Real-time torque control using discrete-time recurrent high-order neural networks

This paper presents a discrete-time direct current (DC) motor torque tracking controller, based on a recurrent high-order neural network to identify the plant model. In order to train the neural identifier, the extended Kalman filter (EKF) based training algorithm is used. The neural identifier is in series-parallel configuration that constitutes a well approximation method of the real plant by the neural identifier. Using the neural identifier structure that is in the nonlinear controllable form, the block control (BC) combined with sliding modes (SM) control techniques in discrete-time are applied. The BC technique is used to design a nonlinear sliding manifold such that the resulting sliding mode dynamics are described by a desired linear system. For the SM control technique, the equivalent control law is used in order to the plant output tracks a reference signal. For reducing the effect of unknown terms, it is proposed a specific desired dynamics for the sliding variables. The control problem is solved by the indirect approach, where an appropriate neural network (NN) identification model is selected; the NN parameters (synaptic weights) are adjusted according to a specific adaptive law (EKF), such that the response of the NN identifier approximates the response of the real plant for the same input. Then, based on the designed NN identifier a stabilizing or reference tracking controller is proposed (BC combined with SM). The proposed neural identifier and control applicability are illustrated by torque trajectory tracking for a DC motor with separate winding excitation via real-time implementation.     

Multistability of discrete-time recurrent neural networks with unsaturating piecewise linear activation functions

This paper studies the multistability of a class of discrete-time recurrent neural networks with unsaturating piecewise linear activation functions. It addresses the nondivergence, global attractivity, and complete stability of the networks. Using the local inhibition, conditions for nondivergence are derived, which not only guarantee nondivergence, but also allow for the existence of multiequilibrium points. Under these nondivergence conditions, global attractive compact sets are obtained. Complete stability is studied via constructing novel energy functions and using the well-known Cauchy Convergence Principle. Examples and simulation results are used to illustrate the theory.     

Adaptive control of a class of nonlinear discrete-time systemsusing neural networks

Layered neural networks are used in a nonlinear self-tuning adaptive control problem. The plant is an unknown feedback-linearizable discrete-time system, represented by an input-output model. To derive the linearizing-stabilizing feedback control, a (possibly nonminimal) state-space model of the plant is obtained. This model is used to define the zero dynamics, which are assumed to be stable, i.e., the system is assumed to be minimum phase. A linearizing feedback control is derived in terms of some unknown nonlinear functions. A layered neural network is used to model the unknown system and generate the feedback control. Based on the error between the plant output and the model output, the weights of the neural network are updated. A local convergence result is given. The result says that, for any bounded initial conditions of the plant, if the neural network model contains enough number of nonlinear hidden neurons and if the initial guess of the network weights is sufficiently close to the correct weights, then the tracking error between the plant output and the reference command will converge to a bounded ball, whose size is determined by a dead-zone nonlinearity. Computer simulations verify the theoretical result     

Constrained control for uncertain discrete-time linear systems

In this paper the problem of stabilizing uncertain linear discrete-time systems under state and control linear constraints is studied. Many formulations of this problem have been given in the literature. Here we consider the case of finding a linear state feedback control law making a given polytope in the state space positively invariant while the control remains bounded within prefixed values under the effect of all the uncertainty sequences belonging to a given polytope in the perturbations space. A necessary and sufficient condition for the existence of a solution of this problem is first given. This condition leads to a set of linear constraints which can be solved using linear programming tecniques by defining an appropriate objective function. A worked example shows the effectiveness of the proposed algorithm. © 1998 John Wiley & Sons, Ltd.     

Extended dissipative output-feedback control for discrete-time bidirectional associative memory neural networks via delay-partitioning approach

This paper is concerned with the analysis of an extended dissipativity performance for a class of bidirectional associative memory (BAM) neural networks (NNs) having time-varying delays. To achieve this, the idea of the delay-partitioning approach is used, where the range of time-varying delay factors is partitioned into a finite number of equidistant subintervals. A delay-partitioning based Lyapunov–Krasovskii function is introduced on these intervals, and some new delay-dependent extended dissipativity results are established in terms of linear matrix inequalities, which also depend on the partition size of the delay factor. Further, numerical examples are performed to acknowledge the extended dissipativity performance of delayed discrete-time BAM NN; further, four case studies were explored with their simulations to validate the impact of the delay-partitioning approach.     

Stability analysis of discrete-time recurrent neural networks

We address the problem of global Lyapunov stability of discrete-time recurrent neural networks (RNNs) in the unforced (unperturbed) setting. It is assumed that network weights are fixed to some values, for example, those attained after training. Based on classical results of the theory of absolute stability, we propose a new approach for the stability analysis of RNNs with sector-type monotone nonlinearities and nonzero biases. We devise a simple state-space transformation to convert the original RNN equations to a form suitable for our stability analysis. We then present appropriate linear matrix inequalities (LMIs) to be solved to determine whether the system under study is globally exponentially stable. Unlike previous treatments, our approach readily permits one to account for non-zero biases usually present in RNNs for improved approximation capabilities. We show how recent results of others on the stability analysis of RNNs can be interpreted as special cases within our approach. We illustrate how to use our approach with examples. Though illustrated on the stability analysis of recurrent multilayer perceptrons, the approach proposed can also be applied to other forms of time-lagged RNNs.     

Continuous attractors of discrete-time recurrent neural networks

This paper studies the continuous attractors of discrete-time recurrent neural networks. Networks in discrete time can directly provide algorithms for efficient implementation in digital hardware. Continuous attractors of neural networks have been used to store and manipulate continuous stimuli for animals. A continuous attractor is defined as a connected set of stable equilibrium points. It forms a lower dimensional manifold in the original state space. Under some conditions, the complete analytical expressions for the continuous attractors of discrete-time linear recurrent neural networks as well as discrete-time linear-threshold recurrent neural networks are derived. Examples are employed to illustrate the theory.     

Optimal control for stochastic linear quadratic singular system using neural networks

In this paper, optimal control for stochastic linear singular system with quadratic performance is obtained using neural networks. The goal is to provide optimal control with reduced calculus effort by comparing the solutions of the matrix Riccati differential equation (MRDE) obtained from well known traditional Runge–Kutta (RK) method and nontraditional neural network method. To obtain the optimal control, the solution of MRDE is computed by feed forward neural network (FFNN). Accuracy of the solution of the neural network approach to the problem is qualitatively better. The advantage of the proposed approach is that, once the network is trained, it allows instantaneous evaluation of solution at any desired number of points spending negligible computing time and memory. The computation time of the proposed method is shorter than the traditional RK method. An illustrative numerical example is presented for the proposed method.     

On discrete-time linear quadratic control

The discrete-infinite time stochastic control system with complete observation is considered with quadratic cost functional when the coefficients of the system and cost functional are not time-invariant. It has been shown that the optimal control law has the form of time invariant feedback under the assumption that the coefficients have limits as time tends to infinity. In addition, asymptotic property of the solution of the difference Riccati equation with time-varying coefficients are established.     

State estimation for discrete-time neural networks with time-varying delay

This article deals with the problem of delay-dependent state estimation for discrete-time neural networks with time-varying delay. Our objective is to design a state estimator for the neuron states through available output measurements such that the error state system is guaranteed to be globally exponentially stable. Based on the linear matrix inequality approach, a delay-dependent condition is developed for the existence of the desired state estimator via a novel Lyapunov functional. The obtained condition has less conservativeness than the existing ones, which is demonstrated by a numerical example.     

Robust control of linear discrete-time systems

Given a linear discrete-time system with additive disturbances, a general methodology for designing a stable control algorithm is shown. The approach is Lyapunov-based with certain liberty of tailoring the candidate function for a given problem. Comparison to the existing solutions based on a variable structure approach is given.     

Finite-time control of discrete-time linear systems

In this note, we consider the finite-time stabilization of discrete-time linear systems subject to disturbances generated by an exosystem. Finite-time stability can be used in all those applications where large values of the state should not be attained, for instance in the presence of saturations. The main result provided in the note is a sufficient condition for finite-time stabilization via state feedback. This result is then used to find some sufficient conditions for the existence of an output feedback controller guaranteeing finite-time stability. All the conditions are then reduced to feasibility problems involving linear matrix inequalities (LMIs). Some numerical examples are presented to illustrate the proposed methodology.     

基于最小二乘算法及神经网络的非线性离散系统的自适应控制

针对有关文献所设计的控制律，在一较弱的条件下，去掉了符号运算部分，证明该控制律可避免“零除”问题，提高了运算速度。对于这种基于神经网络和LS算法的自适应控制问题，证明了系统状态落入一紧集中，闭环系统的所有信号都是有界的，且系统输出和参考输出之间的跟踪误差收敛于以零为原点的某一有界球中。     

Bounds of the incremental gain for discrete-time recurrent neural networks

As a nonlinear system, a recurrent neural network generally has an incremental gain different from its induced norm. While most of the previous research efforts were focused on the latter, this paper presents a method to compute an effective upper bound of the former for a class of discrete-time recurrent neural networks, which is not only applied to systems with arbitrary inputs but also extended to systems with small-norm inputs. The upper bound is computed by simple optimizations subject to linear matrix inequalities (LMIs). To demonstrate the wide connections of our results to problems in control, the servomechanism is then studied, where a feedforward neural network is designed to control the output of a recurrent neural network to track a set of trajectories. This problem can be converted into the synthesis of feedforward-feedback gains such that the incremental gain of a certain system is minimized. An algorithm to perform such a synthesis is proposed and illustrated with a numerical example.     

High-order repetitive control for discrete-time linear switched systems

This paper is concerned with the design of a high-order repetitive control (RC) law for a class of discrete-time linear switched systems with repetition-varying reference trajectories. First, a high-order RC law, which embeds the characteristic of known variation of the reference trajectories, is proposed to the system, and a two-dimensional (2D) model is presented to describe the control and learning actions of the repetitive control system by using the lifting technique. By choosing appropriate multiple Lyapunov–Krasovskii functions, sufficient conditions for asymptotic stability of the 2D system are derived in the form of a set of linear matrix inequalities. Finally, an example is given to illustrate the effectiveness of the proposed results.     

Adaptive quantized control for linear uncertain discrete-time systems

A direct adaptive control framework for linear uncertain systems for using communication channels is developed. Specifically, the control signals are to be quantized and sent over a communication channel to the actuator. The proposed framework is Lyapunov-based and guarantees partial asymptotic stability, that is, Lyapunov stability of the closed-loop system states and attraction with respect to the plant states. The quantizers are logarithmic and characterized by sector-bound conditions, with the conic sectors adjusted at each time instant by the adaptive controller, in conjunction with the system response. Furthermore, we extend the scheme to the case where the logarithmic quantizer has a deadzone around the origin so that only a finite number of quantization levels is required to achieve practical stability. Finally, a numerical example is provided to demonstrate the efficacy of the proposed approach.     

Low-sensitivity optimal feedback control for linear discrete-time systems

The problem of reducing sensitivity of discrete-time systems to parameter variations is considered. State and output feedback gains are obtained to minimize a quadratic criterion which includes sensitivity functions. Necessary conditions for optimality are derived and numerical examples are discussed.     

A PSO-based weighting method for linear combination of neural networks

This paper presents a new way of computing the weights for combining multiple neural network classifiers based on particle swarm optimization, PSO. The weights are obtained so that they minimize the total classification error rate of the ensemble system. In order to evaluate the effectiveness of the proposed method, we have carried out some experiments on three data sets: 2-D normal, Satimage and Phoneme. Experimental results show that the PSO-based weighting method outperforms the MSE and simple averaging methods, especially for diverse networks.     

An analog implementation of discrete-time cellular neural networks

An analog circuit structure for the realization of discrete-time cellular neural networks (DTCNNs) is introduced. The computation is done by a balanced clocked circuit based on the idea of conductance multipliers and operational transconductance amplifiers. The circuit is proposed for a one-neighborhood on a hexagonal grid, but can also be modified to larger neighborhoods and/or other grid topologies. A layout was designed for a standard CMOS process, and the corresponding HSPICE simulation results are given. A test chip containing 16 cells was fabricated, and measurements of the transfer characteristics are provided. The functional behavior is demonstrated for a simple example.