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Alberto Isidori - One of the best experts on this subject based on the ideXlab platform.

  • global almost Disturbance Decoupling with stability for non minimum phase single input single output nonlinear systems
    Systems & Control Letters, 1996
    Co-Authors: Alberto Isidori
    Abstract:

    The so-called problem of almost Disturbance Decoupling with internal stability (ADDPS) is the following one. Given a system and an (arbitrarily small) number γ > 0, find a feedback law yielding a closed loop system which is stable and in which the gain (in the L2 sense) between the exogenous input and the regulated output is less than or equal to γ. The complete solution of this problem has been known since a long time in the case of linear systems. In the case of nonlinear systems, the only global results available so far in the literature were about SISO systems having an asymptotically stable zero dynamics. In this paper, a new set of results are presented, dealing with nonlinear SISO systems having a possibly unstable zero dynamics, which include the (general) class of linear SISO systems as a special case.

  • a note on almost Disturbance Decoupling for nonlinear minimum phase systems
    Systems & Control Letters, 1996
    Co-Authors: Alberto Isidori
    Abstract:

    This note discusses a recent paper by Marino et al.(Nonlinear H∞ almost Disturbance Decoupling, Systems Control Lett. 23 (1994) 159-168) who have presented a series of interesting results about the problem of almost Disturbance Decoupling, with internal stability, for nonlinear systems.

C H Moog - One of the best experts on this subject based on the ideXlab platform.

  • Disturbance Decoupling in nonlinear impulsive systems
    Conference on Decision and Control, 2019
    Co-Authors: Elena Zattoni, Anna Maria Perdon, Giuseppe Conte, C H Moog
    Abstract:

    This work deals with the problem of structural Disturbance Decoupling by state feedback for nonlinear impulsive systems. The dynamical systems addressed exhibit a hybrid behavior characterized by a nonlinear continuous-time state evolution interrupted by abrupt discontinuities at isolated time instants. The problem considered consists in finding a state feedback such that the system output is rendered totally insensitive to the Disturbance. Both the case of static state feedback and that of dynamic state feedback are considered. A necessary and sufficient condition for the existence of a static state feedback that solves the problem in the multivariable case is proven by defining suitable tools in the context of the differential geometric approach. The situation concerning solvability by a dynamic state feedback is examined in the framework of the differntial algeraic approach. A necessary and sufficient solvaility condition is conjectured and discussed.

  • Invariance, controlled invariance and conditioned invariance in structured systems and applications to Disturbance Decoupling
    2019
    Co-Authors: Giuseppe Conte, Anna Maria Perdon, Elena Zattoni, C H Moog
    Abstract:

    In this paper, dynamical systems whose structure is defined by means of a simple, directed graph are considered. These objects can be used to model structured systems or, more generally, networks of systems and systems of systems, where the relations between state, input and output variables or, respectively, between agents are known only for being zero or nonzero. Using an approach that is conceptually similar to the geometric approach developed for linear time-invariant systems, suitable notions of invariance, controlled invariance and conditioned invariance are introduced and related to the action of feedbacks. The results are used to provide general solvability conditions for Disturbance Decoupling problems expressed in graph-theoretic terms.

  • The Disturbance Decoupling problem for time-delay nonlinear systems
    IEEE Transactions on Automatic Control, 2000
    Co-Authors: C H Moog, R. Castro-linares, M. Velasco-villa, L.a. Marquez-martinez
    Abstract:

    In this paper, the Disturbance Decoupling problem (DDP) for a class of SISO nonlinear systems with multiple delays in the input and the state is studied. A pioneering mathematical approach is introduced for this class of systems and is claimed to be the cornerstone of the problem. Necessary and sufficient conditions are given for the existence of a bicausal feedback that solves the DDP. Sufficient conditions for the existence of a solution within other classes of compensators are included as well.

  • Disturbance Decoupling by measurement feedback for siso nonlinear systems
    IEEE Transactions on Automatic Control, 1999
    Co-Authors: Xiaohua Xia, C H Moog
    Abstract:

    The measurement feedback Disturbance Decoupling problem of nonlinear systems with single-input/single-output and single measurement is considered in this paper. Necessary and sufficient conditions are given for Disturbance Decoupling by static measurement feedback. New necessary conditions and sufficient conditions are presented for Disturbance Decoupling by dynamic measurement feedback.

  • output feedback Disturbance Decoupling in nonlinear systems
    IEEE Transactions on Automatic Control, 1996
    Co-Authors: R Andiarti, C H Moog
    Abstract:

    The problem of Disturbance Decoupling by means of output feedback is addressed. The notion of conditioned invariance is reconsidered in a linear algebraic framework. Using this geometric notion, a necessary and sufficient condition (respectively, necessary condition) is obtained for solving the Disturbance Decoupling problem by quasi-static output feedback (respectively, the Disturbance Decoupling problem by dynamic output feedback (DDDPO)). The necessary conditions for DDDPO which are derived are weaker than the existing ones, a sufficient condition for the Disturbance Decoupling problem by static output feedback is given as well.

Zongli Lin - One of the best experts on this subject based on the ideXlab platform.

  • brief further results on almost Disturbance Decoupling with global asymptotic stability for nonlinear systems
    Automatica, 1999
    Co-Authors: Zongli Lin, Xiangyu Bao, Ben M. Chen
    Abstract:

    As a complement to some new breakthroughs on global almost Disturbance Decoupling problem with stability for nonlinear systems, in a recent note, we identified a class of unstable zero dynamics that are allowed to be affected by Disturbances. The class of the unstable zero dynamics identified in that note is linear and have all the poles at the origin. In this paper, we enlarge such a class of zero dynamics to include any linear system with all its poles in the closed left-half plane. The condition on the way the Disturbance affects this part of zero dynamics is also identified. This enlargement is due to a new scaling technique that views each pair of jw axis zeros as a ''generalized integrator'' and transforms the zero dynamics into a number of chains of ''generalized integrators''.

  • almost Disturbance Decoupling with global asymptotic stability for nonlinear systems with Disturbance affected unstable zero dynamics
    Systems & Control Letters, 1998
    Co-Authors: Zongli Lin
    Abstract:

    The problem of global almost Disturbance Decoupling problem with stability for nonlinear system is revisited and is shown to be solvable for a class of nonlinear systems whose zero dynamics contains a chain of integrators affected by Disturbance. This result complements some recent work on the topic, where unstable zero dynamics is not allowed to be affected by the Disturbances.

  • h sub spl infin almost Disturbance Decoupling with internal stability for linear systems subject to input saturation
    IEEE Transactions on Automatic Control, 1997
    Co-Authors: Zongli Lin
    Abstract:

    For a linear system subject to input saturation and input-additive Disturbances, we show that: (1) the H/sub /spl infin//-almost Disturbance Decoupling problem with local asymptotic stability is always solvable via state feedback as long as the system in the absence of saturation is stabilizable, no matter where the open-loop poles are; and (2) the H/sub /spl infin//-almost Disturbance Decoupling problem with semiglobal asymptotic stability is solvable via state feedback as long as the system in the absence of saturation is stabilizable with all its open-loop poles located in the closed left-half plane. The results generalize those in Lin et al. (1996) by not requiring the Disturbance to be bounded by a known bound, or even bounded.

  • h sub spl infin almost Disturbance Decoupling with internal stability for linear systems subject to input saturation
    Conference on Decision and Control, 1996
    Co-Authors: Zongli Lin
    Abstract:

    For a linear system subject to input saturation and input-additive Disturbances, we show that: 1) the H/sub /spl infin//-almost Disturbance Decoupling problem with local asymptotic stability is always solvable via state feedback as long as the system. In the absence of saturation is stabilizable, no matter where the open loop poles are; 2) the H/sub /spl infin//-almost Disturbance Decoupling problem with semi-global asymptotic stability is solvable via state feedback as long as the system in the absence of saturation is stabilizable with all its open loop poles located in the closed left-halfplane; and 3) the H/sub /spl infin//-almost D-bounded Disturbance Decoupling problem with global asymptotic stability is solvable via state feedback as long as the system in the absence of saturation is stabilizable with all its open loop poles located in the closed left-half plane. The first two results generalize those in Lin et al. (1996) by not requiring the Disturbance to be bounded by a known bound, or even bounded. The third result generalizes those in Lin et al. in two ways: the open loop system does not have to be asymptotically stable, or even critically stable; and the Disturbances can be either magnitude bounded or energy bounded.

Alexey Zhirabok - One of the best experts on this subject based on the ideXlab platform.

  • Disturbance Decoupling in nonlinear hybrid systems
    Nonlinear Analysis: Hybrid Systems, 2018
    Co-Authors: Arvo Kaldmae, Ulle Kotta, Alexey Shumsky, Alexey Zhirabok
    Abstract:

    Abstract The paper studies the problem of Disturbance Decoupling of nonlinear hybrid systems. The hybrid systems under consideration are switched systems that consist of finite automaton, which defines the switching rule, a set of nonlinear discrete-time systems and the so-called mode activator, that defines an input for the automaton. Such systems allow to handle more complex switching rules than just time- or state-dependent switchings. The goal of the paper is to achieve the Disturbance Decoupling by dynamic measurement feedback. The advantage of such feedback is that it does not require estimations of state variables. Sufficient conditions are found under which there exists a dynamic measurement feedback, such that in the closed-loop system the controlled output of the hybrid system does not depend on the Disturbance. An algebraic approach called functions’ algebra is used, which can address in a similar manner both discrete-time systems and discrete-event systems (finite automaton).

  • Disturbance Decoupling in finite automata
    Language and Automata Theory and Applications, 2018
    Co-Authors: Alexey Zhirabok, Alexey Ye Shumsky
    Abstract:

    The paper addresses the Disturbance Decoupling problem by dynamic measurement feedback for finite automata. The mathematical technique called the pair algebra of partitions is used. The paper gives sufficient solvability conditions and a procedure to construct the required feedback.

  • Disturbance Decoupling in nonlinear hybrid systems
    International Conference on Control and Automation, 2016
    Co-Authors: Arvo Kaldmae, Ulle Kotta, Alexey Shumsky, Alexey Zhirabok
    Abstract:

    The problem of Disturbance Decoupling in nonlinear hybrid systems is investigated. The hybrid systems under consideration consist of finite automaton, the set of nonlinear difference equations and the so-called mode activator that coordinates the action of the other two parts. The hybrid controller is found that solves the Disturbance Decoupling problem via measurement feedback under certain (sufficient) solvability conditions. Examples illustrate the details of the solution.

  • faulty plant reconfiguration based on Disturbance Decoupling methods
    Asian Journal of Control, 2016
    Co-Authors: Arvo Kaldmae, Ulle Kotta, Alexey Shumsky, Bin Jiang, Alexey Zhirabok
    Abstract:

    The Disturbance Decoupling problem by dynamic measurement feedback DDDPM for discrete-time nonlinear control systems is considered in this paper. The mathematical approach known under the name "the algebra of functions" is used to derive an algorithm that finds, whenever possible, a measurement feedback which solves the DDDPM. Finally, the applicability of the DDDPM in fault tolerant control FTC is discussed.

  • measurement feedback Disturbance Decoupling in discrete event systems
    International Journal of Robust and Nonlinear Control, 2015
    Co-Authors: Arvo Kaldmae, Ulle Kotta, Alexey Shumsky, Alexey Zhirabok
    Abstract:

    SUMMARY The paper addresses the Disturbance Decoupling problem by dynamic measurement feedback for discrete event systems. The mathematical technique called the pair algebra of partitions is used. The paper gives sufficient solvability conditions and a procedure to compute the required feedback. Copyright © 2014 John Wiley & Sons, Ltd.

Arvo Kaldmae - One of the best experts on this subject based on the ideXlab platform.

  • Disturbance Decoupling in nonlinear hybrid systems
    Nonlinear Analysis: Hybrid Systems, 2018
    Co-Authors: Arvo Kaldmae, Ulle Kotta, Alexey Shumsky, Alexey Zhirabok
    Abstract:

    Abstract The paper studies the problem of Disturbance Decoupling of nonlinear hybrid systems. The hybrid systems under consideration are switched systems that consist of finite automaton, which defines the switching rule, a set of nonlinear discrete-time systems and the so-called mode activator, that defines an input for the automaton. Such systems allow to handle more complex switching rules than just time- or state-dependent switchings. The goal of the paper is to achieve the Disturbance Decoupling by dynamic measurement feedback. The advantage of such feedback is that it does not require estimations of state variables. Sufficient conditions are found under which there exists a dynamic measurement feedback, such that in the closed-loop system the controlled output of the hybrid system does not depend on the Disturbance. An algebraic approach called functions’ algebra is used, which can address in a similar manner both discrete-time systems and discrete-event systems (finite automaton).

  • Disturbance Decoupling in nonlinear hybrid systems
    International Conference on Control and Automation, 2016
    Co-Authors: Arvo Kaldmae, Ulle Kotta, Alexey Shumsky, Alexey Zhirabok
    Abstract:

    The problem of Disturbance Decoupling in nonlinear hybrid systems is investigated. The hybrid systems under consideration consist of finite automaton, the set of nonlinear difference equations and the so-called mode activator that coordinates the action of the other two parts. The hybrid controller is found that solves the Disturbance Decoupling problem via measurement feedback under certain (sufficient) solvability conditions. Examples illustrate the details of the solution.

  • faulty plant reconfiguration based on Disturbance Decoupling methods
    Asian Journal of Control, 2016
    Co-Authors: Arvo Kaldmae, Ulle Kotta, Alexey Shumsky, Bin Jiang, Alexey Zhirabok
    Abstract:

    The Disturbance Decoupling problem by dynamic measurement feedback DDDPM for discrete-time nonlinear control systems is considered in this paper. The mathematical approach known under the name "the algebra of functions" is used to derive an algorithm that finds, whenever possible, a measurement feedback which solves the DDDPM. Finally, the applicability of the DDDPM in fault tolerant control FTC is discussed.

  • measurement feedback Disturbance Decoupling in discrete event systems
    International Journal of Robust and Nonlinear Control, 2015
    Co-Authors: Arvo Kaldmae, Ulle Kotta, Alexey Shumsky, Alexey Zhirabok
    Abstract:

    SUMMARY The paper addresses the Disturbance Decoupling problem by dynamic measurement feedback for discrete event systems. The mathematical technique called the pair algebra of partitions is used. The paper gives sufficient solvability conditions and a procedure to compute the required feedback. Copyright © 2014 John Wiley & Sons, Ltd.

  • measurement feedback Disturbance Decoupling in discrete time nonlinear systems
    Automatica, 2013
    Co-Authors: Arvo Kaldmae, Alexey Shumsky, Ille Kotta, Alexey Zhirabok
    Abstract:

    The paper studies the Disturbance Decoupling problem by the dynamic measurement feedback for discrete-time nonlinear control systems. To address the problem the algebraic approach, called the algebra of functions, is applied, which allows the system description also depend on non-differentiable functions. A necessary and sufficient condition is given in terms of controlled and (h,f)-invariant functions. Also, algorithms are derived, which find invariant functions and the required feedback. The algorithms are implemented in Mathematica software which is made available over the internet.