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

• Final Report Year: 2023

Final Report Abstract

Networked and embedded control systems (NCSs) are becoming increasingly prevalent in many safety-critical applications, including aerospace, transportation, energy, and healthcare, due to their cost-effectiveness and reconfigurability. However, the use of communication networks in feedback control loops adds complexity to the analysis and design of NCSs. The digital channels used for data transfer from sensors to controllers limit the amount of data that can be transferred per unit of time, which can result in quantization errors that negatively impact control performance. To address this issue, a project was undertaken to extend the theory of invariance entropy to nondeterministic control systems. The project’s main achievements include the establishment of the notion of invariance feedback entropy (IFE) to characterize the minimal feedback data rate for set invariance for nondeterministic control systems. Additionally, several elementary properties of the IFE were established. For large interconnected networks, the computational complexity was countered by establishing an upper bound of the IFE in terms of the IFEs of smaller subsystems. Algorithms were also developed for the numerical computation of an upper bound of the IFE, which is applicable to any general nonlinear system. Furthermore, the project established a notion of reachability entropy and related it to reach-while-stay specification, which is a finite time property. A procedure was described to numerically compute an upper bound of the reachability entropy. A modular approach was also provided to compute an upper bound of the restoration entropy for large-scale networks by looking at them as interconnections of smaller subsystems. For minimal data rate for state estimation, restoration entropy is a relatively robust quantity than the topological entropy. Finally, the IFE was used to study the minimal feedback data rates to enforce regular safety properties. The project’s achievements have extended the theory of invariance entropy to nondeterministic control systems and have practical implications for the design of NCSs in safety-critical applications.

Publications

• Compositional Quantification of Invariance Feedback Entropy for Networks of Uncertain Control Systems. IEEE Control Systems Letters, 4(4), 827-832.
  Tomar, Mahendra Singh & Zamani, Majid
  
• Invariance Feedback Entropy of Uncertain Control Systems. IEEE Transactions on Automatic Control, 66(12), 5680-5695.
  Tomar, Mahendra Singh; Rungger, Matthias & Zamani, Majid
  
• Modular Computation of Restoration Entropy for Networks of Systems: A Dissipativity Approach. IEEE Control Systems Letters, 6, 3289-3294.
  Tomar, Mahendra Singh & Zamani, Majid
  
• Numerical over-approximation of invariance entropy via finite abstractions. Systems & Control Letters, 170, 105395.
  Tomar, M.S.; Kawan, C. & Zamani, M.
  
• On a notion of entropy for reachability properties. 2022 American Control Conference (ACC), 781-786. IEEE.
  Tomar, Mahendra Singh & Zamani, Majid
  
• Toward Minimal Data Rate Enforcing Regular Safety Properties: An Invariance Entropy Approach. IEEE Control Systems Letters, 7, 1476-1481.
  Tomar, Mahendra Singh & Zamani, Majid