Han-Leih Liu

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.

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.

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.

Combined direct/indirect adaptive fuzzy-neural networks control with state observer and supervisory controller for nonlinear dynamic systems

A state observer-based combined direct/indirect adaptive FNN controller with supervisory controller for a class of uncertain nonlinear dynamic systems is developed in this paper. The combined adaptive FNN controller, whose free parameters can be tuned online by observer-based output feedback control law and adaptive law, is a combination of direct and indirect adaptive FNN controllers. A weighting factor, which is adjusted by trade-off between plant knowledge and control knowledge, appended between indirect adaptive FNN control and direct adaptive FNN control. A supervisory controller is appended into the FNN controller to force the state to be within the constraint set.

On-line intelligent adaptive control for uncertain nonlinear systems using TS-type fuzzy models with maximum allowable computational time for controller

A new Takagi-Sugeno (TS)-type FNN learning architecture is proposed for the on-line identification of the TS-type fuzzy model of the uncertain system. The dynamical optimal learning rule is adopted to update the linearized TS-type fuzzy model to guarantee the convergence of the on-line training process. To improve the convergence speed of the on-line training process, the least-squared identification is applied to identify the initial parameters of the TS-type fuzzy model. Once the linearized TS-type fuzzy model of the uncertain linear system is obtained in real-time environment, the on-line adaptive controller can be easily designed to accomplish the design specifications. A simplified tracking controller is also proposed to perform the tracking of a reference signal for unknown system. Critical constraint criteria are applied to find the computational time for generating the controller signal. Based on this sampling time, suitable equipments are used in actual hardware implementation. Inverted pendulum system is illustrated to track sinusoidal signal.

Indirect adaptive fuzzy-neural control with observer and supervisory control for unknown nonlinear systems

In this paper, we develop an observer-based indirect adaptive fuzzy-neural controller with supervisory mode for a certain class of high order unknown nonlinear dynamical system. The free parameters of the adaptive fuzzy-neural controller with supervisory mode can be tuned on-line by an observer-based output feedback control law and adaptive law, based on the Lyapunov synthesis approach. The fuzzy controller is appended with a supervisory controller. If the fuzzy control system tends to unstable, the supervisory controller starts working to guarantee stability. From the energy point of view, this is a very economical design methodology. 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 learning rate analysis of a certain class of fuzzy neural network

The stable learning rates for a two-layer neural network are discussed first by the Lyapunov stability theorem. This two-layer NN can then be incorporated into a fuzzy neural network (FNN) for a more efficient tuning process by a new genetic algorithm designed in the paper. The main contribution of this methodology is to reduce the searching time by searching only one learning rate in the FNN. All the equations for tuning both the NN and FNN are fully explained.