A unified framework for the flexibility analysis and design of non-linear systems via parametric programming

Abstract

This chapter discusses a new framework based on parametric programming that unifies the solution of the various flexibility analyses and design optimization problems that arise for linear, convex, and nonconvex systems with deterministic or stochastic uncertainties and provides new information on the dependence of a system's flexibility on the values of the design variables. For systems with stochastic parameters described by any kind of continuous probability distribution, the procedures for evaluating the stochastic flexibility and the expected stochastic flexibility metrics are identical for both linear and nonlinear models once the parametric feasibility function expressions have been generated. The use of these expressions is, especially significant for nonlinear systems because they remove all nonlinearity from the intermediate optimization subproblems, something that would not be possible using nonparametric approaches. By considering the subproblems as multiparametric linear programs, the number of problems that needs to solved compared to existing approaches is drastically reduced, because it only increases linearly with the number of uncertain parameters as opposed to exponentially, and parametric information that allows the metrics to be evaluated for any structure and design through a series of function evaluations is obtained.