Novel Ways in Control and Computation: Predictive and Analog

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Control and computation play an increasingly important role throughout science and engineering. Both are enabling technologies. For example, semidefinite programming algorithms, originally developed in the fields of control and optimization, are nowadays important tools in science and engineering. Moreover, it becomes more and more evident that control and computation is a cornerstone in the architecture of living organisms, because information processing, control and computation is often more relevant than the underlying physics. Over the last decades, the interaction between control and computation has been very fruitful. Modern computational methods in control allow nowadays to tackle many challenging problems which could not have been solved without them. On the other hand, methods from control are elementary for the understanding and the development of new computational technologies and numerical algorithms in fields like quantum computation, neuronal networks and analog computation. Despite these fruitful interconnections, many challenges remain in the intersection between control and computation. The long term goal of this research project is to combine and integrate control and computation further in order to understand and to develop solutions for problems where both aspects, control and computation, play a crucial role. To achieve this, we mainly focus in this research project on the following two areas (see also Figure 1): • model predictive control • analog computation. Specifically, the goals of this project include the development of new model predictive control schemes and the use of dynamical systems to solve computational problems in an analog fashion. These problems are representative for typical problems appearing at the intersection between control and computation. Results of this research project might lead to new efficient control schemes for industrial control problems and to new powerful algorithms in numerical mathematics. Furthermore, the results might provide the foundation for the design of new nonlinear analog filters and new analog computational devices with various applications in real-time signal processing and control. The results might also contribute to a better understanding of control and computation in living organisms, as both aspects appear for example in neuronal computation and in genetic regulatory networks.