P.N. Nikiforuk

Absolute stability conditions for discrete-time recurrent neural networks

An analysis of the absolute stability for a general class of discrete-time recurrent neural networks (RNNs) is presented. A discrete-time model of RNNs is represented by a set of nonlinear difference equations. Some sufficient conditions for the absolute stability are derived using Ostrowskis theorem and the similarity transformation approach. For a given RNN model, these conditions are determined by the synaptic weight matrix of the network. The results reported in this paper need fewer constraints on the weight matrix and the model than in previously published studies.

Approximation of discrete-time state-space trajectories using dynamic recurrent neural networks

In this note, the approximation capability of a class of discrete-time dynamic recurrent neural networks (DRNNs) is studied. Analytical results presented show that some of the states of such a DRNN described by a set of difference equations may be used to approximate uniformly a state-space trajectory produced by either a discrete-time nonlinear system or a continuous function on a closed discrete-time interval. This approximation process, however, has to be carried out by an adaptive learning process. This capability provides the potential for applications such as identification and adaptive control. >

Adaptive navigation of mobile robots with obstacle avoidance

A local navigation technique with obstacle avoidance, called adaptive navigation, is proposed for mobile robots in which the dynamics of the robot are taken into consideration. The only information needed about the local environment is the distance between the robot and the obstacles in three specified directions. The navigation law is a first-order differential equation and navigation to the goal and obstacle avoidance are achieved by switching the direction angle of the robot. The effectiveness of the technique is demonstrated by means of simulation examples.

A Recurrent Neural Network for Hierarchical Control of Interconnected Dynamic Systems

A recurrent neural network for the optimal control of a group of interconnected dynamic systems is presented in this paper. On the basis of decomposition and coordination strategy for interconnected dynamic systems, the proposed neural network has a two-level hierarchical structure: several local optimization subnetworks at the lower level and one coordination subnetwork at the upper level. A goal-coordination method is used to coordinate the interactions between the subsystems. By nesting the dynamic equations of the subsystems into their corresponding local optimization subnetworks, the number of dimensions of the neural network can be reduced significantly. Furthermore, the subnetworks at both the lower and upper levels can work concurrently. Therefore, the computation efficiency, in comparison with the consecutive executions of numerical algorithms on digital computers, is increased dramatically. The proposed method is extended to the case where the control inputs of the subsystems are bounded. The stability analysis shows that the proposed neural network is asymptotically stable. Finally, an example is presented which demonstrates the satisfactory performance of the neural network

Cooperative collision avoidance between multiple mobile robots

This paper presents a new collision avoidance technique, called cooperative collision avoidance, for multiple mobile robots. The detection of the danger of collision between two mobile robots is discussed with respect to the geometric aspects of their paths as are cooperative collision avoidance behaviors. The direction control command and the velocity control command for the cooperative collision avoidance are then proposed. The avoidance technique is extended to cases in which the number of mobile robots is more than two. Furthermore, the conditions for collision avoidance are considered with respect to the navigation parameters and guidelines of designing the navigation parameters are obtained. The effectiveness of the proposed technique is demonstrated by means of numerical simulation and navigation experiments using two real mobile robots named Pioneer-1. Q 2000 John Wiley & Sons, Inc.

Fast neural learning and control of discrete-time nonlinear systems

The problem of learning control for a general class of discrete-time nonlinear systems is addressed in this paper using multilayered neural networks (MNNs) with feedforward connections. A suitable extension of the concept of input-output linearization of discrete-time nonlinear systems is used to develop the control schemes for both output tracking and model reference control purposes. The ability of MNNs to model arbitrary nonlinear functions is incorporated to approximate the unknown nonlinear input-output relationship and its inverse using a new weight learning algorithm. In order to overcome the difficulties associated with simultaneous online identification and control in neural networks based adaptive control systems, the new learning control architectures are developed for both adaptive tracking and adaptive model reference control systems with online identification and control ability. The potentials of the proposed methods are demonstrated by simulation examples. >

Active flutter suppression for two-dimensional airfoils

Active flutter suppression for a two-dimensional typical airfoil in an incompressible flow is studied in this paper. The root loci of the systems described by three aerodynamical models, each with a single feedback variable, are first investigated to obtain a physical understanding of these systems. Practical systems that include actuator and gust models are considered next, using linear-quadratic regulator theory. Reduced-order models are constructed using a sequence of truncations based on the modal cost analysis, and modal truncation is examined for several weightings of the cost function. The resulting increases in the performance index and the closed-loop poles are then calculated for each truncation. The essential feedback modes and their associated gains for flutter suppression are determined using this analysis. For a reasonable degree of control, these reduced-order models are sufficiently robust.

Dynamic Recurrent Neural Networks for Control of Unknown Nonlinear Systems

A scheme of dynamic recurrent neural networks (DRNNs) is discussed in this paper, which provides the potential for the learning and control of a general class of unknown discrete-time nonlinear systems which are treated as «black boxes» with multi-inputs and multi-outputs (MIMO). A model of the DRNNs is described by a set of nonlinear difference equations, and a suitable analysis for the input-output dynamics of the model is performed to obtain the inverse dynamics. The ability of a DRNN structure to model arbitrary dynamic nonlinear systems is incorporated to approximate the unknown nonlinear input-output relationship using a dynamic back propagation (DBP) learning algorithm. An equivalent control concept is introduced to develop a model based learning control architecture with simultaneous on-line identification and control for unknown nonlinear plants. The potentials of the proposed methods are demonstrated by simulation results

A new supervised learning algorithm for multilayered and interconnected neural networks

A new learning algorithm is presented for supervised learning of multilayered and interconnected neural networks without using a gradient method. First, fictitious teacher signals for the outputs of each hidden unit are algebraically determined by an error backpropagation (EBP) method. Then, the weight parameters are determined by using an exponentially weighted least squares (EWLS) method. This is called the EBP-EWLS algorithm for a multilayered neural network. For an interconnected neural network, the mathematical description of the neural network is arranged in the form for which the EBP-EWLS algorithm can be applied. Simulation studies have verified the proposed technique.

Neuro-Controller with Dynamic Learning and Adaptation

As is known, many of the attributes of intelligent control in a biological process are due to the interactions of billions of neurons. Changing the weights of neurons alter the behavior of the entire neural network. Learning in a neutral network is accomplished by adjusting the weights, typically to minimize some objective function, and storing these weights as the actual strengths of the interconnections. The authors believe, therefore, that a control technique designed on the principles of neural networks will exhibit a ‘learn-while-performing’ capability. In this paper such a neuro-controller, called the ‘Inverse-Dynamics Adaptive Control (IDAC)’, for a class of unknown linear plants with structural perturbations is presented. Algorithms necessary to implement the IDAC technique are derived in detail. Simulation results show that the IDAC scheme exhibits dynamic learning and adaptation capabilities in the control of unknown complex systems. Noa-priori knowledge of the process to be controlled is necessary for the implementation of this scheme. Furthermore, the plant parameter variations due to the structural or environmental perturbations may be investigated by studying the IDAC parameter trajectories.