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This paper proposes two kinds of data-driven controller tuning. The proposed methods are derived from the approximated model matching errors expressed by the filtered ideal model matching error. The main contribution of the paper is to find out specific filters that characterize the proposed data-driven methods. Similar filters are also presented in the existing virtual reference feedback tuning and fictitious reference iterative tuning as well. The comparison among the filters for the approximations clarifies the relation among them as well as the novelty of the proposed approach. The paper shows two numerical examples: one is a flexible transmission system and the other is a plant with an unstable zero. The numerical examples show the superiority of the proposed method to existing methods.

In this paper, we address a design method of binaural sound reproduction over loudspeakers, which is a virtual realization of three-dimensional audio. The reproduction is achieved by a model matching control to reproduce a desired sound field in a reproduced sound field. It is known that any sound field includes unstable zeros that are originated from the inherent propagation delay. Therefore, the model matching controller including the direct inversion of the reproduced sound field is inevitably unstable and cannot be implemented to actual systems. To avoid this instability, we propose a design method of a stable feedforward controller based on an H8 model matching problem. Additional low gain specification is imposed on the controller to enhance the robustness against modeling errors of the sound field. We apply the design method to actual experimental data of a sound field and also demonstrate through a numerical experiment that the designed controller realizes binaural reproduction accurately.

Having no internal states, static corrective controllers are advantageous over dynamic ones in terms of resource usage, albeit requiring stricter existence conditions. This study presents a novel static corrective control strategy that solves the model matching problem of input/state asynchronous sequential machines. Compared with the previous result, the proposed scheme provides a relaxed existence condition by utilising the model matching indicator that specifies the desirable state at hand. It is shown that the proposed static controller can be designed as long as a corresponding dynamic one exists. The improvement of resource usage in controller synthesis is validated by applying the proposed scheme to the payload data manager in the mass memory unit of satellite systems. [ABSTRACT FROM AUTHOR]

In this study, the problem of calculating the skeleton matrix for asynchronous sequential machine (ASMs) is addressed in the framework of the semi‐tensor product (STP) of matrices. By applying the STP of matrices and Boolean algebra, a new algebraic expression of ASMs is deduced. By utilising the algebraic expression, the skeleton matrix of ASMs can be easily derived, then the notion of generalised skeleton matrix is further defined for the ASMs with infinite cycles or critical races, and an algorithm of calculating the generalised skeleton matrix is also proposed. For the model matching problem of input/output ASMs, a novel approach is proposed to calculate reachability indictor and generalised fused skeleton matrix. Two examples are presented to illustrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

The paper studies the model matching problem for nonlinear systems, described by a higher order input-output differential equation, not necessarily realizable in the state-space form. Only the feedforward solution is looked for. The problem statement and solution rely on the recently introduced concept of a generalized transfer function for nonlinear systems. We require that the transfer functions of the compensated system and that of the prespecified model be equal, like in the linear case. However, in the nonlinear transfer function formalism one does not work with equations but with differential one-forms, and the existence of the compensator is restricted by integrability of the one-form corresponding to the compensator. Necessary and sufficient but nonconstructive solvability conditions are given. The second theorem lists a number of different (constructive) conditions under which the one-form is integrable. Additional freedom is sometimes obtained by forcing the conditions of the second theorem to hold via introducing assumptions suggested by the Euclidean division algorithm. [ABSTRACT FROM AUTHOR]

This paper addresses the model matching problem (MMP) for nonlinear single-input single-output discrete-time systems. The approach is based on the infinitesimal system description in terms of the one-forms that is converted into polynomial system representation by interpreting the polynomial indeterminate as the forward shift operator acting on the one-forms. The polynomial description is then used to derive the generalized transfer function. The problem statement of the MMP (both for the feedforward and feedback cases) is given in terms of the generalized transfer function. In general, the feedforward solution exists under restrictive conditions. Therefore, the subclass of nonlinear control systems is specified for which the solution is guaranteed to exist. The feedback solution exists always. The additional restrictions are specified for the existence of a proper compensator (in both cases). The results of the paper are illustrated by numerous examples, and the feedback solution is compared to the earlier results. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies “fixed zeros” of solutions to the model matching problem for systems over semirings. Such systems have been used to model queueing systems, communication networks, and manufacturing systems. The main contribution of this paper is the discovery of two fixed zero structures, which possess a connection with the extended zero semimodules of solutions to the model matching problem. Intuitively, the fixed zeros provides an essential component that is obtained from the solutions to the model matching problem. For discrete event dynamic systems modeled in max-plus algebra, a common Petri net component constructed from the solutions to the model matching problem can be discovered from the fixed zero structure. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, solution existence conditions for the model matching problem are studied for systems over semirings, which are used in many applications, such as queueing systems, communication networks, and manufacturing systems. The main contribution is the discovery of fixed pole structure in solutions to the model matching problem. This fixed pole structure provides essential information contained in all the solutions to the model matching problem. For a discrete-event dynamic system example, a common Petri net component in the solutions of the model matching problem can be discovered from the fixed pole structure. [Copyright &y& Elsevier]

In this paper we consider a model-based fault detection and isolation problem for linear time-invariant dynamic systems subject to faults and disturbances. We use a state observer scheme that cancels the system dynamics and defines a residual vector signal that is sensitive only to faults and disturbances. We then design a stable fault detection and isolation filter such that the H∞-norm of the transfer matrix function from disturbances to the residual is minimised (for fault detection) subject to the constraint that the transfer matrix function from faults to residual is equal to a pre-assigned diagonal transfer matrix (for isolation of possibly simultaneous occurring faults). Our solution is given in the form of linear matrix inequalities using state-space techniques, as well as a model matching problem using matrix factorisation techniques. A numerical example is given to illustrate the efficiency of the fault detection and isolation filter. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we give a matrix factorization solution to the fault detection (FD) problem for linear time invariant dynamic systems. An FD filter minimizes the sensitivity of the residual signal to disturbances while maintaining a minimum level of sensitivity to faults. More specifically, it minimizes the largest singular value, over the extended imaginary axis, of the transfer matrix from the disturbance to the residual signal vectors subject to the constraint that the singular values of the transfer matrix from the fault to the residual vectors are larger than or equal to 1. We show, through the use of matrix function factorizations and completions, that the problem reduces to a nonstandard model matching problem which is then solved under a mild assumption concerning the rank of a matrix function. We also give an illustrative example. [Copyright &y& Elsevier]

A concept of symmetry for linear systems is defined in terms of input-output relationship. It is shown that there exists a symmetric optimal solution for a symmetric standard H control problem, as well as for a symmetric model matching problem. [ABSTRACT FROM AUTHOR]