Model-matching Problem Research Articles

Model matching for linear systems with delays and 2D systems

Model matching problem for linear systems with delays is considered, via a transfer matrix approach. We deal with a general class of neutral delay-differential systems, which is equivalent to 2D systems, from a realizability point of view. The solution of the problem is based on the decomposition of the ring of the causal rational functions (which is not a principal ideal domain) as the intersection of two suitable principal ideal domains.

Continuous-time envelope-constrained filter design via Laguerre filters and ℋ/sub ∞/ optimization methods

The envelope-constrained filtering problem is concerned with the design of a time-invariant filter to process a given input signal such that the noiseless output of the filter is guaranteed to lie within a specified output mask while minimizing the noise gain of the filter. An algorithm is developed to solve the continuous-time envelope-constrained filter design problem with the /spl Hscr//sub /spl infin// norm of the filter as the cost and an orthonormal set of basis filters. It is shown that the problem can be reformulated and solved as a constrained /spl Hscr//sub /spl infin// model-matching problem. To illustrate the effectiveness of the design method, two numerical examples are presented that deal with the design of equalization filters for digital transmission channels.

Input-output systems whose transmission operators furnish nearly best approximations to a given map

Let {S(A):A ∈A}, whereA is a subset of an infinite-dimensional normed linear spaceL, be a class of general nonlinear input-output systems that are governed by operator equations relating the input, state, and output, all of which are in extended spaces. IfQ is a given operator from a specified set ¯D i, of inputs into the space of outputs ¯H 0, the problem we consider is to find, for a given ɛ>0, a “parameter”A e∈A such that the transmission operatorR(A e) ofS(A e) furnishes a nearly best (or ɛ-best) approximation toQ from allR(A),A ∈A. Here the “distance” betweenQ andR(A) is defined as the supremum of distances betweenQz andR(A)z taken over allz ∈ ¯D i. In Theorems 2 through 5 we show that ifS(A) is “normal” (Definition 2),A satisfies some mild requirement andL contains a fundamental sequence, then establishingA e∈A reduces to minimizing a certain continuous functional on a compact subset ofR n, and thus can be carried out by conventional methods. The applications of results are illustrated by the example of a model-matching problem for a nonlinear system, and of optimal tracking.

A Note on State Space Solutions to the Model-Matching Problem via Generalized Popov Theory

A new state-space characterization of all solutions to the model-matching problem - one and two block cases - are obtained as a direct application of the generalized Riccati theory. The derivation is simple and straightforward, and points out that the so-called “Signature Condition” is a powerfull tool in treating H control problems.

On the relation between state feedback and full information regulators in nonlinear singular H/sub ∞/ control

In this paper the relationship between state feedback control laws and full information control laws, i.e. control laws which make explicit use of the disturbance signals, is discussed in the framework of nonlinear singular H/sub /spl infin// control. In particular, it is shown that any (polynomial) full information control law can always be approximated by a state feedback control law, provided that a certain (arbitrarily small) amount of performance is sacrificed. Moreover, the obtained result is used to give alternative proofs and generalizations to some existing results in the area of global disturbance attenuation for nonlinear systems and to establish some new and interesting results regarding the problem of approximate model matching.

Model matching under external and input-output equivalence

The model-matching problem for systems described by external models is considered in frameworks of both external and input-output equivalence. Necessary conditions for the solvability of the problem are produced, and it is shown that in certain cases these conditions are also sufficient. In the case where necessary and sufficient conditions exist, the solutions of the problem are obtained in a constructive way and a parametrization of solutions is given.

A decentralized control design method for model-matching robustness problems

The design of decentralized controllers in the model-matching robustness formulation is presented. The results here include a parametrization of generalized observers for robust decentralized control, and the selection of a design parameter to trade-off between the model-matching and the robustness design. The technique has been sucessfully applied to the decentralized damping control design of interarea modes in a power system with two control devices.

H∞-Optimal Observer-Based Controller Design for Nonlinear Multivariable Systems

We propose a novel algorithm to synthesize anH∞-optimal observer-based controller for a nonlinear multivariable system. Based on the parametrization of the observer-based controller, a necessary and sufficient condition to achieve robust stability is developed. Moreover, the Nevanlinna–Pick interpolation theory is employed to test the solvability condition of the robust stabilization problem. Optimal robustness can be achieved via the technique ofH∞-optimization. The exact solution of the model-matching problem induced by the stability criterion is solved by the method of noniterative computation of theH∞-norm.

Method of Moment Restrictions in Robust Control and Filtering

The minimax control and filtering problems are considered for the linear MIMO system acted on by a stochastic input. The input has a meaning of the disturbance in the control problem and it consists of the noise and signal in the filtering one. The performance index is the maximum of the system output variance over the class of inputs, which is specified by the moment restrictions. The problem is to minimize the performance index over the given class of regulators or filters. It includes the H2 and H∞ optimal control and filtering problems as the special cases. The solution obtained involves the solution of some auxiliary convex optimization problem and the solution of the standard model-matching problem. The approach is based on the theory of generalized Chebyshev-type inequalities.

ILC for non-minimum phase system

In this paper we propose a design method of an iterative learning controller (ILC) for a non-minimum phase (NMP) system by model-matching theory. The ILC consists of two learning filters acting on both the previous input signal and the previous error signal. To design the learning filters, we convert the convergence condition of the ILC into the model-matching problem and get the stable and proper learning filter by solving the Nevanlinna's algorithm. To show the usefulness of the proposed algorithm, some design examples are included.

A simplified frequency-domain approach to super-optimization

The paper presents a continuous time polynomial approach to class k- and super-optimization of the model-matching problem. By requiring the largest singular value of intermediate ℋ∞ optimal solutions to have multiplicity one, the approach is able to resort to a simplified dimension reduction technique.

Model Matching Problem for Systems over a Ring and Applications to Delay-Differential Systems

The main result of the paper is a geometric necessary and sufficient condition for the existence of solution of the Model matching Problem for systems over a ring. The result is obtained by considering an associated Disturbance Decoupling problem. An application to the case of delay-diffemtial systems is illustrated by an example.

The partial model matching or partial disturbance rejection problem: geometric and structural solutions

The partial model matching problem (or equivalently, the partial disturbance rejection problem) is revisited. It has been initially introduced in Emre and Silverman (1980) and amounts to matching the first k Markov parameters of the plant with those of the model. This obviously finds all its interest when no solution exists to the exact problem. The authors give both geometric and structural solutions to these problems. The geometric solution is in terms of the steps of the well known supremal output nulling controlled invariant subspace algorithm. The structural conditions amount to comparing some list of integers, namely some orders of zeros at infinity.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Comments on a Structural Approach to the Nonlinear Model Matching Problem

It is shown that, under certain regularity assumptions, the sufficient conditions for solvability of the model matching problem (MMP) in terms of structural invariants presented by Moog, Perdon, and Conte [SIAM J. Control Optim., 29 (1991), pp. 769–785] are also necessary. The seeming controversy involving the example of Huijberts is resolved.

Mixed H∞ optimisation with model-matching

This paper describes a class of the mixed H/sub infinity / optimisation with model-matching problems. The sensitivity and stability margin objectives are integrated in the model-matching design, respectively. Both approaches give a means of directly accessing the sensitivity/robustness objectives through a trade-off on the perfect model-matching objective. These applications to the known H/sub infinity / theory thus deal with important objectives such as multivariable interaction, which cannot be easily captured in the existing mixed sensitivity design. >

Coupling operators, wedderburn-forney spaces, and generalized inverses

The pole-zero structure of a transfer function has been analyzed by two distinct approaches: module-theoretic (coordinate-free) and analytic (basis-dependent). The former (the Wyman-Sain-Conte-Perdon school) emphasizes pole modules, zero modules, exact sequences of maps, and abstract realization theory; applications developed include the model-matching problem, zero structure of one-sided inverses, and connections with geometric systems theory. The latter (the Gohberg school) works with pole chains, zero chains, matrix equations, and concrete factorization theory (minimal, Wiener-Hopf, inner-outer) and interpolation (zero-pole, Lagrange- Sylvester, Nevanlinna-Pick). In this paper we make explicit the connection between the two approaches. In particular, we describe the zero-pole exact sequence of a transfer function without a pole or zero at infinity in the coordinate system provided by a global left null-pole triple. An important tool for us, and an object of interest in its own right, is a generalized inverse G × of a transfer function G. We relate the poles of G × with the zeros of G. We also show that if the pole module of G × is isomorphic to the zero module of G, then left (right) pole pairs of G × are left (right) null pairs of G.

On asymptotic model matching

In this paper we consider the problem of asymptotic model matching, in which the objective is to force the plant to behave asymptotically like a reference model in response to an exogenous input. Conditions for solvability via a linear time-invariant controller are well known; here we prove that under a closed-loop causality constraint, moving to a nonlinear time-varying controller affords no reduction of these conditions. We explore the ramifications of this result to the (ideal) model reference adaptive control problem, demonstrating that (i) an upper bound on the plant relative degreemust be known, and (ii) the plant zeros in the closed right half-planemust lie in a finite set. We also derive a bound on the achievable asymptotic performance in the event that the solvability conditions fail to hold.

Parametric study of adaptive generalized predictive controllers

and Conclusions The solution to the closed-loop model-matching problem based on a factorization approach requires one to search the set of all admissible function parameters. A possible search procedure was presented, and the solution space was given in terms of a set of linear algebraic equations, i.e., Eq. (25). The procedure is computer-assisted, and it is based on minimizing a mean-square error criteria. The procedure may be extended to account for minimizing the sensitivity function as well as to account for integrity conditions. In both cases, the solution space will remain linear. Acknowledgment This research was in part funded by the Department of Defense.

Model-matching approach to H∞ filtering

The H∞ filtering problem of state estimation for LTI systems is considered. The LTI system is driven at its input and corrupted at its output by processes with known energy bounds (but unknown spectral densities), and state estimates are sought such that the energy of the estimation error is minimised. The H∞ fitering problem is formulated as a model-matching problem and is solved using a state-space based algebraic approach. A characterisation for a family of H∞ filters is obtained in the form of a linear fractional transformation. It is shown that the H∞ filter generalises the Kalman filter and a condition is given under which the H∞ filter reduces to the Kalman filter. A derivation for minimum-entropy H∞ filters is given.

State-space solution of the causal factorization problem

Given rational matrix functions, G, H, and R, a necessary and sufficient condition is given for the existence of a causal solution to the equation GXH=R. A formula is given for a solution of the equation when it exists, and this particular solution is used to parameterize the set of all causal solutions of the equation. The results are specialized to the case when the function G is identically equal to identity. Applications of the author's results include exact model matching and disturbance decoupling problems. >