Iterative-interpolation algorithms for model reduction
Multimodeling control via system balancing.
Nonregular decoupling with stability of two-output systems
In this paper we present a solution to the decoupling problem with stability of linear multivariable systems with 2 outputs, using nonregular static state feedback. The problem is tackled using an algebraic-polynomial approach, and the main idea is to test the conditions for a decoupling compensator with stability to be feedback realizable. It is shown that the problem has a solution if and only if Morse’s list is greater than or equal to the infinite and unstable structure of the proper and stable...
On the Morgan problem with stability
Output average consensus over heterogeneous multi-agent systems via two-level approach
In this paper, a novel two-level framework was proposed and applied to solve the output average consensus problem over heterogeneous multi-agent systems. This approach is mainly based on the recent technique of system abstraction. For given multi-agent systems, we first constructed their abstractions as the upper level and solved their average consensus problem by leveraging well-known results for single integrators. Then the control protocols for physical agents in the lower level were synthesized...
Parametrization of observer based compensators in the frequency domain
Partial disturbance decoupling problem for structured transfer matrix systems by measurement feedback
Partial disturbance decoupling problems are equivalent to zeroing the first, say Markov parameters of the closed-loop system between the disturbance and controlled output. One might consider this problem when it is not possible to zero all the Markov parameters which is known as exact disturbance decoupling. Structured transfer matrix systems are linear systems given by transfer matrices of which the infinite zero order of each nonzero entry is known, while the associated infinite gains are unknown...
Random projections and hotelling's T² statistics for change detection in high-dimensional data streams
The method of change (or anomaly) detection in high-dimensional discrete-time processes using a multivariate Hotelling chart is presented. We use normal random projections as a method of dimensionality reduction. We indicate diagnostic properties of the Hotelling control chart applied to data projected onto a random subspace of Rn . We examine the random projection method using artificial noisy image sequences as examples.
Realization of nonlinear input-output equations in controller canonical form
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...
Reduced order controllers for Burgers' equation with a nonlinear observer
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...
Reduction and transfer equivalence of nonlinear control systems: Unification and extension via pseudo-linear algebra
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...
Reduction of large circuit models via low rank approximate gramians
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...
Riccati-like flows and matrix approximations
Robust adaptive stabilization of linear time-invariant dynamic systems by using fractional-order holds and multirate sampling controls.
Routh-type model reduction revisited
A computationally simple method for generating reduced-order models that minimise the norm of the approximation error while preserving a number of second-order information indices as well as the steady-state value of the step response, is presented. The method exploits the energy-conservation property peculiar to the Routh reduction method and the interpolation property of the -optimal approximation. Two examples taken from the relevant literature show that the suggested techniques may lead to...
Semi-smooth Newton methods for the Signorini problem
Semi-smooth Newton methods are analyzed for the Signorini problem. A proper regularization is introduced which guarantees that the semi-smooth Newton method is superlinearly convergent for each regularized problem. Utilizing a shift motivated by an augmented Lagrangian framework, to the regularization term, the solution to each regularized problem is feasible. Convergence of the regularized problems is shown and a report on numerical experiments is given.
Simplification of the generalized state equations
The paper studies the problem of lowering the orders of input derivatives in nonlinear generalized state equations via generalized coordinate transformation. An alternative, computation-oriented proof is presented for the theorem, originally proved by Delaleau and Respondek, giving necessary and sufficient conditions for existence of such a transformation, in terms of commutativity of certain vector fields. Moreover, the dual conditions in terms of 1-forms have been derived, allowing to calculate...
The partial non interacting problem: Structural and geometric solutions
The structure of nonlinear time delay systems
Multivariable nonlinear systems with time delays are considered. The delays are supposed to be constant but not commensurate. The goal of this paper is to give a structure algorithm which displays some system invariants for this class of systems.
Une nouvelle transformation des réseaux de Petri généralisés : l’abstraction généralisée
Cet article introduit une nouvelle transformation des réseaux de Petri généralisés appelée l’abstraction généralisée. C’est une réduction dont nous montrons qu’elle conserve les invariants du réseau de départ et les propriétés structurelles les plus importantes. Une fonction de transformation de marquages nous permet d’introduire l’étude de la conservation des propriétés comportementales.