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A novel method for the design of switching surfaces for discretized MIMO nonlinear systems

100%

Luis-Delgado J., Al-Hadithi B., Jiménez A.

International Journal of Applied Mathematics and Computer Science

2017

tom 27

nr 1

5-17

Designing variable structure control with sliding mode (VSC-SM) control schemes needs a switching function or a sliding surface which guarantees the global stability of the closed-loop system. Despite the fact that a wide range of design approaches has been proposed for solving this mathematical problem, the number of proposed methodologies for nonlinear systems is not very extensive, especially for discrete time nonlinear MIMO systems, and most of them require some coordinate system transformation. Therefore, it is not an easy task to find a design scheme that can be applied to discrete time nonlinear MIMO systems. The proposed methodology introduces a mathematical tool: a switching surface equation for a class of MIMO nonlinear systems through an explicit equation without any coordinate transformation. This equation makes use of an implicit linearizing process via the Taylor expansion that allows the use of linear procedures for the design of switching surfaces and the forward Euler method to obtain a discrete time dynamics representation. An illustrative example is included to show the advantages of the proposed design methodology.

Beta fuzzy logic systems approximation properties in the mimo case

86%

Alimi A. M., Hassine R., Selmi M.

International Journal of Applied Mathematics and Computer Science

2003

tom 13

nr 2

225-238

Many researches have been interested in the approximation properties of Fuzzy Logic Systems (FLS), which, like neural networks, can be seen as approximation schemes. Almost all of them tackled the Mamdani fuzzy model, which was shown to have many interesting approximation features. However, only in few cases the Sugeno fuzzy model was considered. In this paper, we are interested in the zero-order Multi-Input-Multi-Output (MIMO) Sugeno fuzzy model with Beta membership functions. This leads to Beta Fuzzy Logic Systems (BFLS). We show that BFLSs are universal approximators. We also prove that they possess the best approximation property and the interpolation characteristic.

Ograniczanie wyników

2 International Journal of Applied Mathematics and Computer Science

1 Al-Hadithi B.

1 Alimi A. M.

1 Hassine R.

1 Jiménez A.

1 Luis-Delgado J.

1 Selmi M.

1 2017

1 2003

Wyniki wyszukiwania

A novel method for the design of switching surfaces for discretized MIMO nonlinear systems

Beta fuzzy logic systems approximation properties in the mimo case