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

Neural-adaptive controller for an isolated power converter

The paper presents the design of a neural-adaptive controller for an isolated power converter. Accurate estimation of the unknown parameters is taken into account in both theoretical and practical domains when considering intelligent control techniques. Despite the construction of the mathematical model for the converter, some unstructured parameters have not been included in the model. The proposed resilient controller is designed to adapt to both structured and unstructured factors and provide the appropriate output. The neurons or activation functions of the controller compensate for the unstructured properties of the converter. With an increase in the number of neurons, the converter's output gains more resilience and flexibility, even in the presence of changes in the reference values. The adaptive gain is augmented proportionally to enhance the system's resilience in achieving the target output voltage. The controller's stability study is conducted using the Lyapunov Function. The derivative of the Lyapunov function's convergence yields the adaptation law, which modifies the weights associated with the converter's neurons and aligns with the reference model to achieve the desired outcome. The results are validated using the OPAL-RT real-time simulator platform.

Optimal Bounded Ellipsoid Identification With Deterministic and Bounded Learning Gains: Design and Application to Euler-Lagrange Systems

This article proposes an effective optimal bounded ellipsoid (OBE) identification algorithm for neural networks to reconstruct the dynamics of the uncertain Euler-Lagrange systems. To address the problem of unbounded growth or vanishing of the learning gain matrix in classical OBE algorithms, we propose a modified OBE algorithm to ensure that the learning gain matrix has deterministic upper and lower bounds (i.e., the bounds are independent of the unpredictable excitation levels in different regressor channels and, therefore, are capable of being predetermined a priori). Such properties are generally unavailable in the existing OBE algorithms. The upper bound prevents blow-up in cases of insufficient excitations, and the lower bound ensures good identification performance for time-varying parameters. Based on the proposed OBE identification algorithm, we developed a closed-loop controller for the Euler-Lagrange system and proved the practical asymptotic stability of the closed-loop system via the Lyapunov stability theory. Furthermore, we showed that inertial matrix inversion and noisy acceleration signals are not required in the controller. Comparative studies confirmed the validity of the proposed approach.

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.

Fuzzy Control and Filtering for Nonlinear Singularly Perturbed Markov Jump Systems

This article addresses the H_∞ control and filtering problems for Markov jump singularly perturbed systems approximated by Takagi-Sugeno fuzzy models. The underlying transition probabilities (TPs) are assumed to vary randomly in a finite set, which is characterized by a higher level TP matrix. The mode- and variation-dependent fuzzy static output-feedback controller (SOFC) and filter are designed, respectively, to fulfill the control and filtering purposes. To facilitate the fuzzy SOFC synthesis, the closed-loop system is transformed into a fuzzy piecewise-homogeneous Markov jump singularly perturbed descriptor system (MJSPDS) by descriptor representation. A rigorous proof of mean-square exponential admissibility for the resulting fuzzy MJSPDS is presented. The criterion ensuring the mean-square exponential stability of the fuzzy filtering error system is further formed based on similar procedures. By setting the specific forms of the related matrix variables, the solutions for the predesigned fuzzy SOFC and filter are furnished, respectively. Finally, feasibility and validities of the developed fuzzy control and filtering results are verified by two practical examples.

RNN for Perturbed Manipulability Optimization of Manipulators Based on a Distributed Scheme: A Game-Theoretic Perspective

In order to leverage the unique advantages of redundant manipulators, avoiding the singularity during motion planning and control should be considered as a fundamental issue to handle. In this article, a distributed scheme is proposed to improve the manipulability of redundant manipulators in a group. To this end, the manipulability index is incorporated into the cooperative control of multiple manipulators in a distributed network, which is used to guide manipulators to adjust to the optimal spatial position. Moreover, from the perspective of game theory, this article formulates the problem into a Nash equilibrium. Then, a neural network with anti-noise ability is constructed to seek and approximate the optimal strategy profile of the Nash equilibrium problem with time-varying parameters. Theoretical analyses show that the neural network model has the superior global convergence and noise immunity. Finally, simulation results demonstrate that the neural network is effective in real-time cooperative motion generation of multiple redundant manipulators under perturbations in distributed networks.

Identification and Control of Nonlinear Systems Using Neural Networks: A Singularity-Free Approach

In this paper, identification and control for a class of nonlinear systems with unknown constant or variable control gains are investigated. By reformulating the original system dynamic equation into a new form with a unit control gain and introducing a set of filtered variables, a novel neural network (NN) estimator is constructed and a new estimation error is used to update the augmented weights. Based on the identification results, two singularity-free NN indirect adaptive controllers are developed for nonlinear systems with unknown constant control gains or variable control gains, respectively. Because the singularity problem is eradicated, the proposed methods remove limitations on parameter estimates that are used to guarantee the positiveness of the estimated control gain. Consequently, a more accurate estimation result can be achieved and the system state can track the given reference signal more precisely. The effectiveness of the proposed identification and control algorithms are tested and the superiority of the proposed singularity-free approach is demonstrated by simulation results.

A Novel Neural Networks Ensemble Approach for Modeling Electrochemical Cells

Accurate modeling of electrochemical cells is nowadays mandatory for achieving effective upgrades in the fields of energetic efficiency and sustainable mobility. Indeed, these models are often used for performing accurate State-of-Charge (SoC) estimations in energy storage systems used in microgrids or powering pure electric and hybrid cars. To this aim, a novel neural networks ensemble approach for modeling electrochemical cells is proposed in this paper. Herein, the system identification has been faced by means of a gray box technique, in which different and specialized neural networks are used for identifying the unknown internal behaviors of the cell. In particular, the a priori knowledge on the system dynamic is used for defining the network architecture. Specifically, each nonlinear function appearing in the system equations is approximated by a distinct neural network. The proposed model has been validated upon three different data sets both in terms of model accuracy and effectiveness in the SoC estimation task. The achieved performances have been compared with those of other computational intelligence approaches proposed in the literature. The results prove the effectiveness of the gray box scheme, achieving very promising performances in both the system identification accuracy and the SoC estimation task.