Consensus tracking problem for linear fractional multi-agent systems with initial state error

In this paper, we discuss the consensus tracking problem by introducing two iterative learning control (ILC) protocols (namely, Dα-type and PDα-type) with initial state error for fractional-order homogenous and heterogenous multi-agent systems (MASs), respectively. The initial state of each agent is fixed at the same position away from the desired one for iterations. For both homogenous and heterogenous MASs, the Dα-type ILC rule is first designed and analyzed, and the asymptotical convergence property is carefully derived. Then, an additional P-type component is added to formulate a PDα-type ILC rule, which also guarantees the asymptotical consensus performance. Moreover, it turns out that the PDα-type ILC rule can further adjust the final performance. Two numerical examples are provided to verify the theoretical results.

Adaptive Control for Dual-Arm Robotic System Based on Radial Basis Function Neural Network

The paper has developed an adaptive control using neural network for controlling a dual-arm robotic system in moving a rectangle object to the desired trajectories. Firstly, the overall dynamics of the manipulators and the object have been derived based on Euler-Lagrangian principle. And then based on the dynamics, a controller has been proposed to achieve the desired trajectories of the grasping object. A radial basis function neural network has been applied to compensate uncertainties of dynamic parameters. The adaptive algorithm has been derived owning to the Lyapunov stability principle to guarantee asymptotical convergence of the closed dynamic system. Finally, simulation work on MatLab has been carried out to reconfirm the accuracy and the effectiveness of the proposed controller.

A Unified Design Approach to Repetitive Learning Control for Systems Subject to Fractional Uncertainties

Fractional uncertainties are involved in many practical systems. Currently, there is a lack of research results about such general class of nonlinear systems in the context of learning control. This paper presents a Lyapunov-synthesis approach to repetitive learning control (RLC) being unified due to the use of the direct parametrization and adaptive bounding techniques. To effectively handle fractional uncertainties, the estimation method for such uncertainties is elaborated to facilitate the controller design and convergence analysis. Its novelty lies in the less requirement for the knowledge about the system undertaken. Unsaturated- and saturated-learning algorithms are, respectively, characterized by which both the boundedness of the variables in the closed-loop system undertaken and the asymptotical convergence of the tracking error are established. Experimental results are provided to verify the effectiveness of the presented learning control.

Multiple Model ILC for Continuous-Time Nonlinear Systems

Multiple model iterative learning control (MMILC) method is proposed to deal with the continuous-time nonlinear system with uncertain and iteration-varying parameters. In this kind of control strategy, multiple models are established to cover the uncertainty of system; a switching mechanism is used to decide the most appropriate model for system in current iteration. For system operating iteratively in a fixed time interval with uncertain or jumping parameters, this kind of MMILC can improve the transient response and control property greatly. Asymptotical convergence is demonstrated theoretically, and the control effectiveness is illustrated by numerical simulation.

Inertial Iteration for Split Common Fixed-Point Problem for Quasi-Nonexpansive Operators

Inspired by the note on split common fixed-point problem for quasi-nonexpansive operators presented by Moudafi (2011), based on the very recent work by Dang et al. (2012), in this paper, we propose an inertial iterative algorithm for solving the split common fixed-point problem for quasi-nonexpansive operators in the Hilbert space. We also prove the asymptotical convergence of the algorithm under some suitable conditions. The results improve and develop previously discussed feasibility problems and related algorithms.

Sequential B-Spline Surface Construction Using Multiresolution Data Clouds

B-spline surfaces are widely used in engineering practices as a flexible and efficient mathematical model for product design, analysis, and assessment. In this paper, we propose a new sequential B-spline surface construction procedure using multiresolution measurements. At each iterative step of the proposed procedure, we first update knots vectors based on bias and variance decomposition of the fitting error and then incorporate new data into the current surface approximation to fit the control points using Kalman filtering technique. The asymptotical convergence property of the proposed procedure is proved under the framework of sieves method. Using numerical case studies, the effectiveness of the method under finite sample is tested and demonstrated.

Endogenous Reactivity in a Dynamic Model of Consumer’s Choice

We move from a boundedly rational consumer model (Naimzada and Tramontana, 2008, 2010) characterized by a gradient-like decisional process in which, under particular parameters conditions, the asymptotical convergence to the optimal choice does not happen but it does under a least squared learning mechanism. In the present paper, we prove that even a less sophisticated learning mechanism leads to convergence to the rational choice and also prove that convergence is ensured when both learning mechanisms are available. The stability results that we obtain give more strength to the rational behavior assumption of the original model; in fact, the less demanding is the learning mechanism ensuring convergence to the rational behavior, the higher is the probability that even quite naive consumers will learn the composition of their optimum consumption bundles.

Iterative Learning Control for Remote Control Systems with Communication Delay and Data Dropout

Iterative learning control (ILC) is applied to remote control systems in which communication channels from the plant to the controller are subject to random data dropout and communication delay. Through analysis, it is shown that ILC can achieve asymptotical convergence along the iteration axis, as far as the probabilities of the data dropout and communication delay are knowna priori. Owing to the essence of feedforward-based control ILC can perform trajectory-tracking tasks while both the data-dropout and the one-step delay phenomena are taken into consideration. Theoretical analysis and simulations validate the effectiveness of the ILC algorithm for network-based control tasks.