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

TL;DR

This paper addresses the output regulation problem for linear systems with sporadically sampled measurements governed by stochastic processes, proposing a hybrid regulator and stability conditions ensuring mean exponential stability.

Contribution

It introduces a novel hybrid regulator design combining a hybrid observer, internal model, and stabilizer for stochastic sampling scenarios, extending existing methods.

Findings

The proposed regulator achieves output regulation under stochastic sampling.

The stability conditions are expressed as LMIs, enabling practical design.

The approach is validated through a numerical example.

Abstract

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.