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Realization of nonlinear input-output equations in controller canonical form

Arvo Kaldmäe, Ülle Kotta (2018)

Kybernetika

In this paper necessary and sufficient conditions are given which guarantee that there exists a realization of a set of nonlinear higher order differential input-output equations in the controller canonical form. Two cases are studied, corresponding respectively to linear and nonlinear output functions. The conditions are formulated in terms of certain sequence of vector spaces of differential 1-forms. The proofs suggest how to construct the transformations, necessary to obtain the specific state...

Realization problem for a class of positive continuous-time systems with delays

Tadeusz Kaczorek (2005)

International Journal of Applied Mathematics and Computer Science

The realization problem for a class of positive, continuous-time linear SISO systems with one delay is formulated and solved. Sufficient conditions for the existence of positive realizations of a given proper transfer function are established. A procedure for the computation of positive minimal realizations is presented and illustrated by an example.

Realization problem for positive multivariable discretetime linear systems with delays in the state vector and inputs

Tadeusz Kaczorek (2006)

International Journal of Applied Mathematics and Computer Science

The realization problem for positive multivariable discrete-time systems with delays in the state and inputs is formulated and solved. Conditions for its solvability and the existence of a minimal positive realization are established. A procedure for the computation of a positive realization of a proper rational matrix is presented and illustrated with examples.

Realization theory for linear and bilinear switched systems: A formal power series approach

Mihály Petreczky (2011)

ESAIM: Control, Optimisation and Calculus of Variations

The paper represents the first part of a series of papers on realization theory of switched systems. Part I presents realization theory of linear switched systems, Part II presents realization theory of bilinear switched systems. More precisely, in Part I necessary and sufficient conditions are formulated for a family of input-output maps to be realizable by a linear switched system and a characterization of minimal realizations is presented. The paper treats two types of switched systems. The...

Realization theory for linear and bilinear switched systems: A formal power series approach

Mihály Petreczky (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is the second part of a series of papers dealing with realization theory of switched systems. The current Part II addresses realization theory of bilinear switched systems. In Part I [Petreczky, ESAIM: COCV, DOI: 10.1051/cocv/2010014] we presented realization theory of linear switched systems. More precisely, in Part II we present necessary and sufficient conditions for a family of input-output maps to be realizable by a bilinear switched system, together with a characterization of minimal...

Realization theory for linear and bilinear switched systems: A formal power series approach

Mihály Petreczky (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is the second part of a series of papers dealing with realization theory of switched systems. The current Part II addresses realization theory of bilinear switched systems. In Part I [Petreczky, ESAIM: COCV, DOI: 10.1051/cocv/2010014] we presented realization theory of linear switched systems. More precisely, in Part II we present necessary and sufficient conditions for a family of input-output maps to be realizable by a bilinear switched system, together with a characterization of minimal...

Realization theory for linear and bilinear switched systems: A formal power series approach

Mihály Petreczky (2011)

ESAIM: Control, Optimisation and Calculus of Variations

The paper represents the first part of a series of papers on realization theory of switched systems. Part I presents realization theory of linear switched systems, Part II presents realization theory of bilinear switched systems. More precisely, in Part I necessary and sufficient conditions are formulated for a family of input-output maps to be realizable by a linear switched system and a characterization of minimal realizations is presented. The paper treats two types of switched systems. The...

Realization theory methods for the stability investigation of nonlinear infinite-dimensional input-output systems

Volker Reitmann (2011)

Mathematica Bohemica

Realization theory for linear input-output operators and frequency-domain methods for the solvability of Riccati operator equations are used for the stability and instability investigation of a class of nonlinear Volterra integral equations in a Hilbert space. The key idea is to consider, similar to the Volterra equation, a time-invariant control system generated by an abstract ODE in a weighted Sobolev space, which has the same stability properties as the Volterra equation.

Receding horizon optimal control for infinite dimensional systems

Kazufumi Ito, Karl Kunisch (2002)

ESAIM: Control, Optimisation and Calculus of Variations

The receding horizon control strategy for dynamical systems posed in infinite dimensional spaces is analysed. Its stabilising property is verified provided control Lyapunov functionals are used as terminal penalty functions. For closed loop dissipative systems the terminal penalty can be chosen as quadratic functional. Applications to the Navier–Stokes equations, semilinear wave equations and reaction diffusion systems are given.

Receding horizon optimal control for infinite dimensional systems

Kazufumi Ito, Karl Kunisch (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The receding horizon control strategy for dynamical systems posed in infinite dimensional spaces is analysed. Its stabilising property is verified provided control Lyapunov functionals are used as terminal penalty functions. For closed loop dissipative systems the terminal penalty can be chosen as quadratic functional. Applications to the Navier–Stokes equations, semilinear wave equations and reaction diffusion systems are given.

Receding-horizon control of constrained uncertain linear systems with disturbances

Luigi Chisci, Paola Falugi, Giovanni Zappa (2002)

Kybernetika

The paper addresses receding-horizon (predictive) control for polytopic discrete-time systems subject to input/state constraints and unknown but bounded disturbances. The objective is to optimize nominal performance while guaranteeing robust stability and constraint satisfaction. The latter goal is achieved by exploiting robust invariant sets under linear and nonlinear control laws. Tradeoffs between maximizing the initial feasibility region and guaranteeing ultimate boundedness in the smallest...

Reconfigurability analysis for reliable fault-tolerant control design

Ahmed Khelassi, Didier Theilliol, Philippe Weber (2011)

International Journal of Applied Mathematics and Computer Science

In this paper the integration of reliability evaluation in reconfigurability analysis of a fault-tolerant control system is considered. The aim of this work is to contribute to reliable fault-tolerant control design. The admissibility of control reconfigurability is analyzed with respect to reliability requirements. This analysis shows the relationship between reliability and control reconfigurability defined generally through Gramian controllability. An admissible solution for reconfigurability...

Recursive identification algorithm for dynamic systems with output backlash and its convergence

Ruili Dong, Qingyuan Tan, Yonghong Tan (2009)

International Journal of Applied Mathematics and Computer Science

This paper proposes a recursive identification method for systems with output backlash that can be described by a pseudoWiener model. In this method, a novel description of the nonlinear part of the system, i.e., backlash, is developed. In this case, the nonlinear system is decomposed into a piecewise linearized model. Then, a modified recursive general identification algorithm (MRGIA) is employed to estimate the parameters of the proposed model. Furthermore, the convergence of the MRGIA for the...

Recursive identification of Wiener systems

Włodzimierz Greblicki (2001)

International Journal of Applied Mathematics and Computer Science

A Wiener system, i.e. a cascade system consisting of a linear dynamic subsystem and a nonlinear memoryless subsystem is identified. The a priori information is nonparametric, i.e. neither the functional form of the nonlinear characteristic nor the order of the dynamic part are known. Both the input signal and the disturbance are Gaussian white random processes. Recursive algorithms to estimate the nonlinear characteristic are proposed and their convergence is shown. Results of numerical simulation...

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