Decentralized disturbance accommodation with limited plant model information

Farhad Farokhi, Cédric Langbort, Karl H. Johansson

Research output: Contribution to journalArticlepeer-review

Abstract

This author's work was supported in part by the 2010 AFOSR MURI, "Multi-Layer and Multi-Resolution Networks of Interacting Agents in Adversarial Environments." Abstract. The design of optimal disturbance accommodation and servomechanism controllers with limited plant model information is studied in this paper. We consider discrete-time linear time-invariant systems that are fully actuated and composed of scalar subsystems, each of which is controlled separately and influenced by a scalar disturbance. Each disturbance is assumed to be generated by a system with known dynamics and unknown initial conditions. We restrict ourselves to control design methods that produce structured dynamic state feedback controllers where each subcontroller, at least, has access to the state measurements of those subsystems that can affect its corresponding subsystem. The performance of such control design methods is compared using a metric called the competitive ratio, which is the worst-case ratio of the cost of a given control design strategy to the cost of the optimal control design with full model information. We find an explicit minimizer of the competitive ratio and show that it is undominated, that is, there is no other control design strategy that performs better for all possible plants while having the same worst-case ratio. This optimal controller can be separated into a static feedback law and a dynamic disturbance observer. For step disturbances, it is shown that this structure corresponds to proportional-integral control.

Original languageEnglish (US)
Pages (from-to)1543-1573
Number of pages31
JournalSIAM Journal on Control and Optimization
Volume51
Issue number2
DOIs
StatePublished - Jul 8 2013

Keywords

  • Large-scale system
  • Linear optimal control problem
  • Linear-quadratic problems
  • Problems with incomplete information

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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