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Closed-loop subspace predictive control

Closed-loop subspace predictive control

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This chapter considers subspace predictive control of systems whose dynamics can be described locally by LTI models. The control algorithm is based on the predictor-based subspace identification framework. In a linear least-squares problem, the observer Markov parameters of the system are recursively estimated. Those parameters are used to construct an output predictor which is in turn used to solve a predictive control problem subject to constraints.

Chapter Contents:

  • Abstract
  • 7.1 Introduction
  • 7.2 Discrete-time identification framework
  • 7.2.1 Preliminaries and notation
  • 7.2.2 Data equations
  • 7.2.3 Relation to the ARX model structure
  • 7.2.4 Closed-loop identification issues
  • 7.2.5 Estimating the predictor Markov parameters
  • 7.2.6 Recursive solution of the parameter estimation problem
  • 7.2.7 Using directional forgetting
  • 7.3 Deriving the subspace predictor
  • 7.4 Setting up the predictive control problem
  • 7.4.1 Real time solution of the QP
  • 7.4.2 Parameter selection
  • 7.5 Concluding remarks
  • 7.5.1 Algorithm summary
  • References

Inspec keywords: Markov processes; recursive estimation; observers; closed loop systems; invariance; least squares approximations; predictive control

Other keywords: LTI model; closed-loop subspace predictive control; SPC; observer Markov parameter; linear least-squares problem; predictor-based subspace identification framework; recursive estimation

Subjects: Interpolation and function approximation (numerical analysis); Markov processes; Optimal control; Simulation, modelling and identification; Control system analysis and synthesis methods

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