This paper focuses on the problem of adaptive neural network (NN) control for a class of nonlinear nonstrict-feedback systems via output feedback. A novel adaptive NN backstepping output-feedback control approach is first proposed for nonlinear nonstrict-feedback systems. The monotonicity of system bounding functions and the structure character of radial basis function (RBF) NNs are used to overcome the difficulties that arise from nonstrict-feedback structure. A state observer is constructed to estimate the immeasurable state variables. By combining adaptive backstepping technique with approximation capability of radial basis function NNs, an output-feedback adaptive NN controller is designed through backstepping approach. It is shown that the proposed controller guarantees semiglobal boundedness of all the signals in the closed-loop systems. Two examples are used to illustrate the effectiveness of the proposed approach.

Observer-Based Adaptive Neural Network Control for Nonlinear Systems in Nonstrict-Feedback Form

This paper presents an automatic way of evolving hierarchical Takagi-Sugeno fuzzy systems (TS-FS). The hierarchical structure is evolved using probabilistic incremental program evolution (PIPE) with specific instructions. The fine tuning of the if - then rule's parameters encoded in the structure is accomplished using evolutionary programming (EP). The proposed method interleaves both PIPE and EP optimizations. Starting with random structures and rules' parameters, it first tries to improve the hierarchical structure and then as soon as an improved structure is found, it further fine tunes the rules' parameters. It then goes back to improve the structure and the rules' parameters. This loop continues until a satisfactory solution (hierarchical TS-FS model) is found or a time limit is reached. The proposed hierarchical TS-FS is evaluated using some well known benchmark applications namely identification of nonlinear systems, prediction of the Mackey-Glass chaotic time-series and some classification problems. When compared to other neural networks and fuzzy systems, the developed hierarchical TS-FS exhibits competing results with high accuracy and smaller size of hierarchical architecture.

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Automatic Design of Hierarchical Takagi–Sugeno Type Fuzzy Systems Using Evolutionary Algorithms

In our view, the most important characteristic of a fuzzy rule-based system is its readability, which is seriously affected by, among other things, the number of features used to design the rule base. Hence, for high-dimensional data, dimensionality reduction through feature selection (not extraction) is very important. Our objective, here, is not to find an optimal rule base for classification but to select a set of useful features that may solve the classification problem. For this, we present an integrated mechanism for simultaneous extraction of fuzzy rules and selection of useful features. Since the feature selection method is integrated into the rule base formation, our scheme can account for possible subtle nonlinear interaction between features, as well as that between features and the tool, and, consequently, can select a set of useful features for the classification job. We have tried our method on several commonly used datasets as well as on a synthetic dataset with dimension varying from 4 to 60. Using a ten-fold cross-validation setup, we have demonstrated the effectiveness of our method.

An Integrated Mechanism for Feature Selection and Fuzzy Rule Extraction for Classification

This paper focuses on the problem of adaptive output-constrained neural tracking control for uncertain nonstrict-feedback systems in the presence of unknown symmetric output dead zone and input saturation. A Nussbaum-type function-based dead-zone model is introduced such that the dynamic surface control approach can be used for controller design. The variable separation technique is employed to decompose the unknown function of entire states in each subsystem into a series of smooth functions. Radial basis function neural networks are utilized to approximate the unknown black-box functions derived from Young’s inequality. With the help of auxiliary first-order filters, the dimensions of neural network input are reduced in each recursive design. A main advantage of the proposed method is that for an $n$ -order nonlinear system, only one adaptation parameter needs to be tuned online. It is rigorously shown that the proposed output-constrained controller guarantees that all the closed-loop signals are semiglobal uniformly ultimately bounded and the tracking error never violates the output constraint.

/pdf/adaptive-neural-dynamic-surface-control-for-nonstrict-4lm7v79pt9.pdf

Adaptive Neural Dynamic Surface Control for Nonstrict-Feedback Systems With Output Dead Zone

Heuristic design of fuzzy inference systems: A review of three decades of research

This paper presents a class of hierarchical fuzzy systems where previous layer outputs are used not in IF-parts, but only in THEN-parts of the fuzzy rules of the current layer. The proposed scheme is shown to be a universal approximator to any real continuous function on a compact set if complete fuzzy sets are used in the IF-parts of the fuzzy rules with singleton fuzzifier and center average defuzzifier. From the example of ball-and-beam control system simulation, it is demonstrated that the proposed scheme approximates with high accuracy a model nonlinear controller with fewer fuzzy rules than a centralized fuzzy system, and its control performance is comparable to that of a nonlinear controller.

A class of hierarchical fuzzy systems with constraints on the fuzzy rules

In classical single-layer fuzzy systems (FSs), the number of rules and the run-time computational requirements increase exponentially with the number of input domains. In this paper, we present a method for converting a multidimensional FS to a two-layer hierarchical FS that reduces the number of rules and improves the run-time efficiency. The first layer of the two-layer system consists of FSs whose rule bases can be represented as linearly independent vectors. The second layer constructs linear combinations of the rule base vectors. The effectiveness of the hierarchical conversion in reducing the number of rules and improving efficiency is demonstrated on a classic control problem and a simulated higher dimensional FS.

M.G. Joo

Papers

A class of hierarchical fuzzy systems with constraints on the fuzzy rules

A Method of Converting a Fuzzy System to a Two-Layered Hierarchical Fuzzy System and Its Run-Time Efficiency