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Algorithms for data-driven H-norm estimation

Algorithms for data-driven H-norm estimation

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In this chapter, the problem of estimating in a model-free manner the H norm of a linear dynamic system is discussed at a tutorial level. Two recently developed methods for addressing this problem are presented, namely the power iterations method and a class of multi-armed bandit (MAB) algorithms. Due to reasons of space, many details are omitted, but references are provided to complement this exposition.

Chapter Contents:

  • 8.1 Motivation and problem formulation
  • 8.1.1 Problem formulation
  • 8.2 Power iterations
  • 8.2.1 Power iterations in linear algebra
  • 8.2.2 Power iterations for linear dynamical systems
  • 8.2.3 An example
  • 8.3 Multi-armed bandits
  • 8.3.1 Stochastic multi-arm bandits in a nutshell
  • 8.3.2 H∞-norm estimation as an MAB problem
  • 8.3.3 Regret lower bounds and optimal algorithms
  • 8.3.3.1 Regret lower bound in ΠSF
  • 8.3.3.2 Regret lower bound in Π
  • 8.3.4 The weighted Thompson sampling (WTS) algorithm
  • 8.3.5 An illustrative example
  • 8.4 Extensions to nonlinear systems
  • 8.4.1 de Bruijn graphs and prime cycles
  • 8.4.2 Finding the optimal stationary sequence
  • 8.5 Discussion and extensions
  • References

Inspec keywords: H∞ control; linear systems; iterative methods

Other keywords: MAB algorithm; data-driven H∞-norm estimation; multiarmed bandit algorithms; linear dynamic system; norm estimation

Subjects: Other topics in statistics; Optimisation techniques; Optimal control; Interpolation and function approximation (numerical analysis)

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