A Case Study Comparing Both Stochastic and Worst-Case Robust Control Co-Design Under Different Control Structures

Abstract

Motivated by current gaps in uncertain control co-design (UCCD) literature, this brief is focused on some of the implementation of these formulations, with an emphasis on optimal control structures, and uncertainty propagation techniques. Specifically, we propose three optimal control structures for UCCD problems: (i) open-loop multiple-control (OLMC), (ii) multistage control (MSC), and (iii) open-loop single-control (OLSC). Stochastic in expectation UCCD (SE-UCCD) and worst-case robust UCCD (WCR-UCCD) formulations are implemented for a simplified strain-actuated solar array case study. Solutions to the OLMC SE-UCCD problem are obtained using generalized Polynomial Chaos (gPC) expansion and Monte Carlo simulation (MCS). The OLMC and MSC WCR-UCCD problems are solved by leveraging the structure of the linear program, leading to polytopic uncertainties. Insights gained underscore the role of the control structure and UCCD formulations in managing the tradeoffs between risk and performance.