Information measures for control: invariance and reachability

• Applicant: Professor Dr. Majid Zamani
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: from 2018 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 395594770

In classical control, sensors and controllers are often connected through point-to-point wiring. In networked control systems (NCSs), they are spatially distributed, and communication networks are utilized for data transfer. Compared to classical control systems, NCSs provide many advantages such as reduced wiring, low installation and maintenance costs, and ease of modification. NCSs are being used in many areas such as automobiles, intelligent buildings, and smart manufacturing. Unfortunately, the use of communication networks in feedback loops makes the analysis of NCSs much more complex. The use of digital channels for data transfer from sensors to controllers limits the amount of data that can be transferred per unit of time, due to the finite bandwidth of the channel. This introduces quantization errors that can adversely affect the control performance.The problem of control and state estimation over a communication channel with a limited bit rate have attracted a lot of attentions in the past two decades. A tight lower bound on the data rate of a digital channel between the coder and the controller, to achieve some control tasks such as invariance can be characterized in terms of a notion of entropy which is described as an intrinsic property of the system and is independent of the choice of the coder and controller. For example, the notion of invariance entropy for deterministic control systems characterizes the minimal data rate of a communication channel, which is necessary to make a given subset of the state space invariant. As an example, for deterministic linear control systems, the minimal data rate has been characterized in terms of only the unstable eigenvalues of the system.This research proposal aims at designing and analyzing information measures for nondeterministic control systems to explain minimal data rates that are necessary for the realization of reachability properties. Given two subsets of the state space $T$ and $Q$ with $T \subseteq Q$, the reachability objective is to find a controller so that all trajectories of the closed loop starting in $Q$ reach the target set $T$ in finite time, while never leaving the set $Q$. The design of controllers for solving complex logical tasks is a challenge that cannot be tackled with classical design schemes. The so-called abstraction-based controller synthesis method is relatively recent and has proved to be a promising scheme. Unfortunately, the available implementations lead to an immense computational complexity, which prevents a wide-spread application of this method in practice. For the second phase of this project, we aim to use the developed information measures to quantify the computational complexity underling the abstraction-based synthesis approach, and thus answer the so far open question about its limitations: is the currently observed immense computational complexity a consequence of poorly designed algorithms or is this complexity a fundamental limitation?

• DFG Programme: Research Grants