Chiang-Ju Chien

An output recurrent fuzzy neural network based iterative learning control for nonlinear systems

In this paper, we present a design method for a discrete-time iterative learning control system by using output recurrent fuzzy neural network (ORFNN). Two ORFNNs are employed to design the control structure. One is used as an identifier called output recurrent fuzzy neural identifier (ORFNI) and the other used as a controller called output recurrent fuzzy neural controller (ORFNC). The ORFNI for identification of the unknown plant is introduced to provide the plant sensitivity which is then applied to the design of ORFNC. All the weights of ORFNI and ORFNC will be tuned during the control iteration and identification process respectively in order to achieve a desired learning performance. The adaptive laws for the weights of ORFNI and ORFNC and the analysis of learning performances are determined via a Lyapunov like analysis. It is shown that the identification error will asymptotically converge to zero and output tracking error will asymptotically converge to a residual set which depends on the initial resetting error.

An observer based adaptive iterative learning control for robotic systems

In this paper, an observer based adaptive iterative learning control is proposed for robotic systems. Due to the joint velocities are assumed to be not measurable, a state observer is introduced to design the iterative learning controller. We first derive an observation error model based on an tracking error observer. Then we apply an averaging filter to design the ILC algorithm. A fuzzy neural learning component using a filtered fuzzy neural network is presented to solve the problem of unknown nonlinearities. A robust learning component using sliding-mode like design is used to overcome the uncertainties, including fuzzy neural approximation error and the error induced by using state estimation errors. We show that all the adjustable parameters as well as internal signals remain bounded for all iterations. Finally, the norm of output tracking error will asymptotically converge to a tunable residual set as iteration goes to infinity.

An FNN-Based adaptive iterative learning control for a class of nonlinear discrete-time systems

In this paper, a fuzzy neural network is applied to design a discrete adaptive iterative learning controller for a class of nonlinear discrete-time systems. The fuzzy neural network is used as a function approximator to compensate the unknown certainty equivalent controller. The problem of function approximation error is solved by a technique of time-varying boundary layer. This boundary layer is then utilized to construct an auxiliary error function for the design of adaptive laws. In order to achieve a desired learning performance, the FNN parameter and the width of boundary layer will be tuned during the iteration processes. Based on a Lyapunov-like analysis, we show that all adjustable parameters as well as the internal signals remain bounded for all iterations and the output tracking error will asymptotically converge to a residual set whose size depends on the width of boundary layer as iteration goes to infinity.

Analysis of human gait using an Inverted Pendulum Model

IPM(Inverted Pendulum Model) has been widely used for modeling of human motion gaits. There is a common condition in most of these models, the reaction force between the floor and the humanoid must go through the CoG (Center of Gravity) of the a humanoid or human being. However, the recent bio-mechanical studies show that there are angular moments around the CoG of a human being during human motion. In other words, the reaction force does not necessarily pass through the CoG. In this paper, the motion of IPM is analyzed by taking into consideration two kinds of rotational moments, namely around the pivot and around the CoG. The human motion has been decomposed into the sagittal plane and front plane in the double support phase and single support phase. The motions of the IPM in these four different phases are derived by solving four differential equations with boundary conditions. Simulation results show that a stable human gait is synthesized by using our proposed IPM.

Observer based adaptive control of nonlinear systems using filtered-FNN design

In this paper, we consider the observer based adaptive control design problem for output tracking of nonlinear systems. As we assume that the states are not measurable, a state error observer is introduced to design the adaptive controller. Based on a derived error model, a filtered fuzzy neural network using estimated states as network input is applied to design the main component of the adaptive controller. In order to compensate for the uncertainties from the network approximation error and unknown input gain, we use a normalization signal to construct a bounding function as a robust control term. Finally, an averaging filter is proposed to solve the design issue of relative degree problem. We show by a Lyapunov analysis that all the adjustable parameters as well as internal signals in the closed loop system remain bounded. Furthermore, the norm of output tracking error will asymptotically converge to a tunable residual set as time goes to infinity. Finally, we discuss the extension of the proposed design to an iterative learning control issue for nonlinear systems without state measurement.

A Fuzzy Neural Network Direct Adaptive Iterative Learning Controller for Robotic Systems

Abstract This paper studies the iterative learning control of robotic systems with repetitive tasks. A fuzzy neural network is applied to design a direct adaptive iterative learning controller. The fuzzy neural network is introduced for compensation of the unknown certainty equivalent controller. A new adaptive law using mixed time-domain and iteration-domain adaptation is developed. It is shown that the finiteness of control parameters and control input can be guaranteed for all the time interval during each iteration without using parameter projection.

Model reference adaptive iterative learning control for nonlinear systems using observer design

In this paper, we propose an observer based model reference adaptive iterative learning control (MRAILC) using model reference adaptive control strategy for more general class of uncertain nonlinear systems with non-canonical form and iteration-varying reference trajectories. Due to the system state vector is assumed to be unmeasurable, a state tracking error observer is applied for state tracking error estimation. Based on the state tracking error observer and a mixed time-domain and s-domain technique, a relative degree one output observation error model whose inputs are some uncertain nonlinearities and filtered signals which is derived to solve the relative degree problem caused by the system states are not measurable. Besides, we also apply some auxiliary signals and an averaging filter to transfer the original output observation error to a new formulation so that we can implement the AILC without using differentiators. The filtered fuzzy neural network (filtered-FNN) using the system state estimation vector as the input vector is applied for approximation of the unknown plant nonlinearities. In order to overcome the lumped uncertainties associated with function approximation error and state estimation error, a normalization signal is applied as a bounding function for designing a robust AILC. The stabilization learning component is used to guarantee the boundedness of internal signals. Based on a Lyapunov like analysis, we show that all the adjustable parameters as well as internal signals remain bounded for all iterations and the norm of output tracking error will asymptotically converge to a tunable residual set.

Reinforcement fuzzy-neural adaptive iterative learning control for nonlinear systems

This paper proposes a new fuzzy neural network based reinforcement adaptive iterative learning controller for a class of nonlinear systems. Different from some existing reinforcement learning schemes, the reinforcement adaptive iterative learning controller has the advantages of rigorous proofs without using an approximation of the plant Jacobian. The critic is appended into the reinforcement adaptive iterative learning controller to generate the reinforcement signal, which provides a degree of satisfaction about the tracking performance. In addition, the reinforcement signal can be further applied in the weight adaptation rules. Iterative learning components of the reinforcement adaptive iterative learning controller are designed to compensate for the uncertainties of plant nonlinearities. The overall adaptive scheme guarantees all adjustable parameters and the internal signals remain bounded for all iterations. Moreover, the norm of tracking error vector at each time instant will asymptotically converge to a tunable residual set as iteration goes to infinity even the initial state error exists. Finally, a simulation result is given to demonstrate the learning performance of the fuzzy neural network based reinforcement adaptive iterative learning controller.