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.
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.
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...
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...
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...
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 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.
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...
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...
A new approach to manage actuator redundancy in the presence of faults is proposed based on reliability indicators and a reference governor. The aim is to preserve the health of the actuators and the availability of the system both in the nominal behavior and in the presence of actuator faults. The use of reference governor control allocation is a solution to distribute the control efforts among a redundant set of actuators. In a degraded situation, a reconfigured control allocation strategy is...
A method for reducing controllers for systems described by partial differential equations (PDEs) is applied to Burgers' equation with periodic boundary conditions. This approach differs from the typical approach of reducing the model and then designing the controller, and has developed over the past several years into its current form. In earlier work it was shown that functional gains for the feedback control law served well as a dataset for reduced order basis generation via the proper orthogonal...
We propose a general reduced-order filtering strategy adapted to Unscented Kalman Filtering for any choice of sampling points distribution. This provides tractable filtering algorithms which can be used with large-dimensional systems when the uncertainty space is of reduced size, and these algorithms only invoke the original dynamical and observation operators, namely, they do not require tangent operator computations, which of course is of considerable benefit when nonlinear operators are considered....
We propose a general reduced-order filtering strategy adapted to Unscented Kalman Filtering for any choice of sampling points distribution. This provides tractable filtering algorithms which can be used with large-dimensional systems when the uncertainty space is of reduced size, and these algorithms only invoke the original dynamical and observation operators, namely, they do not require tangent operator computations, which of course is of considerable benefit when nonlinear operators are considered....
The paper applies the pseudo-linear algebra to unify the results on reducibility, reduction and transfer equivalence for continuous- and discrete-time nonlinear control systems. The necessary and sufficient condition for reducibility of nonlinear input-output equation is presented in terms of the greatest common left factor of two polynomials describing the behaviour of the ‘tangent linearized system’ equation. The procedure is given to find the reduced (irreducible) system equation that is transfer...
We describe a model reduction algorithm which is well-suited for the reduction of large linear interconnect models. It is an orthogonal projection method which takes as the projection space the sum of the approximate dominant controllable subspace and the approximate dominant observable subspace. These approximate dominant subspaces are obtained using the Cholesky Factor ADI (CF-ADI) algorithm. We describe an improvement upon the existing implementation of CF-ADI which can result in significant...
In this paper we review the concept of regional boundary observability, developed in (Michelitti, 1976), by means of sensor structures. This leads to the so-called boundary strategic sensors. A characterization of such sensors which guarantees regional boundary observability is given. The results obtained are applied to a two-dimensional system, and various cases of sensors are considered. We also describe an approach which leads to the estimation of the initial boundary state, which is illustrated...