Robust and optimal control

Robust and optimal control

Kobe, Japan • December 1996 | John Doyle
This paper provides a brief review of the historical relationship between modern optimal control and robust control, highlighting how the latter has become mainstream and integrated into optimal control methods, particularly in H-infinity theory. The author traces the origins of robust control back to the 1970s, where critiques of LQG robustness led to the development of singular values and the H-infinity norm for robustness analysis. The 1980s saw the rise of H-infinity control, with significant research focusing on input-output settings and operator-theoretic methods. However, these methods faced challenges in handling multi-input multi-output (MIMO) systems. The paper discusses the evolution of state-space methods and the development of simpler controller formulae, emphasizing the role of linear matrix inequalities (LMIs). It also explores the integration of H-infinity control with other modern control topics and the potential for combining H2 and H-infinity control for robust performance. Finally, the paper touches on other important areas such as L1, μ, and real parameters, but notes that H-infinity theory has the most direct connections to optimal control.This paper provides a brief review of the historical relationship between modern optimal control and robust control, highlighting how the latter has become mainstream and integrated into optimal control methods, particularly in H-infinity theory. The author traces the origins of robust control back to the 1970s, where critiques of LQG robustness led to the development of singular values and the H-infinity norm for robustness analysis. The 1980s saw the rise of H-infinity control, with significant research focusing on input-output settings and operator-theoretic methods. However, these methods faced challenges in handling multi-input multi-output (MIMO) systems. The paper discusses the evolution of state-space methods and the development of simpler controller formulae, emphasizing the role of linear matrix inequalities (LMIs). It also explores the integration of H-infinity control with other modern control topics and the potential for combining H2 and H-infinity control for robust performance. Finally, the paper touches on other important areas such as L1, μ, and real parameters, but notes that H-infinity theory has the most direct connections to optimal control.
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