Asynchronous Systems for Constraint Satisfaction: Filtering and Stability

We discuss the formulation of, and stability conditions for, a set of generally asynchronous signal processing systems for solving a class of constraint satisfaction problems. Problems within this class are specifically those where a quadratic conservation principle is known to exist, as commonly occurs in stationarity conditions associated with a variety of convex and nonconvex optimization problems. With the intent of addressing a wide range of system architectures, the presented stability results are formulated for use with both a generally asynchronous update protocol, modeled as sample-and-hold subsystems triggered by independent Bernoulli processes, and also first-order filtering of the asynchronous updates. Numerical examples are provided by illustration and reference, indicating system behavior consistent with the presented stability results.