirements it puts on the execution of the optimization. This thesis offers an efficient implementation of an optimization problem occurring in the context of linear stochastic systems subject to constraints. Modelling of the linear system is done in continuous time and comprises both a deterministic and stochastic model part. To obtain a parsimonious parametrization, transfer functions are used. Also the cost function of the control problem is formulated in continuous time. This thesis analyzes the behaviour of the corresponding discretized control problems for increasingly fast sampling rate. Convergence theorems are proved for the case of uniform sampling with sampling time tending to zero.
Often a single deterministic model is not sufficient to capture the behavior of a system. The description may then be augmented with a stochastic part quantifying the degree of confidence in the deterministic model part. The presentation bridges the gap between deterministic and stochastic descriptions for sufficiently regular linear time-variant systems on state space form. It is shown how a description in terms of stochastic differential equations (SDE) results if one requires the state equations to hold in the sense of distributions. In particular it becomes clear why the stochastic integral appearing in the SDE must be defined the way it is.