Static Output Feedback: On Essential Feasible Information Patterns
George Pappas, Sergio Pequito, Soummya Kar, A. Pedro Aguiar, Joao Carvalho

Citation
George Pappas, Sergio Pequito, Soummya Kar, A. Pedro Aguiar, Joao Carvalho. "Static Output Feedback: On Essential Feasible Information Patterns". 54th IEEE Conference on Decision and Control, 8, 24, March, 2015.

Abstract
In this paper, for linear time-invariant plants, where a collection of possible inputs and outputs are known a priori, we address the problem of determining the communication between outputs and inputs, i.e., information patterns, such that desired control objectives of the closed-loop system (for instance, stabilizability) through static output feedback may be ensured. We address this problem in the structural system theoretic context. To this end, given a specified structural pattern (locations of zeros/non-zeros) of the plant matrices, we introduce the concept of essential information patterns, i.e., communication patterns among inputs and outputs that satisfy the following conditions: (i) ensure arbitrary spectrum assignment of the closed-loop system, using static output feedback constrained to the information pattern, for almost all possible plant instances with the specified structural pattern; and (ii) any communication failure precludes the resulting information pattern from attaining the pole placement objective in (i). Subsequently, we study the problem of determining essential information patterns. First, we provide several necessary and sufficient conditions to verify whether a specified information pattern is an essential information or not. Further, we show that such conditions can be verified by resorting to polynomially complexity (in the dimensions of the state, input and output) algorithms. Although such verification can be performed efficiently, it is shown that the problem of determining essential information patterns is in general NP-hard. The main results of the paper are illustrated through examples.

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• HTML

  George Pappas, Sergio Pequito, Soummya Kar, A. Pedro Aguiar,
  Joao Carvalho. <a
  href="http://www.terraswarm.org/pubs/529.html"
  >Static Output Feedback: On Essential Feasible
  Information Patterns</a>, 54th IEEE Conference on
  Decision and Control, 8, 24, March, 2015.

• Plain text

  George Pappas, Sergio Pequito, Soummya Kar, A. Pedro Aguiar,
  Joao Carvalho. "Static Output Feedback: On Essential
  Feasible Information Patterns". 54th IEEE Conference on
  Decision and Control, 8, 24, March, 2015.

• BibTeX

  @inproceedings{PappasPequitoKarAguiarCarvalho15_StaticOutputFeedbackOnEssentialFeasibleInformationPatterns,
      author = {George Pappas and Sergio Pequito and Soummya Kar
                and A. Pedro Aguiar and Joao Carvalho},
      title = {Static Output Feedback: On Essential Feasible
                Information Patterns},
      booktitle = {54th IEEE Conference on Decision and Control},
      pages = {8},
      day = {24},
      month = {March},
      year = {2015},
      abstract = {In this paper, for linear time-invariant plants,
                where a collection of possible inputs and outputs
                are known a priori, we address the problem of
                determining the communication between outputs and
                inputs, i.e., information patterns, such that
                desired control objectives of the closed-loop
                system (for instance, stabilizability) through
                static output feedback may be ensured. We address
                this problem in the structural system theoretic
                context. To this end, given a specified structural
                pattern (locations of zeros/non-zeros) of the
                plant matrices, we introduce the concept of
                essential information patterns, i.e.,
                communication patterns among inputs and outputs
                that satisfy the following conditions: (i) ensure
                arbitrary spectrum assignment of the closed-loop
                system, using static output feedback constrained
                to the information pattern, for almost all
                possible plant instances with the specified
                structural pattern; and (ii) any communication
                failure precludes the resulting information
                pattern from attaining the pole placement
                objective in (i). Subsequently, we study the
                problem of determining essential information
                patterns. First, we provide several necessary and
                sufficient conditions to verify whether a
                specified information pattern is an essential
                information or not. Further, we show that such
                conditions can be verified by resorting to
                polynomially complexity (in the dimensions of the
                state, input and output) algorithms. Although such
                verification can be performed efficiently, it is
                shown that the problem of determining essential
                information patterns is in general NP-hard. The
                main results of the paper are illustrated through
                examples.},
      URL = {http://terraswarm.org/pubs/529.html}
  }
  

Posted by Sergio Pequito on 27 Mar 2015.
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