One of the most, and at the same time, relevant and challenging tasks when dealing with dynamical systems is the problem of tracking, which can also be viewed as a problem of regulation of dynamical systems in control theory. From our prospective, this problem is not only relevant as is but, in our opinion, can be related to neural networks and their application in machine learning. In particular, the problem of classificationClassification of input signals as elements of time-varying sequence or image datasets may be considered as a problem of how well the system tracks the input signal, that is, how well the input signal can be recognized or classified at the system’s output. The rational behind this is that the reference input signal would be tracked or followed and thus classified easier and more accurately if the system is capable of recognizing it. Among process control schemes, the internal model control [4–6, 13, 14] is chosen for its simplicity of formulation and reliable and accurate performance for a large scale of complex dynamical systems. By performance we mean that the system tracks a wide variety of, in general, time-varying reference signals within the desired accuracy specifications. Depending on the information about the process, a number of different identification procedures can be performed to model the process. If the process is treated as a “black box” then usually identification is done based on a class of training signals. This class of training signals has to be carefully chosen so that the system would be able to track both signals which belong to the same class and the ones that don’t. Thus, not only it is important to be able to learn about the process based on the input-output relationship but this learning will also depend on the choice of the reference signals for which this relationship is established. For example, a class of smoothen step signals was found to be very effective in identifying complex and, for the designer, unknown nonlinear systems [19]. This may be explained by recognizing that a smoothen step signal while simple has wider spectrum than a constant or a sinusoidal signal which, on their own, contain only one component in the spectrum. On the other hand, how to choose training signals in machine learning applications may be restricted by the available datasets and their contents.

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A Modified Internal Model Control Approach

  • Dušan Stipanović

摘要

One of the most, and at the same time, relevant and challenging tasks when dealing with dynamical systems is the problem of tracking, which can also be viewed as a problem of regulation of dynamical systems in control theory. From our prospective, this problem is not only relevant as is but, in our opinion, can be related to neural networks and their application in machine learning. In particular, the problem of classificationClassification of input signals as elements of time-varying sequence or image datasets may be considered as a problem of how well the system tracks the input signal, that is, how well the input signal can be recognized or classified at the system’s output. The rational behind this is that the reference input signal would be tracked or followed and thus classified easier and more accurately if the system is capable of recognizing it. Among process control schemes, the internal model control [4–6, 13, 14] is chosen for its simplicity of formulation and reliable and accurate performance for a large scale of complex dynamical systems. By performance we mean that the system tracks a wide variety of, in general, time-varying reference signals within the desired accuracy specifications. Depending on the information about the process, a number of different identification procedures can be performed to model the process. If the process is treated as a “black box” then usually identification is done based on a class of training signals. This class of training signals has to be carefully chosen so that the system would be able to track both signals which belong to the same class and the ones that don’t. Thus, not only it is important to be able to learn about the process based on the input-output relationship but this learning will also depend on the choice of the reference signals for which this relationship is established. For example, a class of smoothen step signals was found to be very effective in identifying complex and, for the designer, unknown nonlinear systems [19]. This may be explained by recognizing that a smoothen step signal while simple has wider spectrum than a constant or a sinusoidal signal which, on their own, contain only one component in the spectrum. On the other hand, how to choose training signals in machine learning applications may be restricted by the available datasets and their contents.