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How to make a dynamic system unidentifiable is an important but still openissue. It not only requires that the parameters of the systems but also theequivalent systems cannot be identified by any identification approaches. Thus,it is a much more challenging problem than the existing analysis of parameteridentifiability. In this paper, we investigate the problem of dynamicunidentifiability and design the controller to make the system dynamicsunidentifiable. Specifically, we first define dynamic unidentifiability bytaking both system parameters and equivalent systems into consideration. Then,we obtain the necessary and sufficient condition for unidentifiability based onthe Fisher Information Matrix. This condition is derived by analysis of therelationship between the unidentifiable parameters and the Hessian matrix ofthe system function. Next, we propose a controller design scheme for ensuringdynamic unidentifiability under linear system models. We prove that forcontrollable and observable linear time-invariant systems, the requirement ofunidentifiability is equivalent to the requirement of a low-rank controller.Then, the low-rank controller design problem is solved by transforming it intoa model order reduction problem. We demonstrate the effectiveness of our methodby simulation.

Unidentifiability of System Dynamics: Conditions and Controller Design