Variability analysis and robust design of electronic system using cellular evolutionary strategies and interval arithmetic techniques

Abstract

Many real systems are difficult to model and control due to incomplete knowledge of the system behavior and the availability of only short-term or unreliable data records. Hence, the uncertainty, which results from both the measurement and modeling process, should be taken into account when making predictions or designing systems.Although this type of analysis, from input to output, can provide useful information to the decision-maker, we present an approach in which the inverse problem (robust design) can also be solved especially when there are specifications or constraints for the outputs. That is, we move from output to input and determine the effect of such specification in the inputs.This paper proposes innovative approaches based on the use of Interval Arithmetic (IA) and Cellular Evolutionary Strategies (CES) as alternative techniques to perform sensitivity and uncertainty analysis and to obtain robust system design. The proposed approaches are powerful tools that the decision-maker should use to validate and design any kind of systems.Interval Arithmetic is an alternative technique to find the sensitive elements of a design, to calculate how system accuracy varies as parameters vary. IA is able to consider simultaneously the effects of uncertainty of all of the parameters on a system accuracy and to provide strict bounds (the minimum and maximum values) with only one evaluation. CES are a recent approach that combines the Evolution Strategy techniques with concepts from Cellular Automata in order to obtain, by an iterative process, the maximum size of each deviation (robust design), while IA is used as a checking technique that guarantees the feasibility of the design.The approach used is an indirect method based on optimization instead of a direct method based on mapping from the output into the input space. CES does not rely on mathematical prerequisites to be applied and can be used for linear and non-linear constraints. The proposed approach is illustrated by an example applied to a circuit system. Results are compared with those obtained using a general non-linear optimization package.

A Survey of Applications of Interval Analysis to Robust Control

“…Piazzi and Visioli (1998b) propose a new feedforward/feedback synthesis design with the aim of minimizing the worst-case settling-time relative to the transition. Rocco et al (2001) propose an approach based on the combination of two tools: Interval Analysis and CES (Cellular Evolutionary Strategies). The result is the achieving of only one interval evaluation and of the exact range of the constraint functions inside the generated box.…”