Robustness analysis for the certification of digital controller implementations

Abstract

Despite recent advances in the field of Networked Control Systems (NCS), the gap between the control design stage and the implementation stage on a physical platform remains significant. The simplifying assumptions made in the analysis of NCS are often not precise enough for realistic embedded control systems, and engineers must resort to time-consuming simulations and multiple redesign and testing phases before the performance of a system is judged adequate. Moreover, simulation-based methods do not typically provide rigorous performance or stability guarantees. We approach the problem of certifying a digital controller implementation from an input-output, robust control perspective. Following a standard method for analyzing sampled-data systems, we view the implementation step as a perturbation of a nominal linear time-invariant model. Nonlinearities and disturbances due to implementation effects are treated as uncertainty blocks and characterized via Integral Quadratic Constraints (IQCs), such as gain bounds. From our modeling discussion emerge some important types of uncertainties. We discuss some new gain bounds for one of them, namely an aperiodic sample-and-hold operator with uncertain sampling times. Two important features of the robust control approach are i) this approach is modular, i.e., the analysis of different uncertainty blocks can be done and refined separately, and the results combined in the study of a complete complex system; ii) the guarantees on the stability and performance of the implemented system can be obtained automatically via efficient computational tools.