Novel Ways in Control and Computation: Predictive and Analog

控制和计算在整个科学和工程中发挥着越来越重要的作用。两者都是使能技术。例如，最初在控制和优化领域中开发的半定规划算法，现在是科学和工程中的重要工具。此外，越来越明显的是，控制和计算是生物体结构的基石，因为信息处理、控制和计算往往比基础物理学更相关。在过去的几十年里，控制和计算之间的相互作用已经非常富有成效。控制中的现代计算方法现在可以解决许多具有挑战性的问题，如果没有它们，这些问题就无法解决。另一方面，控制方法是理解和发展量子计算、神经网络和模拟计算等领域的新计算技术和数值算法的基础。尽管这些富有成效的互连，许多挑战仍然存在于控制和计算之间的交叉点。这个研究项目的长期目标是进一步将控制和计算联合收割机和集成，以便理解和开发控制和计算这两个方面都起着至关重要作用的问题的解决方案。为了实现这一点，我们主要集中在以下两个领域的研究项目（见图1）：·模型预测控制·模拟计算。具体来说，该项目的目标包括开发新的模型预测控制方案和使用动态系统来解决模拟方式的计算问题。这些问题代表了控制与计算交叉点出现的典型问题。该研究项目的结果可能会导致新的有效的工业控制问题的控制方案和新的强大的数值数学算法。研究结果为设计新型非线性模拟滤波器和新型模拟计算器件提供了理论基础。这些结果也可能有助于更好地理解生物体中的控制和计算，因为这两个方面都出现在神经元计算和遗传调控网络中。

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.