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Ülle Kotta - One of the best experts on this subject based on the ideXlab platform.
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Adjoint Polynomial Formulas for Nonlinear State-Space Realization
IEEE Transactions on Automatic Control, 2014Co-Authors: Juri Belikov, Ülle Kotta, Maris TonsoAbstract:This paper focuses on computational aspects of the Realization of nonlinear multi-input multi-output systems. Instead of the algorithmic solutions, provided in earlier works, the explicit formulas are presented, which enable to compute the differentials of the State coordinates directly from the polynomial description of the nonlinear system. The solution is based on the concept of adjoint polynomials and requires a minimal amount of computations. The formulas are implemented in computer algebra system Mathematica and made available online via web Mathematica tools.
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transfer equivalence and Realization of nonlinear input output delta differential equations on homogeneous time scales
IEEE Transactions on Automatic Control, 2010Co-Authors: Daniele Casagrande, Ülle Kotta, Maris Tonso, Malgorzata WyrwasAbstract:Nonlinear control systems on homogeneous time scales are studied. First the concepts of reduction and irreducibility are extended to higher order delta-differential input-output equations. Subsequently, a definition of system equivalence is introduced which generalizes the notion of transfer equivalence in the linear case. Finally, the necessary and sufficient conditions are given for the existence of a State-Space Realization of a nonlinear input-output delta-differential equation.
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State Space Realization of bilinear continuous time input output equations
International Journal of Control, 2007Co-Authors: Ülle Kotta, A S I Zinober, Tanel Mullari, P KottaAbstract:This paper studies the realizability property of continuous-time bilinear input-output (i/o) equations in the classical State Space form. Constraints on the parameters of the bilinear i/o model are suggested that lead to realizable models. The paper proves that the 2nd order bilinear i/o differential equation, unlike the discrete-time case, is always realizable in the classical State Space form. The complete list of 3rd and 4th order realizable i/o bilinear models is given and two subclasses of realizable i/o bilinear systems are suggested. Our conditions rely basically upon the property that certain combinations of coefficients of the i/o equations are zero or not zero. We provide explicit State equations for all realizable 2nd and 3rd order bilinear i/o equations, and for one realizable subclass of bilinear i/o equations of arbitrary order.
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State Space Realization of nonlinear input output delta differential equations on homogeneous time scales
IFAC Proceedings Volumes, 2007Co-Authors: Daniele Casagrande, Ülle Kotta, Malgorzata WyrwasAbstract:Abstract The paper studies the nonlinear control systems on time scales that serve as models of time and unify the continuous and discrete time. The Realization problem for single-input single-output nonlinear delta differential systems is studied through the language of differential forms. Necessary and sufficient conditions are given for the existence of a State-Space Realization of the nonlinear input-output delta differential equation, i.e. a higher order delta differential equation relating the input, the output and a finite number of their delta-derivatives. The sufficiency part of the proof gives a constructive procedure (up to the integration of one-forms) for obtaining an observable State-Space description.
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Two Approaches for State Space Realization of NARMA Models: Bridging the Gap
Mathematical and Computer Modelling of Dynamical Systems, 2002Co-Authors: Ülle Kotta, Negar SadeghAbstract:This paper studies the necessary and sufficient conditions for observable Realization of a general class of nonlinear high-order input-output difference equations. In particular, it proves the equivalence of the two seemingly different existing approaches in the literature. The paper also provides a subclass of NARMA input-output models that are guaranteed to have an observable Realization. It is shown that this class covers several important subclasses of existing NARMA models.
Prodromos Daoutidis - One of the best experts on this subject based on the ideXlab platform.
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State Space Realizations for output feedback control of linear differential algebraic equation systems
International Journal of Control, 2001Co-Authors: Aditya Kumar, Ramakrishna Gandikota, Prodromos DaoutidisAbstract:This work addresses the derivation of State-Space Realizations for the output feedback control of linear, high-index differential-algebraic-equation systems that are not controllable at infinity and for which the control inputs appear explicitly in the underlying algebraic constraints. The constrained State Space of such systems depends on the control inputs, and thus, a State-Space Realization cannot be derived independently of the controller design. Motivated by this, initially a dynamic output feedback compensator is designed that yields a modified system for which the algebraic constraints are independent of the new control inputs. For this feedback modified system, a State-Space Realization is then derived which can be used for output feedback controller synthesis.
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State Space Realizations of linear differential algebraic equation systems with control dependent State Space
IEEE Transactions on Automatic Control, 1996Co-Authors: Aditya Kumar, Prodromos DaoutidisAbstract:This note addresses the derivation of State-Space Realizations for the feedback control of linear, high-index differential-algebraic-equation systems that are not controllable at infinity. In particular, a class of systems is considered for which the underlying algebraic constraints involve the control inputs, and thus a State-Space Realization cannot be derived independently of the feedback controller. The proposed methodology involves the design of a dynamic State feedback compensator such that the underlying algebraic constraints in the resulting modified system are independent of the new inputs. A State-Space Realization of the feedback-modified system is then derived that can be used as the basis for controller synthesis.
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feedback regularization and control of nonlinear differential algebraic equation systems
Aiche Journal, 1996Co-Authors: Aditya Kumar, Prodromos DaoutidisAbstract:The feedback control of nonlinear high-index differential-algebraic-equation systems for which the underlying algebraic constraints among the system variables involve the manipulated inputs is addressed in this work. A State-Space Realization of such systems cannot be derived independently of the controller design. In view of this fact, a two-step methodology is proposed for the control of such systems. The first step involves the derivation of a dynamic State-feedback compensator such that in the resulting system, the underlying constraints are independent of the new inputs. In the second step, a State-Space Realization of the feedback modified system is derived and used as the basis for a State-feedback controller synthesis. Application of the developed control methodology is demonstrated on an interconnection of a two-phase exothermic reactor and a condenser.
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control of nonlinear differential algebraic equation systems with disturbances
Industrial & Engineering Chemistry Research, 1995Co-Authors: Aditya Kumar, Prodromos DaoutidisAbstract:We address the control of a class of nonlinear, multivariable, high-index differential-algebraic-equation systems with external disturbances. Initially, an algorithmic procedure is developed to derive an equivalent State-Space Realization of the constrained system, valid for arbitrary disturbances. Then, on the basis of the derived State-Space Realization, a feedforward/feedback controller is developed to completely eliminate the effects of the measurable disturbances and induce a well-characterized input/output behavior in the constrained system. The application of the proposed control methodology is illustrated on a high-purity absorption column.
Atsushi Kawakami - One of the best experts on this subject based on the ideXlab platform.
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a State Space Realization form of multi input multi output two dimensional systems
Society of Instrument and Control Engineers of Japan, 1997Co-Authors: Atsushi KawakamiAbstract:We propose a method for obtaining State-Space Realization form of two-dimensional transfer function matrices. It contains free parameters, and we perform various considerations about it. Moreover, we present the conditions so that the State-Space Realization form exists.
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A State-Space Realization form of two-dimensional transfer functions
1997 European Control Conference (ECC), 1997Co-Authors: Atsushi KawakamiAbstract:In this paper, we propose a method for obtaining the State-Space Realization form of two-dimensional transfer functions (2DTF). By using our method, Realization form can be directly obtained from the coefficients of the 2DTF, without performing canonical decomposition of the State equations and solving nonlinear equations. Consider the possibility of reducing the Realization dimension in our State-Space Realization form, and obtain conditions imposed on 2DTF for the reduction. Moreover, we present a class of 2DTF that can be realized with a minimal dimension with respect to both of two variables.
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a State Space Realization form of multi input multi output two dimensional systems
Systems Man and Cybernetics, 1993Co-Authors: Atsushi KawakamiAbstract:In this paper, we propose a method for obtaining State-Space Realization form of two-dimensional transfer function matrices (2DTFM). It can be directly obtained from the coefficients of the given 2DTFM. This State-Space Realization form contains arbitrary constants, and by designating them properly, coefficients can be designated variously. And, we perform various consideration about this State-Space Realization. Moreover, we present the conditions so that the State-Space Realization exists. >
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a State Space Realization form of multi input multi output two dimensional systems
IFAC Proceedings Volumes, 1992Co-Authors: Atsushi KawakamiAbstract:Abstract In this paper, a method for obtaining State-Space Realization form of two-dimensional transfer function matrices (2DTFM), is proposed. It can be directly obtained from the coefficients of the given 2DTFM. This State-Space Realization form contains arbitrary constants, and by designating them properly, coefficients can be designated variously. And, various consideration about this State-Space Realization, is performed. Moreover, the conditions so that the State-Space Realization exists, is presented.
Malgorzata Wyrwas - One of the best experts on this subject based on the ideXlab platform.
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transfer equivalence and Realization of nonlinear input output delta differential equations on homogeneous time scales
IEEE Transactions on Automatic Control, 2010Co-Authors: Daniele Casagrande, Ülle Kotta, Maris Tonso, Malgorzata WyrwasAbstract:Nonlinear control systems on homogeneous time scales are studied. First the concepts of reduction and irreducibility are extended to higher order delta-differential input-output equations. Subsequently, a definition of system equivalence is introduced which generalizes the notion of transfer equivalence in the linear case. Finally, the necessary and sufficient conditions are given for the existence of a State-Space Realization of a nonlinear input-output delta-differential equation.
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State Space Realization of nonlinear input output delta differential equations on homogeneous time scales
IFAC Proceedings Volumes, 2007Co-Authors: Daniele Casagrande, Ülle Kotta, Malgorzata WyrwasAbstract:Abstract The paper studies the nonlinear control systems on time scales that serve as models of time and unify the continuous and discrete time. The Realization problem for single-input single-output nonlinear delta differential systems is studied through the language of differential forms. Necessary and sufficient conditions are given for the existence of a State-Space Realization of the nonlinear input-output delta differential equation, i.e. a higher order delta differential equation relating the input, the output and a finite number of their delta-derivatives. The sufficiency part of the proof gives a constructive procedure (up to the integration of one-forms) for obtaining an observable State-Space description.
Maris Tonso - One of the best experts on this subject based on the ideXlab platform.
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Adjoint Polynomial Formulas for Nonlinear State-Space Realization
IEEE Transactions on Automatic Control, 2014Co-Authors: Juri Belikov, Ülle Kotta, Maris TonsoAbstract:This paper focuses on computational aspects of the Realization of nonlinear multi-input multi-output systems. Instead of the algorithmic solutions, provided in earlier works, the explicit formulas are presented, which enable to compute the differentials of the State coordinates directly from the polynomial description of the nonlinear system. The solution is based on the concept of adjoint polynomials and requires a minimal amount of computations. The formulas are implemented in computer algebra system Mathematica and made available online via web Mathematica tools.
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transfer equivalence and Realization of nonlinear input output delta differential equations on homogeneous time scales
IEEE Transactions on Automatic Control, 2010Co-Authors: Daniele Casagrande, Ülle Kotta, Maris Tonso, Malgorzata WyrwasAbstract:Nonlinear control systems on homogeneous time scales are studied. First the concepts of reduction and irreducibility are extended to higher order delta-differential input-output equations. Subsequently, a definition of system equivalence is introduced which generalizes the notion of transfer equivalence in the linear case. Finally, the necessary and sufficient conditions are given for the existence of a State-Space Realization of a nonlinear input-output delta-differential equation.