04.12.16 - 09.12.16, Seminar 16491

Symbolic-Numeric Methods for Reliable and Trustworthy Problem Solving in Cyber-Physical Domains

Diese Seminarbeschreibung wurde vor dem Seminar auf unseren Webseiten veröffentlicht und bei der Einladung zum Seminar verwendet.


With the advent of cyber-physical systems that are increasingly penetrating our life, we are facing an ever-growing and permanent dependency on their reliable availability, continued function, and situationally adequate behavior even in highly sensitive application domains. As cyber-physical systems comprise complex, heteromorphic software systems, their reliability engineering calls for combinations of theories and methods traditionally considered separate. While we have recently seen some of the necessary combinations blossom, e.g., the theory of hybrid systems bridging continuous control with reactive systems, other areas remain less developed and explored. A prominent one is the role of numerics in cyber-physical systems: while it is obvious that cyber-physical systems increasingly rely on numerical software components, e.g., in signal processing or in state representation and extrapolation during situation assessment and planning, specific methods for addressing the issues associated, like consequences of numerical inaccuracy and methods for confining propagation of errors, are just in their infancy. This is in stark contrast to the use of numerics in more mature branches of computing, like signal processing or numerical analysis, where quantization effects as well as genesis and propagation of numerical error is well understood and dedicated methods for controlling it in critical application, like various forms of interval-based numerical algorithms, are readily available. The aforementioned “traditional” methods are, however, not versatile enough to cope with the cyber-physical setting, where numerical results, like state extrapolations over significant temporal horizons, enter into complex and safety-critical decision making, rendering error propagation potentially highly discontinuous. It seems that future critical applications, like automated driving contributing to the EU’s “Vision Zero” of eliminating fatalities in road-bound traffic, consequently call for novel means of analyzing and controlling the impact of numerics on system correctness, complemented by pertinent means of verification for establishing the safety case. The germs of such methods obviously have to be sought in the research areas relevant to problem solving in cyber-physical domains:

  1. Design and analysis methods for hybrid discrete-continuous phenomena, in particular verification of numerical reactive systems such as embedded floating-point programs and hybrid systems, including novel means of error-propagation analysis;
  2. Verified numerics and arithmetic constraint, including verified integrations, interval or otherwise set-based methods and arithmetic constraint solving involving symbolic and/or numeric reasoning, and
  3. Planning and rigorous optimization in arithmetic domains, enclosing reactive and in-advance planning and optimization methods in complexly constrained spaces, robotics, astrodynamics and more.

The seminar aims at getting together prominent researchers from all the aforementioned areas, targeting a cross-fertilization between their fields of expertise and facilitating transfer of concepts, methods, and tools between the domains. The consequential combination of up to now only loosely coupled areas will shed light on how advanced numerical methods can help improve the state of the art in rigorously interpreting and controlling cyber-physical phenomena, and it will naturally include the broad set of domain-specific solutions to the pertinent issues of predicting the performance impact and controlling the propagation of error in various schemes of numeric and blended symbolic-numeric computation.