Discrete-time minimal control synthesis adaptive algorithm

This article proposes a discrete-time Minimal Control Synthesis (MCS) algorithm for a class of single-input single-output discrete-time systems written in controllable canonical form. As it happens with the continuous-time MCS strategy, the algorithm arises from the family of hyperstability-based di...

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Published in:	International journal of control Vol. 83; no. 12; pp. 2641 - 2657
Main Authors:	di Bernardo†, M., di Gennaro, F., Olm, J.M., Santini, S.
Format:	Journal Article
Language:	English
Published:	Abingdon Taylor & Francis Group 01.12.2010 Taylor & Francis Taylor & Francis Ltd
Subjects:	Adaptative systems Applied sciences Computer science; control theory; systems Control system synthesis Control theory. Systems discrete-time Exact sciences and technology minimal control synthesis model reference adaptive control Studies Control robustness Slow variation Control program Control synthesis Continuous time Adaptive control Canonical form Hyperstability Reference model Asymptotic stability Minimum time minimal control synthesis Uncertain system Continuous control Model reference adaptive control systems Discrete time SISO system discrete-time model reference adaptive control Formal verification
ISSN:	0020-7179, 1366-5820
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Abstract	This article proposes a discrete-time Minimal Control Synthesis (MCS) algorithm for a class of single-input single-output discrete-time systems written in controllable canonical form. As it happens with the continuous-time MCS strategy, the algorithm arises from the family of hyperstability-based discrete-time model reference adaptive controllers introduced in (Landau, Y. (1979), Adaptive Control: The Model Reference Approach, New York: Marcel Dekker, Inc.) and is able to ensure tracking of the states of a given reference model with minimal knowledge about the plant. The control design shows robustness to parameter uncertainties, slow parameter variation and matched disturbances. Furthermore, it is proved that the proposed discrete-time MCS algorithm can be used to control discretised continuous-time plants with the same performance features. Contrary to previous discrete-time implementations of the continuous-time MCS algorithm, here a formal proof of asymptotic stability is given for generic n-dimensional plants in controllable canonical form. The theoretical approach is validated by means of simulation results.
AbstractList	This article proposes a discrete-time Minimal Control Synthesis (MCS) algorithm for a class of single-input single-output discrete-time systems written in controllable canonical form. As it happens with the continuous-time MCS strategy, the algorithm arises from the family of hyperstability-based discrete-time model reference adaptive controllers introduced in (Landau, Y. (1979), Adaptive Control: The Model Reference Approach, New York: Marcel Dekker, Inc.) and is able to ensure tracking of the states of a given reference model with minimal knowledge about the plant. The control design shows robustness to parameter uncertainties, slow parameter variation and matched disturbances. Furthermore, it is proved that the proposed discrete-time MCS algorithm can be used to control discretised continuous-time plants with the same performance features. Contrary to previous discrete-time implementations of the continuous-time MCS algorithm, here a formal proof of asymptotic stability is given for generic n-dimensional plants in controllable canonical form. The theoretical approach is validated by means of simulation results.
Author	di Gennaro, F. di Bernardo†, M. Santini, S. Olm, J.M.
Author_xml	– sequence: 1 givenname: M. surname: di Bernardo† fullname: di Bernardo†, M. organization: Department of Systems and Computer Engineering , The University of Naples Federico II – sequence: 2 givenname: F. surname: di Gennaro fullname: di Gennaro, F. organization: Department of Systems and Computer Engineering , The University of Naples Federico II – sequence: 3 givenname: J.M. surname: Olm fullname: Olm, J.M. email: josep.olm@upc.edu organization: Department of Applied Mathematics IV , Universitat Politècnica de Catalunya – sequence: 4 givenname: S. surname: Santini fullname: Santini, S. organization: Department of Systems and Computer Engineering , The University of Naples Federico II
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Keywords	Control robustness Slow variation Control program Control synthesis Continuous time Adaptive control Canonical form Hyperstability Reference model Asymptotic stability Minimum time minimal control synthesis Uncertain system Continuous control Model reference adaptive control systems Discrete time SISO system discrete-time model reference adaptive control Formal verification
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SubjectTerms	Adaptative systems Applied sciences Computer science; control theory; systems Control system synthesis Control theory. Systems discrete-time Exact sciences and technology minimal control synthesis model reference adaptive control Studies
Title	Discrete-time minimal control synthesis adaptive algorithm
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