Adaptive disturbance attenuation via logic-based switching

The problem of attenuating unknown and possibly time-varying disturbances acting on a linear time-invariant dynamical system is addressed by means of an adaptive switching control approach. Given a family of pre-designed stabilizing controllers, a supervisory unit infers in real-time the potential behavior of each candidate controller and selects the one providing the best potential performance. To this aim, a set of test functionals is defined, which is shown to enjoy favorable inference properties under certain assumptions on the nature of the disturbances. Both persistent-memory and finite-memory test functionals are analyzed. Further, an implementation of the switching controller is proposed which always guarantees stability of the feedback loop, even if the disturbance characteristics are such that the switching is persistent. Simulation results are provided to show the effectiveness of the proposed method.