Chi-Hsu Wang

Comments on "Direct adaptive fuzzy-neural control with state observer and supervisory controller for unknown nonlinear dynamical systems"

In this paper, an observer-based direct adaptive fuzzy-neural network (FNN) controller with supervisory mode for a certain class of high order unknown nonlinear dynamical system is presented. The direct adaptive control (DAC) has the advantage of less design effort by not using FNN to model the plant. By using an observer-based output feedback control law and adaptive law, the free parameters of the adaptive FNN controller can be tuned on-line based on the Lyapunov synthesis approach. A supervisory controller is appended into the FNN controller to force the state to be within the constraint set. Therefore, if the FNN controller cannot maintain the stability, the supervisory controller starts working to guarantee stability. On the other hand, if the FNN controller works well, the supervisory controller will be de-activated. The overall adaptive scheme guarantees the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded. Simulation results also show that our initial control effort is much less than those in previous works, while preserving the tracking performance.

Dynamical optimal training for interval type-2 fuzzy neural network (T2FNN)

Type-2 fuzzy logic system (FLS) cascaded with neural network, type-2 fuzzy neural network (T2FNN), is presented in this paper to handle uncertainty with dynamical optimal learning. A T2FNN consists of a type-2 fuzzy linguistic process as the antecedent part, and the two-layer interval neural network as the consequent part. A general T2FNN is computational-intensive due to the complexity of type 2 to type 1 reduction. Therefore, the interval T2FNN is adopted in this paper to simplify the computational process. The dynamical optimal training algorithm for the two-layer consequent part of interval T2FNN is first developed. The stable and optimal left and right learning rates for the interval neural network, in the sense of maximum error reduction, can be derived for each iteration in the training process (back propagation). It can also be shown both learning rates cannot be both negative. Further, due to variation of the initial MF parameters, i.e., the spread level of uncertain means or deviations of interval Gaussian MFs, the performance of back propagation training process may be affected. To achieve better total performance, a genetic algorithm (GA) is designed to search optimal spread rate for uncertain means and optimal learning for the antecedent part. Several examples are fully illustrated. Excellent results are obtained for the truck backing-up control and the identification of nonlinear system, which yield more improved performance than those using type-1 FNN.

Adaptive hybrid intelligent control for uncertain nonlinear dynamical systems

A new hybrid direct/indirect adaptive fuzzy neural network (FNN) controller with a state observer and supervisory controller for a class of uncertain nonlinear dynamic systems is developed in this paper. The hybrid adaptive FNN controller, the free parameters of which can be tuned on-line by an observer-based output feedback control law and adaptive law, is a combination of direct and indirect adaptive FNN controllers. A weighting factor, which can be adjusted by the tradeoff between plant knowledge and control knowledge, is adopted to sum together the control efforts from indirect adaptive FNN controller and direct adaptive FNN controller. Furthermore, a supervisory controller is appended into the FNN controller to force the state to be within the constraint set. Therefore, if the FNN controller cannot maintain the stability, the supervisory controller starts working to guarantee stability. On the other hand, if the FNN controller works well, the supervisory controller will be deactivated. The overall adaptive scheme guarantees the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded. Two nonlinear systems, namely, inverted pendulum system and Chuas (1989) chaotic circuit, are fully illustrated to track sinusoidal signals. The resulting hybrid direct/indirect FNN control systems show better performances, i.e., tracking error and control effort can be made smaller and it is more flexible during the design process.

Observer-based indirect adaptive fuzzy-neural tracking control for nonlinear SISO systems using VSS and H∞ approaches

Fuzzy control is a model free approach, i.e., it does not require a mathematical model of the system under control. An observer-based indirect adaptive fuzzy neural tracking control equipped with VSS and H∞ control algorithms is developed for nonlinear SISO systems involving plant uncertainties and external disturbances. Three important control methods, i.e., adaptive fuzzy neural control scheme, VSS control design and H∞ tracking theory, are combined to solve the robust nonlinear output tracking problem. A modified algebraic Riccati-like equation must be solved to compensate the effect of the approximation error via adaptive fuzzy neural system on the H∞ control. The overall adaptive scheme guarantees the stability of the resulting closed-loop system in the sense that all the states and signals are uniformly bounded and arbitrary small attenuation level of the external disturbance on the tracking error can be achieved. The simulation results confirm the validity and performance of the advocated design methodology.

Dynamic optimal learning rates of a certain class of fuzzy neural networks and its applications with genetic algorithm

The stability analysis of the learning rate for a two-layer neural network (NN) is discussed first by minimizing the total squared error between the actual and desired outputs for a set of training vectors. The stable and optimal learning rate, in the sense of maximum error reduction, for each iteration in the training (back propagation) process can therefore be found for this two-layer NN. It has also been proven in this paper that the dynamic stable learning rate for this two-layer NN must be greater than zero. Thus it Is guaranteed that the maximum error reduction can be achieved by choosing the optimal learning rate for the next training iteration. A dynamic fuzzy neural network (FNN) that consists of the fuzzy linguistic process as the premise part and the two-layer NN as the consequence part is then illustrated as an immediate application of our approach. Each part of this dynamic FNN has its own learning rate for training purpose. A genetic algorithm is designed to allow a more efficient tuning process of the two learning rates of the FNN. The objective of the genetic algorithm is to reduce the searching time by searching for only one learning rate, which is the learning rate of the premise part, in the FNN. The dynamic optimal learning rates of the two-layer NN can be found directly using our innovative approach. Several examples are fully illustrated and excellent results are obtained for the model car backing up problem and the identification of nonlinear first order and second order systems.

Adaptive asymmetric fuzzy neural network controller design via network structuring adaptation

This paper proposes a self-structuring fuzzy neural network (SFNN) using asymmetric Gaussian membership functions in the structure and parameter learning phases. An adaptive self-structuring asymmetric fuzzy neural-network control (ASAFNC) system which consists of an SFNN controller and a robust controller is proposed. The SFNN controller uses an SFNN with structure and parameter learning phases to online mimic an ideal controller, simultaneously. The structure learning phase consists of the growing-and-pruning algorithms of fuzzy rules to achieve an optimal network structure, and the parameter learning phase adjusts the interconnection weights of neural network to achieve favorable approximation performance. The robust controller is designed to compensate for the modeling error between the SFNN controller and the ideal controller. An online training methodology is developed in the Lyapunov sense, and thus the stability of the closed-loop control system can be guaranteed. Finally, the proposed ASAFNC system is applied to a second-order chaotic dynamics system. The simulation results show that the proposed ASAFNC can achieve favorable tracking performance.

Direct adaptive fuzzy-neural control with state observer and supervisory controller for unknown nonlinear dynamical systems

In this paper, an observer-based direct adaptive FNN controller with supervisory mode for a certain class of high order unknown nonlinear dynamical system is presented. The direct adaptive control (DAC) has the advantage of less design effort by not using FNN to model the plant. By using an observer-based output feedback control law and adaptive law, the free parameters of the adaptive FNN controller can be tuned online based on the Lyapunov synthesis approach. A supervisory controller is appended into the FNN controller to force the state to be within the constraint set. Therefore, if the FNN controller cannot maintain the stability, the supervisory controller starts working to guarantee stability. On the other hand, if the FNN controller works well, the supervisory controller will be de-activated. The overall adaptive scheme guarantees the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded.

On the Equivalence of a Table Lookup (TL) Technique and Fuzzy Neural Network (FNN) With Block Pulse Membership Functions (BPMFs) and Its Application to Water Injection Control of an Automobile

This paper presents an alternative method to design a fuzzy neural network (FNN) using a set of nonoverlapped block pulse membership functions (BMPFs), and this FNN with nonoverlapped BPMFs will be shown to be equivalent to the conventional table lookup (TL) technique. Therefore, the hidden links between TL and FNN techniques are revealed in this paper that provides a methodology to design a TL controller based on the FNN design concept. In order to do so, a new direct formula is first developed to generate the fuzzy rules from the premise part in FNN. This direct formula not only guarantees a one-to-one mapping that maps the fuzzy membership functions onto the fuzzy rules, but also alleviates the coding effort during hardware implementation. It is further elaborated that the FNN with nonoverlapped BPMFs has the advantage of faster online training that requires less computation time, but at the cost of more memory requirement to store the fuzzy rules. The application of this new approach has been applied successfully in the water injection control of a turbo-charged automobile with excellent results.

The Bounded Capacity of Fuzzy Neural Networks (FNNs) Via a New Fully Connected Neural Fuzzy Inference System (F-CONFIS) With Its Applications

In this paper, a fuzzy neural network (FNN) is transformed into an equivalent three-layer fully connected neural inference system (F-CONFIS). This F-CONFIS is a new type of a neural network whose links are with dependent and repeated weights between the input layer and hidden layer. For these special dependent repeated links of the F-CONFIS, some special properties are revealed. A new learning algorithm with these special properties is proposed in this paper for the F-CONFIS. The F-CONFIS is therefore applied for finding the capacity of the FNN. The lower bound and upper bound of the capacity of the FNN can be found from a new theorem proposed in this paper. Several examples are illustrated with satisfactory simulation results for the capacity of the F-CONFIS (or the FNN). These include “within capacity training of the FNN,” “over capacity training of the FNN,” “training by increasing the capacity of the FNN,” and “impact of the capacity of the FNN in clustering Iris Data.” It is noted that the finding of the capacity of the F-CONFIS, or FNN, has its emerging values in all engineering applications using fuzzy neural networks. This is to say that all engineering applications using FNN should not exceed the capacity of the FNN to avoid unexpected results. The clustering of Iris data using FNN illustrated in this paper is one of the most relevant engineering applications in this regards.

A new learning algorithm for a fully connected neuro-fuzzy inference system.

A traditional neuro-fuzzy system is transformed into an equivalent fully connected three layer neural network (NN), namely, the fully connected neuro-fuzzy inference systems (F-CONFIS). The F-CONFIS differs from traditional NNs by its dependent and repeated weights between input and hidden layers and can be considered as the variation of a kind of multilayer NN. Therefore, an efficient learning algorithm for the F-CONFIS to cope these repeated weights is derived. Furthermore, a dynamic learning rate is proposed for neuro-fuzzy systems via F-CONFIS where both premise (hidden) and consequent portions are considered. Several simulation results indicate that the proposed approach achieves much better accuracy and fast convergence.