The paper proposes a Tensor Product (TP) model transformation based framework requiring minimal human intuition to numerically reconstruct Linear Time Invariant, Takagi-Sugeno (TS) fuzzy model based Linear Parameter Varying and quasi Linear Parameter Vary- ing representations of state-space models. The proposed framework facilitates the manipulation of the structure of the system matrix, the parameter vector - including state elements - and the vertex systems. The motivation behind this capability is that all of these structural components strongly influence the control design and the resulting control performance. An important feature of the framework is that it is agnostic towards the formulation of the state-space model, i.e. whether it is given using soft-computing based techniques or closed formulae. The proposed approach is an extension of the TP model based control design framework and inherits all of its advantageous properties, e.g. it can be easily used to find minimal representations, including the Higher Order Singular Value based canonical form; and it supports the clear formulation of complexity / accuracy trade-offs and allows for conversions to various types of convex representations, making for a flexible way to manipulate the weighting and antecedent functions. The paper gives examples to show how the framework can be used in a routine-like fashion and to highlight how it can be applied to the problem of finding useful TS fuzzy model variations of a given model.

The motivation behind 15 years of continuous development within the topic of the Tensor Product (TP) model transformation is that the greater the number of parameters or components of the Takagi Sugeno (TS) fuzzy model one can manipulate, the larger the complexity reduction or control optimization one can achieve. The paper proposes a radically new type of extension to the TP model transformation: while earlier variants of the TP model transformation focused on how the antecedent - consequent fuzzy set system of a given TS fuzzy model could be varied, the present work, in contrast, focuses on how the number of inputs to a given TS fuzzy model can be manipulated. The proposed extension is capable of changing the number of inputs or transforming the non-linearity between the fuzzy rules and the input dimensions. These new features considerably increase the modeling power of the TP model transformation, allowing for further complexity reduction and more powerful control optimisation to be achieved. The paper provides two examples to show how the proposed extension can be used in a routine-like fashion.

The tensor product (TP) model transformation defines and numerically reconstructs the Higher‐Order Singular Value Decomposition (HOSVD) of functions. It plays the same role with respect to functions as HOSVD does for tensors (and SVD for matrices). The need for certain advantageous features, such as rank/complexity reduction, trade‐offs between complexity and accuracy, and a manipulation power representative of the TP form, has motivated novel concepts in TS fuzzy model based modelling and control. The latest extensions of the TP model transformation, called the multi‐ and generalised TP model transformations, are applicable to a set functions where the dimensionality of the outputs of the functions may differ, but there is a strict limitation on the dimensionality of their inputs, which must be the same. The paper proposes an extended version that is applicable to a set of functions where both the input and output dimensionalities of the functions may differ. This makes it possible to transform complete multicomponent systems to TS fuzzy models along with the above‐mentioned advantages.

One of the primary objectives underlying the extensive 20-year development of the TS Fuzzy model transformation (originally known as TP model transformation) is to establish a framework capable of generating alternative Fuzzy rules for a given TS Fuzzy model, thereby manipulating the associated convex hull to enhance further design outcomes. The existing methods integrated into the TS Fuzzy model transformation offer limited capabilities in deriving only a few types of loose and tight convex hulls. In this article, we propose a radically new approach that enables the derivation of an infinite number of alternative Fuzzy rules and, hence, convex hulls in a systematic and tractable manner. The article encompasses the following key novelties. Firstly, we develop a Fuzzy rule interpolation method, based on the pseudo TS Fuzzy model transformation and the antecedent Fuzzy set rescheduling technique, that leads to a smooth transition between the Fuzzy rules and the corresponding convex hulls. Then, we extend the proposed concept with the antecedent Fuzzy set refinement and reinforcement technique to tackle large-scale problems characterized by a high number of inputs and Fuzzy rules. The paper also includes demonstrative examples to illustrate the theoretical key steps, and concludes with an examination of a real complex engineering problem to showcase the effectiveness and straightforward execution of the proposed convex hull manipulation approach.

In this paper, we make an initial effort to define the scope and goals of “Cognitive Control (CoCo)”, which intends to be a research initiative for bringing about a novel generation of control systems which - in a certain sense - reflect the behavior of humans while solving everyday tasks. Very briefly stated, through the use of a rich inventory of available modeling techniques, control theory has achieved profound results in model-based control approaches. However, these solutions do not seem to begin to approach the true level of human intelligence. We are convinced that by the synthesis of these “tools” from a particular point of view the great efficiency of human intelligence can be integrated/fused with the complementary virtues of our machines (e.g. high computing power, fast operation, etc.), and our CoCo initiative can be realized and applied in practice.

The primary goal of the paper is to introduce the Relaxed TS Fuzzy model transformation, a method that enhances the original TS Fuzzy model transformation in two ways. First, it focuses on achieving a more efficient reduction of the number of antecedent fuzzy sets – hence, the fuzzy rules of the TS Fuzzy models – while minimizing the approximation error. Second, it aims to reduce the computational load required for the transformation process. With the first enhancement, the proposed transformation strikes a better balance between the number of fuzzy rules and the approximation accuracy of TS Fuzzy models. With the second enhancement, a unique pre- and post-processing of the TS Fuzzy model transformation is introduced leading to the radical computational improvements. The core part of the original TS Fuzzy model transformation is the Higher Order Singular Value Decomposition (HOSVD) used to balance the approximation quality with the number of fuzzy rules by truncating singular values. The HOSVD itself is a computationally intensive algorithm, the possibilities for advancements in its implementation seem to be limited as much research has focused on its optimization in the past and had reached its pinnacle in terms of computational complexity more than a decade ago. Therefore, the approach presented in this paper does not concentrates directly on enhancing HOSVD further, but instead proposes a unique pre- and post-processing technique for the tensor on which HOSVD is applied, tailored to the special characteristics of the TS Fuzzy model and the system model under consideration. Following a description of the proposed enhancements, the paper presents numerical examples and two examples of real-world engineering models to demonstrate the effectiveness of the Relaxed TS Fuzzy model transformation compared to the original TS Fuzzy model transformation.