Numerical Optimal Control DRAFT

Foreword Optimal control regards the optimization of dynamic systems. Thus, it bridges two large and active research communities of applied mathematics, each with their own journals and conferences. A scholar of numerical optimal control has to acquire basic numerical knowledge within both fields, i.e. numerical optimization on the one hand, and system theory and numerical simulation on the other hand. Within this text, we start by rehearsing basic concepts from both fields. Hereby, we give numerical optimization the larger weight, as dynamic system simulation is often covered rather well in engineering and applied mathematics curricula, and basic optimization concepts such as convexity or optimality conditions and Lagrange multipliers play a crucial role in numerical methods for optimal control. The course is intended for students of engineering and the exact sciences as well as for interested PhD students and besides the abovementioned fields requires only knowledge of linear algebra and numerical analysis. The course should be accompanied by computer exercises, and its aim is to give an introduction into numerical methods for solution of optimal control problems, in order to prepare the students for using and developing these methods themselves for specific applications in science and engineering. The course is divided into four major parts [for each of which we also give a few references for further reading]. This script was written while the author was visiting ETH Zurich in spring 2011 to give a one semester master course on numerical optimal control.