Robust and optimal control

  title={Robust and optimal control},
  author={John Doyle},
  journal={Proceedings of 35th IEEE Conference on Decision and Control},
  pages={1595-1598 vol.2}
  • J. Doyle
  • Published 17 August 1995
  • Mathematics
  • Proceedings of 35th IEEE Conference on Decision and Control
This paper will very briefly review the history of the relationship between modern optimal control and robust control. The latter is commonly viewed as having arisen in reaction to certain perceived inadequacies of the former. More recently, the distinction has effectively disappeared. Once-controversial notions of robust control have become thoroughly mainstream, and optimal control methods permeate robust control theory. This has been especially true in H-infinity theory, the primary focus of… 

Neo-Robust Control Theory – Analysis on The Robust Sensitivity and Bandwidth – ∗

It is revealed, both theoretically and via the IEEJ HDD benchmark, that by using the phase information of uncertainty, much higher robust performance can be achieved than the existing small-gain and passivity approaches.

Fundamental Problems in Adaptive Control

1 The paper identifies three fundamental problems in adaptive control: the need to work with models of plants which may be very accurate but are virtually never exact; the inability to know, given an

Neo-robust control theory (part II)

It is revealed, both theoretically and via the IEEJ HDD benchmark, that by using the phase information of uncertainty, much higher robust performance can be achieved than the existing small-gain and passivity approaches.

The effects of redundant control inputs in optimal control

A necessary and sufficient condition is presented to strictly decrease the quadratic optimal performance index after control input extensions and these results show an essential difference between single-input and multi-input control systems.


Some of the concepts and outstanding issues for a new methodology that blends robust nonadaptive mixed µ-synthesis and stochastic hypothesis-testing concepts leading to the so-called RMMAC architecture are illustrated.

Robust stability of iterative learning control schemes

A notion of robust stability is developed for iterative learning control in the context of disturbance attenuation. The size of the unmodelled dynamics is captured via a gap distance, which in turn

On convexified robust control synthesis

Robust model predictive control: reflections and opportunities

The past three decades have witnessed important developments in the theory and practice of model predictive control (MPC). In particular, considerable effort has been devoted to robust MPC theory.

Neo-robust control theory for factorized uncertainty

  • Kang‐Zhi LiuB. Shirnen
  • Mathematics
    Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference
  • 2009
The idea of neo-robust control is extended to a class of uncertain systems with factorized uncertainty, which is good at describing the uncertainties arising in process control systems.

Positive real method for robust control problems

  • Liu ZhiYao Yu
  • Mathematics
    Proceedings of the 31st Chinese Control Conference
  • 2012
This paper discusses the robust design problems for systems with positive real property. In such case, an effective method is to make the nominal closed loop system strongly positive real or strictly



Linear control theory with an H ∞ 0E optimality criterion

This expository paper sets out the principal results in ${\bf H}_\infty $ control theory in the context of continuous-time linear systems. The focus is on the mathematical theory rather than

H/sub infinity /-optimal control with state-feedback

A H/sub infinity /-optimal control problem in which the measured outputs are the states of the plant is considered. The main result shows that the infimum of the norm of the closed-loop transfer

Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory

The problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time-domain results on the quadratic stabilization of uncertain systems and the

Least squares stationary optimal control and the algebraic Riccati equation

The optimal control of linear systems with respect to quadratic performance criteria over an infinite time interval is treated. Both the case in which the terminal state is free and that in which the

Robust stability with time-varying structured uncertainty

  • J. Shamma
  • Mathematics
    IEEE Trans. Autom. Control.
  • 1994
It is shown that robust stability holds only if there exist constant scalings which lead to a small gain condition, and the notion of stability here is finite-gain stability over finite-energy signals.

Optimal guaranteed cost control of discrete‐time uncertain linear systems

This paper considers the problem of constructing a controller which quadratically stabilizes an uncertain system and minimizes a guaranteed cost bound on a quadratic cost function. The solution is

The robust H2 control problem: a worst-case design

  • A. Stoorvogel
  • Mathematics, Computer Science
    IEEE Trans. Autom. Control.
  • 1993
An explicit expression is given for the worst-case H/sub 2/ norm when the disturbance system is allowed to vary over all nonlinear, time-varying and possibly noncausal systems with bounded L/ sub 2/-induced operator norm.

Sets and Constraints in the Analysis Of Uncertain Systems

This thesis is concerned with the analysis of dynamical systems in the presence of model uncertainty. The approach of robust control theory has been to describe uncertainty in terms of a structured

A state space approach to H ∞ optimal control

Simple state-space formulae are derived for all controllers solving a standard H∞ problem: for a given number γ≥0, find all controllers such that the H∞ norm of the closed-loop transfer function is