Péter Baranyi

TP model transformation as a way to LMI-based controller design

The main objective of this paper is to propose a numerical controller design methodology. This methodology has two steps. In the first step, tensor product (TP) model transformation is applied, which is capable of transforming a dynamic system model, given over a bounded domain, into TP model form, including polytopic or Takagi-Sugeno model forms. Then, in the second step, Lyapunovs controller design theorems are utilized in the form of linear matrix inequalities (LMIs). The main novelty of this paper is the development of the TP model transformation of the first step. It does not merely transform to TP model form, but it automatically prepares the transformed model to all the specific conditions required by the LMI design. The LMI design can, hence, be immediately executed on the result of the TP model transformation. The secondary objective of this paper is to discuss that representing a dynamic model in TP model form needs to consider the tradeoff between the modeling accuracy and computational complexity. Having a controller with low computational cost is highly desired in many cases of real implementations. The proposed TP model transformation is developed and specialized for finding a complexity minimized model according to a given modeling accuracy. Detailed control design examples are given.

Reduction of fuzzy rule base via singular value decomposition

Introduces a singular value-based method for reducing a given fuzzy rule set. The method conducts singular value decomposition of the rule consequents and generates certain linear combinations of the original membership functions to form new ones for the reduced set. The present work characterizes membership functions by the conditions of sum normalization (SN), nonnegativeness (NN), and normality (NO). Algorithms to preserve the SN and NN conditions in the new membership functions are presented. Preservation of the NO condition relates to a high-dimensional convex hull problem and is not always feasible in which case a closed-to-NO solution may be sought. The proposed method is applicable regardless of the adopted inference paradigms. With product-sum-gravity inference and singleton support fuzzy rule base, output errors between the full and reduced fuzzy set are bounded by the sum of the discarded singular values. The work discusses three specific applications of fuzzy reduction: fuzzy rule base with singleton support, fuzzy rule base with nonsingleton support (which includes the case of missing rules), and the Takagi-Sugeno-Kang (TSK) model. Numerical examples are presented to illustrate the reduction process.

A generalized concept for fuzzy rule interpolation

The concept of fuzzy rule interpolation in sparse rule bases was introduced in 1993. It has become a widely researched topic in recent years because of its unique merits in the topic of fuzzy rule base complexity reduction. The first implemented technique of fuzzy rule interpolation was termed as /spl alpha/-cut distance based fuzzy rule base interpolation. Despite its advantageous properties in various approximation aspects and in complexity reduction, it was shown that it has some essential deficiencies, for instance, it does not always result in immediately interpretable fuzzy membership functions. This fact inspired researchers to develop various kinds of fuzzy rule interpolation techniques in order to alleviate these deficiencies. This paper is an attempt into this direction. It proposes an interpolation methodology, whose key idea is based on the interpolation of relations instead of interpolating /spl alpha/-cut distances, and which offers a way to derive a family of interpolation methods capable of eliminating some typical deficiencies of fuzzy rule interpolation techniques. The proposed concept of interpolating relations is elaborated here using fuzzy- and semantic-relations. This paper presents numerical examples, in comparison with former approaches, to show the effectiveness of the proposed interpolation methodology.

Comprehensive analysis of a new fuzzy rule interpolation method

The first published result in fuzzy rule interpolation was the /spl alpha/-cut based fuzzy rule interpolation, termed as KH fuzzy rule interpolation, originally devoted for complexity reduction. A modified version of the KH approach has been presented by Yam et al. (1999), which eliminates the subnormality problem while at the same time intending to maintain the advantageous computational properties of the original method. This paper presents a comprehensive analysis of the new method, which includes detailed comparison with the original KH fuzzy rule interpolation method concerning the explicit functions of the methods, preservation of piecewise linearity, and stability. The fuzziness of the conclusion with respect to the fuzziness of the observation is also investigated in comparison with several interpolation techniques. All these comparisons shows that the new method preserves the advantageous properties of the KH method and alleviates its most significant disadvantage, the problem of subnormality.

From differential equations to PDC controller design via numerical transformation

This paper proposes a transformation method capable of transforming analytically given differential equations of dynamic models into Takagi-Sugeno fuzzy inference model (TS fuzzy model), whereupon various parallel distributed compensation (PDC) controller design techniques can readily be executed. Joining the transformation method and the PDC techniques leads to a controller design framework. The transformation method is specialized to minimize the number of fuzzy rules in the resulting TS fuzzy model according to a given acceptable transformation error, the PDC design thus results in a computational complexity minimized controller which is highly desired in many cases of real applications. The paper presents examples to show the effectiveness of the proposed transformation.

Fuzzy Control System Performance Enhancement by Iterative Learning Control

This paper suggests low-cost fuzzy control solutions that ensure the improvement of control system (CS) performance indices by merging the benefits of fuzzy control and iterative learning control (ILC). The solutions are expressed in terms of three fuzzy CS (FCS) structures that employ ILC algorithms and a unified design method focused on Takagi-Sugeno proportional-integral fuzzy controllers (PI-FCs). The PI-FCs are dedicated to a class of servo systems with linear/linearized controlled plants characterized by second-order dynamics and integral type. The invariant set theorem by Krasovskii and LaSalle with quadratic Lyapunov function candidates is applied to guarantee the convergence of the ILC algorithms and enable proper setting of the PI-FC parameters. The linear PI controller parameters tuned by the extended symmetrical optimum method are mapped onto the PI-FC ones by the modal equivalence principle. Real-time experimental results for a dc-based servo speed CS are included.

Trajectory Tracking by TP Model Transformation: Case Study of a Benchmark Problem

The main objective of this paper is to study the recently proposed tensor-product-distributed-compensation (TPDC)-based control design framework in the case of tracking control design of a benchmark problem. The TPDC is a combination of the tensor product model transformation and the parallel distributed compensation framework. In this paper, we investigate the effectiveness of the TPDC design. We study how it can be uniformly and readily executed without analytical derivations. We show that the TPDC is straightforward and numerically tractable, and is capable of guaranteeing various different control performances via linear matrix inequality (LMI) conditions. All these features are studied via the state feedback trajectory control design of the translational oscillations with an eccentric rotational proof mass actuator system. The trajectory tracking capability for various tracking commands is optimized here by decay rate LMI conditions. Constraints on the output and control of the closed-loop system are also considered by LMI conditions. We present numerical simulations of the resulting closed-loop system to validate the control design

Tensor-product model-based control of two-dimensional aeroelastic system

Use of a recently introduced numerical robust-control design method to stabilize aeroelastic systems according to different control specifications is studied. This numerical design is based on the tensor-product model transformation and the parallel-distributed-compensation design framework. An alternative description of aeroelastic models is also proposed as a gateway to various recent linear-matrix-inequality-based control theories. This study is conducted through an example that focuses attention on the state-variable-feedback controller design to the prototypical aeroelastic wing section with structural nonlinearity. This type of model has been traditionally used for the theoretical as well as experimental analysis of two-dimensional aeroelastic behavior and exhibits limit-cycle oscillation without control effort. Numerical simulations to provide empirical validation of the resulting controllers are presented. Comparison to former alternative control solutions is also presented.

VirCA as Virtual Intelligent Space for RT-Middleware

In this paper, VirCA 1 (Virtual Collaboration Arena) is introduced as a Virtual Intelligent Space that is organically connected to the RT-Middleware framework. The paper presents the conceptual background of the VirCA system and its relation to RT-Middleware. The scope of possible applications are discussed via working examples.

Interpolation with function space representation of membership functions

This paper generalizes a previous Cartesian approach for interpolating fuzzy rules comprised of membership functions with finite number of characteristic points. Instead of representing membership functions as points in Cartesian spaces, they now become elements in the space of square, integrable function. Interpolation is thus conducted between the antecedent and consequent function spaces. The generalized representation allows an extended class of membership functions satisfying two monotonicity conditions to be accommodated in the interpolation process. They include the popular bell-shaped membership functions, which were not possible before with the Cartesian representation. The work also extends the similarity triangle-based interpolation technique from the previous Cartesian representation to the new representation. Ensuing issues on computational complexity and nonunique conclusion are discussed. Other concepts such as spanning set and extensibility functions are also presented under the generalized framework. Examples to illustrate the extended approach and to compare with the Cartesian approach are given.