Figures of Merit for Control Verification

Abstract

This paper proposes a methodology for evaluating a controller's ability to satisfy a set of closed-loop specifications when the plant has an arbitrary functional dependency on uncertain parameters. Control verification metrics applicable to deterministic and probabilistic uncertainty models are proposed. These metrics, which result from sizing the largest uncertainty set of a given class for which the specifications are satisfied, enable systematic assessment of competing control alternatives regardless of the methods used to derive them. A particularly attractive feature of the tools derived is that their efficiency and accuracy do not depend on the robustness of the controller. This is in sharp contrast to Monte Carlo based methods where the number of simulations required to accurately approximate the failure probability grows exponentially with its closeness to zero. This framework allows for the integration of complex, high-fidelity simulations of the integrated system and only requires standard optimization algorithms for its implementation.

A Verification-Driven Approach to Control Analysis and Tuning

“…In what follows, we assume that the uncertainty set ∆ = R(p, m) is given, and that the nominal design pointd belongs to Q. The latter assumption holds when ∆ is a subset of the MS in Equation (14). In contrast to the deformations presented thus far, the one required for bounding Q will take place in both the parameter and the design spaces.…”

“…However, their relaxed computational demands make them attractive in spite of their potential drawbacks. Because the framework in Reference [14] allows for a rigorous analysis of any given design point, the inaccuracies resulting from such drawbacks can be detected a posteriori.…”

“…Clearly, X is not unique. The following expressions, derived in detail in the companion paper [14], enable the calculation of several exclusion sets in p-and u-spaces. The first one is…”

“…This section presents a summary of the developments in Reference [14] that are essential to this paper. Interested readers should resort to this reference for additional details.…”

“…The search for robustly optimal controllers can be efficiently made by constraining the admissible design space to these bounding sets. In regard to control tuning, we propose strategies that improve the robust characteristics of a baseline controller by maximizing the control verification metrics proposed in Reference [14]. Formulations that alleviate the numerical burden of solving a min-max problem are also proposed.…”