Nonlinear systems identification and control via dynamic multitime scales neural networks

Adaptive Neural Partial State Tracking Control for Full-State-Constrained Uncertain Singularly Perturbed Nonlinear Systems and Its Applications to Electric Circuit

This paper is concerned with the adaptive neural network (NN) partial tracking control problem for a class of completely unknown multi-input multi-output (MIMO) singularly perturbed nonlinear systems possessing time-varying asymmetric state constraints. To satisfy the constraints, we utilize the state-depended transformation technique to convert the original state-constrained system to an equivalent unconstrained one, then the state constraint problem can be solved by ensuring its stability. Partial state tracking can be achieved without the violation of state constraints. The adaptive tracking controllers are designed by using singular perturbation theory and the adaptive control method, in which NNs are used to approximate unknown nonlinear functions. The ill-conditioned numerical problems lurking in the controller design process are averted and the closed-loop system stability can be guaranteed by introducing an appropriate Lyapunov function with singular perturbation parameter. Finally, a practical example is given to demonstrate the effectiveness of our proposed adaptive NN tracking control scheme.

Intrinsic neural timescales: temporal integration and segregation

We are continuously bombarded by external inputs of various timescales from the environment. How does the brain process this multitude of timescales? Recent resting state studies show a hierarchy of intrinsic neural timescales (INT) with a shorter duration in unimodal regions (e.g., visual cortex and auditory cortex) and a longer duration in transmodal regions (e.g., default mode network). This unimodal-transmodal hierarchy is present across acquisition modalities [electroencephalogram (EEG)/magnetoencephalogram (MEG) and fMRI] and can be found in different species and during a variety of different task states. Together, this suggests that the hierarchy of INT is central to the temporal integration (combining successive stimuli) and segregation (separating successive stimuli) of external inputs from the environment, leading to temporal segmentation and prediction in perception and cognition.

Designing and Implementation of Stable Sinusoidal Rough-Neural Identifier

A rough neuron is defined as a pair of conventional neurons that are called the upper and lower bound neurons. In this paper, the sinusoidal rough-neural networks (SR-NNs) are used to identify the discrete dynamic nonlinear systems (DDNSs) with or without noise in series-parallel configuration. In the identification of periodic nonlinear systems, sinusoidal activation functions provide more efficient neural networks than the sigmoidal activation functions. Based on the Lyapunov stability theory, an online learning algorithm is developed to train the SR-NNs. The asymptotically convergence of the identification error to zero and the boundedness of parameters as well as predictions are proved. SR-NNs are used to identify some DDNSs and the cement rotary kiln (CRK). CRK is a complex nonlinear system in the cement factory, which produces the cement clinker. The experiments show that the SR-NNs in the identification of nonlinear systems have better performances than multilayer perceptrons (MLPs), sinusoidal neural networks, and rough MLPs, particularly in the presence of noise.

An Alternating Identification Algorithm for a Class of Nonlinear Dynamical Systems

While modeling nonlinear systems by combining a linear model with a nonlinear compensation term, namely, virtual unmodeled dynamics (VUD), the parameter estimation of the linear model and the learning-based VUD estimate influences and interacts with each other simultaneously. This paper aims to develop an alternating identification scheme for resolving such a challenging problem, where a projection algorithm is employed to identify the linear model and a feedforward neural network is used to model the VUD of a class of nonlinear dynamical systems. An open-loop estimation algorithm on the VUD is first presented under the known linear model, followed by an alternating identification algorithm for completely unknown nonlinear systems. Algorithm description is given and some simulation studies on multiple input and multiple output nonlinear systems are carried out to illustrate the effectiveness of our proposed modeling techniques.

Identification and Control for Singularly Perturbed Systems Using Multitime-Scale Neural Networks

Many well-established singular perturbation theories for singularly perturbed systems require the full knowledge of system model parameters. In order to obtain an accurate and faithful model, a new identification scheme for singularly perturbed nonlinear system using multitime-scale recurrent high-order neural networks (NNs) is proposed in this paper. Inspired by the optimal bounded ellipsoid algorithm, which is originally designed for discrete-time systems, a novel weight updating law is developed for continuous-time NNs identification process. Compared with other widely used gradient-descent updating algorithms, this new method can achieve faster convergence, due to its adaptively adjusted learning rate. Based on the identification results, a control scheme using singular perturbation theories is developed. By using singular perturbation methods, the system order is reduced, and the controller structure is simplified. The closed-loop stability is analyzed and the convergence of system states is guaranteed. The effectiveness of the identification and the control scheme is demonstrated by simulation results.

Nonlinear Model Predictive Control Based on a Self-Organizing Recurrent Neural Network

A nonlinear model predictive control (NMPC) scheme is developed in this paper based on a self-organizing recurrent radial basis function (SR-RBF) neural network, whose structure and parameters are adjusted concurrently in the training process. The proposed SR-RBF neural network is represented in a general nonlinear form for predicting the future dynamic behaviors of nonlinear systems. To improve the modeling accuracy, a spiking-based growing and pruning algorithm and an adaptive learning algorithm are developed to tune the structure and parameters of the SR-RBF neural network, respectively. Meanwhile, for the control problem, an improved gradient method is utilized for the solution of the optimization problem in NMPC. The stability of the resulting control system is proved based on the Lyapunov stability theory. Finally, the proposed SR-RBF neural network-based NMPC (SR-RBF-NMPC) is used to control the dissolved oxygen (DO) concentration in a wastewater treatment process (WWTP). Comparisons with other existing methods demonstrate that the SR-RBF-NMPC can achieve a considerably better model fitting for WWTP and a better control performance for DO concentration.