# Networked & Complex Systems

The relevance of networked and complex systems is increasing significantly for controlling and automation in the course of developments like industry 4.0. Modern controlling techniques for these systems have to satisfy particular requirements concerning modularity and scalability. Distributed controlling algorithms are investigated at the chair of automatic control to achieve these requirements.

## Distributed systems & DMPC

A focus of research is on modular, distributed systems, which are composed by a large number of physically coupled subsystems. An example for this kind of systems is a smart grid. Distributed algorithms are predestinated to control high-scaled distributed systems. A popular way is to adapt model predictive controllers (MPC) for distributed systems. In this case, they are called distributed model predictive controllers (DMPC). The research in the environment of DMPC has several fields for research. One is the development of efficient algorithms, which ensure optimal behavior based on shared information and the investigation of stability guarantees for the controlled system by using decomposition schemes and parallel computation. Another field of research focuses on the consideration of the physical coupling between the subsystems. If information about the dynamical behavior of the neighbor of an agent is given, it can be considered in the optimization algorithm. As the considered system is both compley in dynamics and high-scaled, the implementation of controlling algorithms is challenging. To solve this issue, a framework is developed at the chair of automatic control, which uses the modularity of the network for a clear and simple usage. If the network is changing, the framework is able to automatically adapt its algorithm. This framework is used for the controlling of a scalable spring-mass system. The masses represent agents. Each of the agents are fully actuated and the size of the network is varied for the first simulation example. The simulation result for 100 agents is presented in the following video.

It is numerically shown, that the computational effort for each agent is mostly independent of the number of agents. This shows the predestination of the used algorithm for high-scaled distributed systems. Only the outer agents are actuated for another simulation example. As the agents are not able to directly control their neighbors, the controlling task can only be solved with the usage of communication. This task can be solved by using DMPC as well. The simulation result can be seen in the following video.

## Multiphysic systems

An sufficient precise model of technical systems often requires considering the dynamics with respect to time and space. Multiphysic systems have multiple and possible bi-directional physical effects, whose system description leads to coupled partial differential equations. Examples for this kind of system can be found in a lot of fields, as the inductive heating of components, the process in chemical reactors, the treatment of tumors by irradiation or the growing of crystals.

Adequate methods and algorithms for the planning of optimal trajectories of multiphysic systems are developed at the chair. Thereby, the focus lies on approaches which base on optimization. Standard software is used for the numerical solution for the sake of flexible usage. Appropriate approaches and methods for planning optimal control trajectories, optimizing position and geometry of actuators and a systematic handling of constraints is researched particularly. Due to the approach of “first-optimize-then-discretize”, an elegant derivation of the optimality conditions is possible while holding the guarantee, that the structure of the optimality conditions is appropriate for a numerical solution.

For a numerical solution of the optimality conditions is a software framework used, which allows the separation of algorithmic and numeric. A gradient based approach is used, which enables to transfer the numerical solution of the optimality conditions to specialized FEM software packages, e.g. COMSOL Multiphysics. This leads to a simplified handling of the numerical solution of coupled partial differential equations, even if the optimization problem contains complex parts.

A simulation of an optimal surface hardening is executed to present a typical example of use. Optimization parameters for the optimal heating are the control, the positioning and the geometry of the inductor. Overheating of the component is prevented through the optimization.

## Efficient real-time implementation of safety-critical control systems

Control systems are predominantly implemented on real-time computer systems. A major challenge is the sensitivity of control systems to temporal deviations in the input and output of sensor and actuator signals, which occur, for example, in networked systems due to varying signal propagation times (jitter).

Classically, this problem is avoided by strictly synchronous and periodic sampling. However, this approach is reaching its limits, as modern real-time systems are no longer restricted to a single controller, but combine a large number of applications. To make efficient use of computing resources, adaptive scheduling techniques such as mixed-criticality scheduling are required, which, however, lead to greater temporal uncertainties and thus to poorer quality of control. On the other hand, future real-time systems will increasingly consist of distributed and networked structures in which the classic synchronous approach is difficult to implement due to signal propagation times.

The research project “Quality-aware Co-Design of Responsive Real-Time Control Systems“, a cooperation with the Chair of Distributed Systems and Operating Systems, focuses on how the influence of uncertain timing on control can be quantified and used for an efficient yet safe design of real-time control systems.