An Overview of Uncertain Control Co-Design Formulations

TL;DR

This paper reviews and formalizes various uncertain control co-design formulations, addressing limitations in existing methods by providing a generalized framework for capturing uncertainties in dynamic systems.

Contribution

It introduces a comprehensive generalized UCCD formulation and discusses multiple specialized formulations, enhancing understanding of uncertainty modeling without relying on specific solution strategies.

Findings

Developed a generalized UCCD formulation for uncertainty representation

Discussed issues related to objective functions and constraints in UCCD

Presented specialized formulations like stochastic and robust UCCD

Abstract

This article explores various uncertain control co-design (UCCD) problem formulations. While previous work offers formulations that are method-dependent and limited to only a handful of uncertainties (often from one discipline), effective application of UCCD to real-world dynamic systems requires a thorough understanding of uncertainties and how their impact can be captured. Since the first step is defining the UCCD problem of interest, this article aims at addressing some of the limitations of the current literature by identifying possible sources of uncertainties in a general UCCD context and then formalizing ways in which their impact is captured through problem formulation alone (without having to immediately resort to specific solution strategies). We first develop and then discuss a generalized UCCD formulation that can capture uncertainty representations presented in this article. Issues such as the treatment of the objective function, the challenge of the analysis-type equality constraints, and various formulations for inequality constraints are discussed. Then, more specialized problem formulations such as stochastic in expectation, stochastic chance-constrained, probabilistic robust, worst-case robust, fuzzy expected value, and possibilistic chance-constrained UCCD formulations are presented. Key concepts from these formulations, along with insights from closely-related fields, such as robust and stochastic control theory, are discussed, and future research directions are identified.