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Abstract:

Control systems are prevalent in modern technology with applications ranging from washing machines, hard drives and cars in domestics to high performance production machines in industry. The ever increasing customerdemands have led to rapid advances in sensing, computing and actuation technology, in turn increasing the role of advanced control theory. Thisevolution has led to the introduction of optimization techniques to obtain superior systems.A typical application of control theory is computing the signals required to perform a specific task, such as steering the system from one configuration to another or following a desired trajectory for one or more variables in the system. In addition, the system's performance, such as the execution time or energy consumption, andlimitations must be taken into account, leading to so-called optimal control problems.The problem formulation is key for finding solutions to these problems reliably and efficiently and constitutes the main focus of this thesis. To this end, both the mathematical structure of the system and the signal parameterizations are carefully chosen. A piecewise polynomial parameterization of the signals is adopted, allowing for a small dimensional optimization problem in which system limitations canbe imposed reliably, either by necessary and sufficient semi-definite conditions or a series of sufficient linear relaxations. In addition, so-called differentially flat systems, a generalization of linear systems, exhibit a mathematical structure that is particularly well suited for the problems at hand.For linear systems, the combination of both piecewise polynomials and differential flatness leads to a small-dimensional problem formulation, which can be solved reliably and efficiently. Additionally, time-optimality is achieved through a novel algorithm and system uncertainties are accounted for. For nonlinear differentially flatsystems, the geometric path following problem is tackled by projecting the problem onto the path and by applying a time transformation. By allowing additional freedom in the geometric path, the more general path planning problem can also be solved.