Office of Technology Transfer – University of Michigan

Retrospective Cost Adaptive with Concurrent Model Identification

Technology #6930

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Dennis S. Bernstein
Managed By
Joohee Kim
Licensing Specialist, Physical Sciences & Engineering 734-764-8202

This technology uses past information about some system to infer non-minimum-phase zeros. Non-minimum-phase zeros occur in a large number of physical systems from riding a bike to aerodynamics to vibration. Understanding a system’s non-minimum-phase zeros is crucial to being able to control that system. At the moment, non-minimum-phase zeroes have to be determined empirically, through experience. This technology removes that need, and infers them based on general information about the system.

Applications for autopilots

This technology uses information about how a system has behaved in the past to create a model including non-minimum-phase zeros. It has been shown to work in extreme cases of missile auto-piloting. The technology has applications in military, aerospace, and even automotive industries to help maneuver machinery automatically without first gathering extremely large amounts of data.


  • Aerospace autopilots
  • Military missile autopilots
  • Commercial automotive and naval autopilots


  • Does not need extensive prior data from wind tunnels or similar sources.
  • More rapid method than table lookups used in current missile auto-piloting systems.