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，半定规划算法，最初是在控制和优化领域发展起来的，现在是科学和工程领域的重要工具。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更相关。在过去的几十年里，控制和计算之间的相互作用取得了丰硕的成果。现代计算方法在控制允许当今解决许多具有挑战性的问题，不可能已经解决了他们。另一方面，控制方法对于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是基本的。尽管有这些卓有成效的相互联系，但在控制和计算的交叉领域仍然存在许多挑战。本研究项目的长期目标是进一步结合和整合控制和计算，以便理解和开发控制和计算这两个方面都发挥关键作用的问题的解决方案。为了实现这一点，我们在本研究项目中主要关注以下两个方面（参见图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以模拟方式解决计算问题。这些问题是控制与计算交叉领域出现的典型问题的代表。本课题的研究成果可能为工业控制问题提供新的高效控制方案，并为数值数学提供新的强大算法。研究结果可为新型非线性模拟滤波器和新型模拟计算器件的设计提供依据，在实时信号处理和控制中具有广泛的应用。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例如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.