Robustness Analysis and Robust Design of Uncertain Systems

Abstract

This paper proposes a methodology for the analysis and design of systems subject to parametric uncertainty in which design requirements are specified via hard inequality constraints. Hard constraints are those that must be satisfied for all parameter realizations within a given uncertainty model. Uncertainty models given by norm-bounded perturbations from a nominal parameter value (i.e., hyperspheres) and by sets of independently bounded uncertain variables (i.e., hyperrectangles) are the focus of this paper. These models, which are also quite practical, allow for a rigorous mathematical treatment within the proposed framework. Hard-constraint feasibility is determined by sizing the largest uncertainty set for which the design requirements are satisfied. Assessments of robustness are attained by comparing this set with the actual uncertainty model. These assessments do not suffer from the numerical deficiencies of sampling-based methods. Strategies that enable the comparison of the robustness characteristics of competing design alternatives, the approximation of the robust design space, and the systematic search for designs with improved robustness are also proposed. Because the problem formulation is generic and the tools derived only require standard optimization algorithms for their implementation, this methodology is applicable to a broad range of engineering problems.