Ying-Chung Wang

A Fuzzy-Neural Adaptive Terminal Iterative Learning Control for Fed-Batch Fermentation Processes

A fuzzy-neural adaptive terminal iterative learning controller is proposed in this paper for uncertain fed-batch fermentation processes with iteration-varying initial states. In order to derive a terminal output tracking error model, a technique of sampled-data transformation for differentiation is firstly utilized to transform the fed-batch fermentation process into a sampled-data system. An input and output algebraic function is then derived based on the sampled-data formulation of fed-batch fermentation process as well as the differential mean value theorem. According to the derived terminal output tracking error model, a fuzzy neural network is applied to approximate the unknown terminal desired input. In order to overcome a lumped uncertainty from the error induced by fuzzy-neural function approximation and the unknown initial states, an iteration-varying boundary layer is developed to construct an auxiliary terminal output error. This auxiliary terminal output error is then used to derive suitable adaptive laws for the weights of fuzzy neural network and the width of boundary layer. Based on a Lyapunov-like analysis, we show that the boundedness of control parameters, control input, and process output are guaranteed for each iteration. Furthermore, the norm of terminal output error will asymptotically converge to a tunable residual set whose size depends on the width of boundary layer as iteration number goes to infinity.

Sample-data adaptive iterative learning control for a class of unknown nonlinear systems

Using a technique of sampled-data transformation for differentiation and integration, a sampled-data adaptive iterative learning control is presented for a class of nonlinear systems. The main control structure is designed by a fuzzy system used as a function approximator to compensate for an unknown certainty equivalent controller. The robustness problem due to function approximation error and input disturbance is solved by a technique of time-varying boundary layer which is utilized to construct an auxiliary error function for adaptive law design. Stability and convergence of the learning system is proved via a Lyapunov-like analysis if the adaptation gains satisfy a convergence condition. Since the convergence condition depends on the upper bound of system unknown input/output coupling function, an identifier based on fuzzy system design is further proposed to estimate the unknown bound. The adaptive laws for the fuzzy parameters are investigated to guarantee that identification error will asymptotically converge to zero. Finally, a numerical example is given to demonstrate the effectiveness of the iterative learning control system.

An observer-based adaptive iterative learning controller for MIMO nonlinear systems with delayed output

An observer based adaptive iterative learning control (AILC) is proposed for MIMO nonlinear systems with delayed output in this paper. Since the system state vector is unavailable for measurement, we apply the state tracking error observer to solve the problem of unmeasurable system state vector for the design of AILC. By using the state tracking error observer, a mixed time-domain and s-domain technique is first applied to derive an output observation error model. The output observation error model will become a decoupled MIMO linear systems whose input vector is the system uncertain vector and each diagonal element is a stable transfer function with relative degree one. Then, the output observation error model is further transformed by introducing an averaging filter matrix and some auxiliary signal vectors so that the AILC can be implemented without using differentiators. Based on the derived output observation error model, an MIMO filtered fuzzy neural network using delayed state estimation vector and state estimation vector as the input vector is applied to approximate the unknown system nonlinear function vector. Besides, a normalization signal is applied as a bounding function to design a robust learning component for compensation of the lumped uncertainties vector caused by function approximation error vector, state estimation error vector and delayed system output vector. Finally, a stabilization learning component is used to guarantee the boundedness of internal signals. Based on Lyapunov-like analysis, it is shown that all the adjustable parameters as well as internal signals remain bounded for all iterations. The norm of output tracking error vector will asymptotically converge to a tunable residual set whose size depends on some design parameters of averaging filter.

An adaptive terminal iterative learning control for nonaffine nonlinear discrete-time systems

A new adaptive terminal iterative learning controller is presented in this paper for nonaffine nonlinear discrete-time systems with iteration-varying desired terminal output and random initial system output. A terminal output tracking error model is firstly derived by using the system function and the differential mean value theorem since it is assumed only system terminal output is measurable. Based on the derived terminal output tracking error model, an iteration-varying boundary layer and a dead-zone like auxiliary terminal error are proposed to design an adaptive terminal iterative learning controller. The iterative learning controller and the width of boundary layer are updated from trial to trial in order to compensate for an unknown nominal desired terminal input and an unknown uncertain desire terminal input respectively. Based on a Lyapunov like analysis, we show that the boundedness of control input, system output and width of boundary layer are guaranteed for each iteration and each time instant. Furthermore, the norm of terminal output error will asymptotically converge to a tunable residual set whose size depends on the width of boundary layer as iteration number goes to infinity.

On the fuzzy discrete-time AILC for a class of nonlinear MIMO systems

A fuzzy discrete-time adaptive iterative learning control for a class of uncertain nonlinear discrete-time MIMO systems with random disturbance is proposed in this paper. Since the plant nonlinearity is unknown, a fuzzy system is firstly used as a function approximator to compensate the unknown ideal certainty equivalent controller. Besides, an adaptive time-varying boundary layer is introduced not only to overcome the problem of function approximation error and random disturbance but also to construct an auxiliary error function for the design of adaptive laws. 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.

Adaptive Iterative Learning Control for Freeway Traffic Flow Systems Using Improved Bacterial Foraging Optimized Desired Traffic Densities Planning

In this paper, we propose a discrete fuzzy-neural adaptive iterative learning control (AILC) for freeway traffic flow systems with random initial resetting errors, iteration-varying desired traffic densities, and random bounded off-ramp traffic volumes using traffic densities, space mean speeds, and on-ramp waiting queues design. It is assumed that the system nonlinear functions and input gains are unknown for controller design. An adaptive fuzzy-neural network controller and an adaptive robust controller are applied to compensate for the unknown system nonlinearities and input gains, respectively. Moreover, to deal with the disturbances from random bounded off-ramp traffic volumes, a dead-zone like auxiliary error with a time-varying boundary layer is introduced as a bounding parameter. This proposed auxiliary error is also utilized to construct the adaptive laws without using the bound of the input gain. The traffic density tracking error is shown to converge along the axis of learning iteration to a residual set whose level of magnitude depends on the width of boundary layer. Besides, since the nice desired traffic densities designed for the coordinated control objective of the AILC for freeway traffic flow systems are generally unknown, the improved bacterial forging optimization (IBFO) algorithm is used to optimize the fitness function, which is constructed by the coordinated control objective including (1) minimum total travel time, (2) minimum on-ramp average waiting time, and (3) minimum changes of desired traffic densities. Finally, a computer simulation example is used to verify the learning performance of the proposed fuzzy-neural AILC for freeway traffic flow systems using IBFO-based desired traffic densities planning.

Sampled-data iterative learning control for nonlinear systems with iteration varying lengths

This note addresses the problem of sampled-data iterative learning control (SDILC) for continuous-time nonlinear systems with randomly iteration varying lengths. To deal with the iteration varying trial lengths, a P-type ILC scheme with a modified tracking error is proposed. Sufficient conditions are derived to ensure the convergence of the nonlinear system at each sampling instant. An illustrative example is carried out to verify the effectiveness of the proposed ILC algorithm.

An adaptive iterative learning control for discrete-time nonlinear systems with iteration-varying uncertainties

In this paper, we present a new adaptive iterative learning controller for a class of discrete-time nonlinear systems with iteration-varying uncertainties including initial tracking error, system parameters and external disturbance. The learning objective is to control the nonlinear system to track an iteration-varying desired trajectory after suitable numbers of learning iterations. The main challenge for the iterative learning control design is that all the system parameters are iteration-varying. After separating the system parameters into a pure time-varying component and an iteration-varying component, the system dynamics are divided into an iteration-independent nominal part and an iteration-dependent uncertain part. An adaptive iterative learning controller is then designed to control the nominal dynamics and an iteration-varying boundary layer with dead-zone like auxiliary error is proposed to compensate for the iteration-varying uncertainties. The control parameters and the width of boundary layer are updated from trial to trial in order to guarantee the stability and convergence of the learning system. In addition to ensure the boundedness of control signals for each iteration and each time instant, we also prove that the norm of output error will asymptotically converge to a residual set whose size depends on the width of boundary layer as iteration number goes to infinity.