A posteriori real-time recurrent learning schemes for a recurrentneural network based nonlinear predictor

Recurrent neural networks (RNNs) are well established for the nonlinear and nonstationary signal prediction paradigm. Appropriate learning algorithms, such as the real-time recurrent learning (RTRL) algorithm, have been developed for that purpose. However, little is known about the RNN time-management policy. Here, insight is provided into the time-management of the RNN, and an a posteriori approach to the RNN based nonlinear signal prediction paradigm is offered. Based upon the chosen time-management policy, algorithms are developed, from the a priori learning-a priori error strategy through to the a posteriori learning-a posteriori error strategy. Compared with the a priori algorithms, the a posteriori algorithms offered are shown to provide a better prediction performance with little further expense in terms of computational complexity. Simulations undertaken on speech using the newly introduced algorithms confirm the theoretical results     

Multiresolution FIR neural-network-based learning algorithm applied to network traffic prediction

In this paper, a multiresolution finite-impulse-response (FIR) neural-network-based learning algorithm using the maximal overlap discrete wavelet transform (MODWT) is proposed. The multiresolution learning algorithm employs the analysis framework of wavelet theory, which decomposes a signal into wavelet coefficients and scaling coefficients. The translation-invariant property of the MODWT allows alignment of events in a multiresolution analysis with respect to the original time series and, therefore, preserving the integrity of some transient events. A learning algorithm is also derived for adapting the gain of the activation functions at each level of resolution. The proposed multiresolution FIR neural-network-based learning algorithm is applied to network traffic prediction (real-world aggregate Ethernet traffic data) with comparable results. These results indicate that the generalization ability of the FIR neural network is improved by the proposed multiresolution learning algorithm.     

A neural-network-based controller for a single-link flexiblemanipulator using the inverse dynamics approach

This paper presents an intelligent-based control strategy for tip position tracking control of a single-link flexible manipulator. Motivated by the well-known inverse dynamics control strategy for rigid-link manipulators, two feedforward neural networks (NNs) are proposed to learn the nonlinearities of the flexible arm associated with the inverse dynamics controller. The redefined output approach is used by feeding back this output to guarantee the minimum phase behavior of the resulting closed-loop system. No a priori knowledge about the nonlinearities of the system is needed and the payload mass is also assumed to be unknown. The network weights are adjusted using a modified online error backpropagation algorithm that is based on the propagation of output tracking error, derivative of that error and the tip deflection of the manipulator. The real-time controller is implemented on an experimental test bed. The results achieved by the proposed NN-based controller are compared experimentally with conventional proportional-plus-derivative-type and standard inverse dynamics controls to substantiate and verify the advantages of our proposed scheme and its promising potential in identification and control of nonlinear systems     

Robust cerebellar model articulation controller design for unknown nonlinear systems

In this study, a robust cerebellar model articulation controller (RCMAC) is designed for unknown nonlinear systems. The RCMAC is comprised of a cerebellar model articulation controller (CMAC) and a robust controller. The CMAC is utilized to approximate an ideal controller, and the weights of the CMAC are on-line tuned by the derived adaptive law based on the Lyapunov sense. The robust controller is designed to guarantee a specified H/sup /spl infin// robust tracking performance. In the RCMAC design, the sliding-mode control method is utilized to derive the control law, so that the developed control scheme has more robustness against the uncertainty and approximation error. Finally, the proposed RCMAC is applied to control a chaotic circuit. Simulation results demonstrate that the proposed control scheme can achieve favorable tracking performance with unknown the controlled system dynamics.     

A recurrent neural network for nonlinear convex optimization subject to nonlinear inequality constraints

This paper presents a novel recurrent neural network for solving nonlinear convex programming problems subject to nonlinear inequality constraints. Under the condition that the objective function is convex and all constraint functions are strictly convex or that the objective function is strictly convex and the constraint function is convex, the proposed neural network is proved to be stable in the sense of Lyapunov and globally convergent to an exact optimal solution. Compared with the existing neural networks for solving such nonlinear optimization problems, the proposed neural network has two major advantages. One is that it can solve convex programming problems with general convex inequality constraints. Another is that it does not require a Lipschitz condition on the objective function and constraint function. Simulation results are given to illustrate further the global convergence and performance of the proposed neural network for constrained nonlinear optimization.     

Robust iterative learning control with rectifying action for nonlinear discrete time-delayed systems

This paper addresses the two-dimensional (2-D) linear inequalities based robust Iterative Learning Control (ILC) for nonlinear discrete systems with time delays. The proposed two-gain ILC rule has a rectifying action to iterative initial error and external disturbances. It guarantees a reduced bound of the ILC tracking error against the iteration-varying initial error and disturbances. For the iteration-invariant initial error and disturbances, the ILC tracking error can be driven to convergence, and a complete tracking to reference trajectory beyond the initial time point is even achieved as the control gain is specifically selected. An example is used to validate the proposed ILC method.     

Persistence of the saddle-node bifurcation for nonlinear systems with slow unmodeled dynamics

This paper investigates the robustness of the saddle-node bifurcation for nonlinear systems under the addition of slow unmodeled dynamics. The robustness is examined in terms of existence and system behavior after bifurcation. Under fairly general conditions, it is shown that if the reduced model of a physical system encounters a saddle-node bifurcation due to a varying parameter, then the original model which includes small unmodeled dynamics will also encounter a saddle-node bifurcation. An error bound is derived between the bifurcation values and the bifurcation points of the reduced model and that of the original model. Furthermore, it is shown that the dynamics after the saddle-node bifurcation of the reduced model and that of the original model are approximately the same. The persistence and non-persistence of saddle-node bifurcations are illustrated by several examples.This work was supported in part by the NSF under grant numbers ECS-8957878 and ECS-8913074, by EPRI contract RP8010-8, and by Taipower Company.     

Memoryless nonlinear system identification with unknown model order

The problem of identifying a general memoryless input/output system from measurements of inputs and the corresponding outputs is considered. The measured output is sought to be represented as the linear combination of known functions of the input with some additive noise. The choice of model order to be used to fit the data is the main issue addressed, and a cost function involving the prediction error and the model order is derived. The cost function under certain approximations is shown to be similar to one obtained by H. Akaike (1969, 1970). If there is a real system generating the data, it is shown that the expected value of this cost function is always minimized at the true value of the order as long as the noise variance satisfies certain conditions. Asymptotic results for some cases are derived. An efficient algorithm is proposed for identifying the model order. Some simulation results using the proposed algorithm are also presented     

A three-phase soft-transition inverter with a novel controlstrategy for zero-current and near zero-voltage switching

This paper proposes a new soft-transition control strategy for a three-phase zero-current-transition (ZCT) inverter circuit. Each phase leg of the inverter circuit consists of an LC resonant tank, two main switches, and two auxiliary switches. The proposed strategy is realized by planning the switching patterns and timings of these four switches based on the load current information. It enables all the main switches and auxiliary switches to be turned on and turned off under zero-current conditions, and achieves a near zero-voltage turn-on for the main switches. Compared with existing ZCT strategies, the diode reverse recovery current and switching turn-on loss are substantially reduced, the current and thermal stresses in the auxiliary devices are evenly distributed over every switching cycle, and the resonant capacitor voltage stress is reduced from twice the DC bus voltage to 1.3-1.4 times the DC bus voltage. The proposed strategy is also suitable for three-phase power-factor-correction (PFC) rectifier applications. The operation principles, including a detailed analyst based on the state-plane technique, and a design rule are described in this paper. The circuit operation is first verified by a computer simulation, and is then tested with a 50-kW three-phase inverter to the full power level together with a three-phase induction motor in a closed-loop speed/torque control. Significant reductions in switching losses and voltage/current stresses over existing techniques have been experimentally demonstrated     

信息物理融合系统软件可信性演化动力学建模

信息物理融合系统(CPS)软件可信性建模是CPS可信软件开发过程中至关重要的一环,现有的形式化方法、软件验证技术并不适合对CPS软件可信性动态演化进行描述和分析。在深入分析CPS可信软件动态演化过程的基础上,结合非线性动力学的基本理论和方法,研究CPS软件可信性演化的动力学机制,对CPS软件在内外双重因素影响下的可信性演化过程进行建模,并分析其可信性演化规律,为CPS软件可信性研究提供了一种新手段。通过对一个工业控制领域中CPS软件的建模与分析,验证了该方法的可行性。     

A general scheme for equalization of space-time block-coded systems with unknown CSI

Recently, space-time block codes (STBCs) have gained much attention as an effective transmit diversity technique to increase the capacity of wireless communication systems. In this paper, we consider a general technique for direct equalization of space-time block-coding systems with unknown channel state information (CSI). This technique is suitable for several existing hybrid STBC schemes, such as STBC/orthogonal-frequency-division multiplexing (STBC-OFDM) and STBC/code-division multiple access (STBC-CDMA). We show that by exploiting the redundancy in the structure of STBC, a zero-forcing equalizer can be constructed without channel estimation. The conditions for the identifiability of the zero-forcing equalizer are also derived to ensure correct equalization. To further improve the performance of the proposed method, a new iterative algorithm is developed by incorporating the finite alphabet property of information symbols. Simulation results show that the proposed algorithms can outperform comparative schemes in most simulation conditions.     

Analysis and design of unknown input observers for a class of 2-D nonlinear systems

This paper considers the analysis and design of asymptotic unknown input observers (UIOs) for a class of two-dimensional (2-D) nonlinear systems. A sufficient condition for the existence of an asymptotic UIO such that the observer estimation error asymptotically converges to zero is first given in terms of a rank condition on the given system matrices. A systematic method is then presented for the design of UIOs using a linear matrix inequality technique. An example is provided to illustrate the effectiveness of the proposed design method.     

Solutions to sample problems in real-time systems

In the last column, the author posed several sample problems that might be encountered in real-time systems. In this issue, the author provides solutions and thoughts on them. Problems discussed include: sliding rocks of Racetrack Playa, setting the fuses on explosive projectiles, image classification, engine control, and parking garage system.     

Interfacing to real-time systems. Part 6

All real-time systems require some sort of interface to the real world. Part 6 of this seven-part series on real-time systems presents an introduction to interfaces. The purpose of the article is to survey the possibilities for interfaces and provide a little overall perspective on interfaces.     

A parametric procedure for imperfectly supervised learning with unknown class probabilities (Corresp.)

A computationally feasible parametric procedure for unsupervised learning has been given by Agrawala [1]. The procedure eliminates the computational difficulties associated with updating using a mixture density by making use of a probabilistic labeling scheme. Shanmugam [2] has given a similar parametric procedure using probabilistic labeling for the more general problem of imperfectly supervised learning. Both procedures assume known class probabilities. In this correspondence a computationally feasible parametric procedure using probabilistic labeling is given for imperfectly supervised learning when the class probabilities are among the unknown statistical parameters.     

An approach to iterative learning control for spatio-temporal dynamics using nD discrete linear systems models

Iterative Learning Control (ILC) is now well established in terms of both the underlying theory and experimental application. This approach is specifically targeted at cases where the same operation is repeated over a finite duration with resetting between successive executions. Each execution is known as a trial and the key idea is to use information from previous trials to update the control input used on the current one with the aim of improving performance from trial-to-trial. In this paper, the subject area is the application of ILC to spatio-temporal systems described by a linear partial differential equation (PDE) using a discrete approximation of the dynamics, where there are a number of construction methods that could be applied. Here explicit discretization is used, resulting in a multidimensional, or nD, discrete linear system on which to base control law design, where n denotes the number of directions of information propagation and is equal to the total number of indeterminates in the PDE. The resulting control laws can be computed using Linear Matrix Inequalities (LMIs) and a numerical example is given. Finally, a natural extension to robust control is noted and areas for further research briefly discussed.     

A process algebraic approach to the specification and analysis ofresource-bound real-time systems

Recently, significant progress has been made in the development of timed process algebras for the specification and analysis of real-time systems. This paper describes a timed process algebra called ACSR, which supports synchronous timed actions and asynchronous instantaneous events. Timed actions are used to represent the usage of resources and to model the passage of time. Events are used to capture synchronization between processes. To be able to specify real systems accurately, ACSR supports a notion of priority that can be used to arbitrate among timed actions competing for the use of resources and among events that are ready for synchronization. The paper also includes a brief overview of other timed process algebras and discusses similarities and differences between them and ACSR     

A posteriori error learning in nonlinear adaptive filters

The authors provide relationships between the a priori and a posteriori errors of adaptation algorithms for real-time output-error nonlinear adaptive filters realised as feedforward or recurrent neural networks. The analysis is undertaken for a general nonlinear activation function of a neuron, and for gradient-based learning algorithms, for both a feedforward (FF) and recurrent neural network (RNN). Moreover, the analysis considers both contractive and expansive forms of the nonlinear activation functions within the networks. The relationships so obtained provide the upper and lower error bounds for general gradient based a posteriori learning in neural networks     

The synchronous approach to reactive and real-time systems

The state of the art in real-time programming is briefly reviewed. The synchronous approach is then introduced informally and its possible impact on the design of real-time and reactive systems is discussed. The authors present and discuss the application fields and the principles of synchronous programming. The major concern of the synchronous approach is to base synchronous programming languages on mathematical models. This makes it possible to handle compilation, logical correctness proofs, and verification of real-time programs in a formal way, leading to a clean and precise methodology for design and programming     

A decentralized indirect adaptive control for a class oftwo-time-scale nonlinear systems with application to flexible-jointmanipulators

In this paper, the problem of an indirect adaptive decentralized control for a class of two-time scale interconnected systems is considered. The concept of an integral manifold is first utilized to construct the dynamics of corrected slow subsystems. Fast subsystems are also constructed to represent the dynamics of the fast modes. A composite control scheme based on full state feedback is then developed to guarantee stability and robustness of the closed-loop system. The controller is designed by taking into account the effects of unmodeled dynamics, identification errors, and parameter variations. Stability analysis of the resulting closed-loop full-order system subject to the composite controller is presented. To demonstrate the application of the proposed algorithm, an example of a two-link flexible-joint manipulator is considered. Simulation results are provided to validate the applicability of the proposed control scheme