Output Regulation of Stochastic Sampled-Data Systems with Post-processing Internal Model

This paper deals with the output regulation problem (ORP) of a linear time-invariant (LTI) system in the presence of sporadically sampled measurement streams with the inter-sampling intervals following a stochastic process. Under such sporadically available measurement streams, a regulator consisting of a hybrid observer, continuous-time post-processing internal model, and stabilizer are proposed, which resets with the arrival of new measurements. The resulting system exhibits a deterministic behavior except for the jumps that occur at random sampling times and therefore the overall closed-loop system can be categorized as a piecewise deterministic Markov process (PDMP). In existing works on ORPs with aperiodic sampling, the requirement of boundedness on inter-sampling intervals precludes extending the solution to the random sampling intervals with possibly unbounded support. Using the Lyapunov-like theorem for the stability analysis of stochastic systems, we offer sufficient conditions to ensure that the overall closed-loop system is mean exponentially stable (MES) and the objectives of the ORP are achieved under stochastic sampling of measurement streams. The resulting LMI conditions lead to a numerically tractable design of the hybrid regulator. Finally, with the help of an illustrative example, the effectiveness of the theoretical results are verified

Pre-processing Nonlinear Output Regulation with Non-Vanishing Measurements

The paper deals with the output regulation problem of linear and nonlinear systems in the presence of measurements that, besides the regulation error, might include also extra outputs non-vanishing in steady state. We first show that, for linear systems, any \u201cpre-processing\u201d internal model-based solution solving the problem in a robust way necessarily relies on a stabilizer blocking the steady state effect of the extra measurements through properly located zeros. Motivated by this, a nonlinear pre-processing design strategy, relying on a \u201cwashout filter\u201d processing the non-vanishing measurements and generating a new output having zero steady state, is presented for nonlinear systems in a semiglobal setting. A new nonlinear non-resonance condition, underlying the stabilizability by output feedback of the cascade of the plant and the filter, is introduced