Research Initiation Award: Stability of Feedback Systems with Sensor or Actuator Failures

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The project will study the problem of integrity in linear, time-invariant, multi- input, multi-output feedback systems. We consider the closed-loop stability of the unity-feedback system under three classes of sensor or actuator failures. In the first class any arbitrary number of loops, including all, may fail; in the second class any number of loops, except all, may fail; in the third class, any loop but only one loop may fail. We analyze the stability of the unity-feedback system with failures in each of the three classes. For the first class of failures, the plant and the compensator have to be stable from the start since the failure of all loops will reduce the configuration to a cascade connection. For a given multi-input multi-output plant which has no unstable hidden modes it is possible to parametrize the class of all compensators that stabilize the closed-loop system. Our goal is to parametrize the class of compensators that achieve integrity for each of the three classes of failures. As expected, such parametrization is possible only for certain classes of plants. The objectives are to identify those plants for which simultaneous stabilization of the nominal plant with each failure can be achieved, to find a systematic method to synthesize compensators that achieve this simultaneous stabilization, and to find the class of all achievable closed-loop transfer functions. This will indicate which performance objectives can be achieved together with integrity. Based on the parametrization of all compensators that the results will also be used in synthesis of compensators for systems with partial loop failures where constant gain factors are introduced in the feedback-loops and extended to an algebraic synthesis method for the case of structured dynamics being introduced in the loops.