H∞ control for networked systems with random communication delays

Copyright [2006] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This note is concerned with a new controller design problem for networked systems with random communication delays. Two kinds of random delays are simultaneously considered: i) from the controller to the plant, and ii) from the sensor to the controller, via a limited bandwidth communication channel. The random delays are modeled as a linear function of the stochastic variable satisfying Bernoulli random binary distribution. The observer-based controller is designed to exponentially stabilize the networked system in the sense of mean square, and also achieve the prescribed H∞ disturbance attenuation level. The addressed controller design problem is transformed to an auxiliary convex optimization problem, which can be solved by a linear matrix inequality (LMI) approach. An illustrative example is provided to show the applicability of the proposed method

Neural Network-based Finite-time Control of Nonlinear Systems with Unknown Dead-zones: Application to Quadrotors

Over the years, researchers have addressed several control problems of various classes of nonlinear systems. This article considers a class of uncertain strict feedback nonlinear system with unknown external disturbances and asymmetric input dead-zone. Designing a tracking controller for such system is very complex and challenging. This article aims to design a finite-time adaptive neural network backstepping tracking control for the nonlinear system under consideration. In addition,  all unknown disturbances and nonlinear functions are lumped together and approximated by radial basis function neural network (RBFNN). Moreover, no prior  information about the boundedness of the dead-zone parameters is required in the controller design. With the aid of a Lyapunov candidate function, it has been shown that the tracking errors converge near the origin in finite-time. Simulation results testify that the proposed control approach can force the output to follow the reference trajectory in a short time despite the presence of  asymmetric input dead-zone and external disturbances. At last, in order to highlight the effectiveness of the proposed control method, it is applied to a quadrotor unmanned aerial vehicle (UAV)

An Adaptive Dynamic Surface Controller for Ultralow Altitude Airdrop Flight Path Angle with Actuator Input Nonlinearity

In the process of ultralow altitude airdrop, many factors such as actuator input dead-zone, backlash, uncertain external atmospheric disturbance, and model unknown nonlinearity affect the precision of trajectory tracking. In response, a robust adaptive neural network dynamic surface controller is developed. As a result, the aircraft longitudinal dynamics with actuator input nonlinearity is derived; the unknown nonlinear model functions are approximated by means of the RBF neural network. Also, an adaption strategy is used to achieve robustness against model uncertainties. Finally, it has been proved that all the signals in the closed-loop system are bounded and the tracking error converges to a small residual set asymptotically. Simulation results demonstrate the perfect tracking performance and strong robustness of the proposed method, which is not only applicable to the actuator with input dead-zone but also suitable for the backlash nonlinearity. At the same time, it can effectively overcome the effects of dead-zone and the atmospheric disturbance on the system and ensure the fast track of the desired flight path angle instruction, which overthrows the assumption that system functions must be known

Unknown dynamics estimator-based output-feedback control for nonlinear pure-feedback systems

Most existing adaptive control designs for nonlinear pure-feedback systems have been derived based on backstepping or dynamic surface control (DSC) methods, requiring full system states to be measurable. The neural networks (NNs) or fuzzy logic systems (FLSs) used to accommodate uncertainties also impose demanding computational cost and sluggish convergence. To address these issues, this paper proposes a new output-feedback control for uncertain pure-feedback systems without using backstepping and function approximator. A coordinate transform is first used to represent the pure-feedback system in a canonical form to evade using the backstepping or DSC scheme. Then the Levant's differentiator is used to reconstruct the unknown states of the derived canonical system. Finally, a new unknown system dynamics estimator with only one tuning parameter is developed to compensate for the lumped unknown dynamics in the feedback control. This leads to an alternative, simple approximation-free control method for pure-feedback systems, where only the system output needs to be measured. The stability of the closed-loop control system, including the unknown dynamics estimator and the feedback control is proved. Comparative simulations and experiments based on a PMSM test-rig are carried out to test and validate the effectiveness of the proposed method

Nonlinear Dynamic Surface Control of Chaos in Permanent Magnet Synchronous Motor Based on the Minimum Weights of RBF Neural Network

This paper is concerned with the problem of the nonlinear dynamic surface control (DSC) of chaos based on the minimum weights of RBF neural network for the permanent magnet synchronous motor system (PMSM) wherein the unknown parameters, disturbances, and chaos are presented. RBF neural network is used to approximate the nonlinearities and an adaptive law is employed to estimate unknown parameters. Then, a simple and effective controller is designed by introducing dynamic surface control technique on the basis of first-order filters. Asymptotically tracking stability in the sense of uniformly ultimate boundedness is achieved in a short time. Finally, the performance of the proposed controller is testified through simulation results

Variable neural networks for adaptive control of nonlinear systems

This paper is concerned with the adaptive control of continuous-time nonlinear dynamical systems using neural networks. A novel neural network architecture, referred to as a variable neural network, is proposed and shown to be useful in approximating the unknown nonlinearities of dynamical systems. In the variable neural networks, the number of basis functions can be either increased or decreased with time, according to specified design strategies, so that the network will not overfit or underfit the data set. Based on the Gaussian radial basis function (GRBF) variable neural network, an adaptive control scheme is presented. The location of the centers and the determination of the widths of the GRBFs in the variable neural network are analyzed to make a compromise between orthogonality and smoothness. The weight-adaptive laws developed using the Lyapunov synthesis approach guarantee the stability of the overall control scheme, even in the presence of modeling error(s). The tracking errors converge to the required accuracy through the adaptive control algorithm derived by combining the variable neural network and Lyapunov synthesis techniques. The operation of an adaptive control scheme using the variable neural network is demonstrated using two simulated example

Adaptive neural network cascade control system with entropy-based design

A neural network (NN) based cascade control system is developed, in which the primary PID controller is constructed by NN. A new entropy-based measure, named the centred error entropy (CEE) index, which is a weighted combination of the error cross correntropy (ECC) criterion and the error entropy criterion (EEC), is proposed to tune the NN-PID controller. The purpose of introducing CEE in controller design is to ensure that the uncertainty in the tracking error is minimised and also the peak value of the error probability density function (PDF) being controlled towards zero. The NN-controller design based on this new performance function is developed and the convergent conditions are. During the control process, the CEE index is estimated by a Gaussian kernel function. Adaptive rules are developed to update the kernel size in order to achieve more accurate estimation of the CEE index. This NN cascade control approach is applied to superheated steam temperature control of a simulated power plant system, from which the effectiveness and strength of the proposed strategy are discussed by comparison with NN-PID controllers tuned with EEC and ECC criterions