Differential Neural Network Identifier for Dynamical Systems With Time-Varying State Constraints.

This study presents a state nonparametric identifier based on neural networks with continuous dynamics, also known as differential neural networks (DNNs). The laws for adjusting their parameters are developed using a control barrier Lyapunov functions (BLFs). The motivation for using the BLF comes from the preliminary information of the system states, which remain in a predefined time-depending set characterized by state or purely time-dependent functions. In this study, time-dependent state constraints are supposed to be known in advance continuous-time functions. The obtained learning laws require solving differential continuous-time Riccati equations and nonlinear differential equations for the learning laws that depend on the identification error and the state restrictions. The developed identifier was evaluated concerning the identifier that does not consider the state restrictions. This comparison included the numerical evaluation of the identifier for a robotic arm intended to reproduce a nonstandard flight simulator. This evaluation confirmed that the identification results were improved using the proposed learning laws and considering that the state limits were not transgressed. The quality indicators based on the mean square error were more minor by 4.2 times.

Averaged sub-gradient integral sliding mode control design for cueing end-effector acceleration of a two-link robotic arm.

Acceleration tracking is a significant problem in aeronautics, automotive, and biomedical technical areas because its solution may yield effective simulation of motion cues. In the case of aeronautics, the proper solution for the tracking problem improves the in-flight simulations for the training of plane pilots. These simulators can be set up using robotic devices that develop controlled motions with the end-effector following the required three-dimensional reference accelerations robustly. Hence, the primary goal of this study is the effective application of the integral sliding mode controller to solve the acceleration tracking problem for the end-effector of a two-link robotic arm. The control design problem is formulated as an optimization of a convex (non-strict) performance functional depending on the difference between the acceleration of the robotic arm and the desired acceleration using the averaged sub-gradient (ASG) descendant method. A novel sliding surface considers the sensitiveness threshold for acceleration dynamics, inspired by the limit of detection in the pilot vestibular apparatus. The proposed controller was analyzed in terms of the finite-time convergence of the sliding surface and the practical stability analysis for the tracking error dynamics. Our main contribution is the design of the online averaged sub-gradient optimization controller based on integral SMCs. The controller solves the end-effector acceleration tracking for a two-link robotic arm, which implements a simplified version of a flight simulator that is considered to be operated under uncertain scenarios and assumes the presence of perturbations and modeling errors. The controller considers the case of incomplete knowledge of the robotic arm model, which adds an extra degree of robustness to the control design. The numerical evaluations demonstrate the attributes of the ASG formulation compared to traditional state feedback control, using the performance functional, the norm of the acceleration tracking error, and the control input variation.

Adaptive modeling of nonnegative environmental systems based on projectional Differential Neural Networks observer.

A new design of a non-parametric adaptive approximate model based on Differential Neural Networks (DNNs) applied for a class of non-negative environmental systems with an uncertain mathematical model is the primary outcome of this study. The approximate model uses an extended state formulation that gathers the dynamics of the DNN and a state projector (pDNN). Implementing a non-differentiable projection operator ensures the positiveness of the identifier states. The extended form allows producing continuous dynamics for the projected model. The design of the learning laws for the weight adjustment of the continuous projected DNN considered the application of a controlled Lyapunov-like function. The stability analysis based on the proposed Lyapunov-like function leads to the characterization of the ultimate boundedness property for the identification error. Applying the Attractive Ellipsoid Method (AEM) yields to analyze the convergence quality of the designed approximate model. The solution to the specific optimization problem using the AEM with matrix inequalities constraints allows us to find the parameters of the considered DNN that minimizes the ultimate bound. The evaluation of two numerical examples confirmed the ability of the proposed pDNN to approximate the positive model in the presence of bounded noises and perturbations in the measured data. The first example corresponds to a catalytic ozonation system that can be used to decompose toxic and recalcitrant contaminants. The second one describes the bacteria growth in aerobic batch regime biodegrading simple organic matter mixture.

Adaptive sliding-mode trajectory tracking control for state constraint master-slave manipulator systems.

This study aims to propose an adaptive state-dependent gain finite-time convergent controller (using the fundamentals of the sliding mode theory) that solves the trajectory tracking for a class of state constraint master-slave robotic system (M-SRS) formed by two manipulators with the same number of articulations. The control design considers the effect of state constraints by implementing a state dependent adaptive gain. A Lyapunov-stability analysis leads to design the gain variation laws yielding proving the finite-time convergence of the sliding surface as well as the asymptotic convergence of the tracking error. The state constraints of the slave system motivate the characterization of the convergence-time as a function of the bounded uncertainties affecting the M-SRS dynamics. The forward-complete setting of the M-SRS justified the application of a robust and exact differentiator which estimated the articulation velocities for the slave robot. The estimated velocities are used as part of the realization of the output feedback controller. Numerical simulations demonstrate that the proposed control scheme provides a smaller quadratic norm of the tracking error compared with the obtained with other controllers (proportional-derivative and conventional sliding modes). The proposed control approach satisfies the state constraints while the sliding manifold converges to the origin in finite-time as justified by the theoretical stability analysis.

Non-singular terminal sliding-mode control for a manipulator robot using a barrier Lyapunov function.

This study introduces a design of robust finite-time controllers that aims to solve the trajectory tracking of robot manipulators with full-state constraints. The control design is based on the construction of a distributed state constraint non-singular terminal sliding mode (CNTSM). The CNTSM design includes the gain self-adapting tuning method, which can ensure finite-time convergence to the sliding surface aside from the states to its corresponding reference trajectories. The implementation of the time-varying gain ensures the fulfillment of the accurate tracking for the references while the position and velocity constraints are satisfied permanently. A barrier Lyapunov function is proposed to develop the finite-time stability analysis of the designed controllers. The CNTSM realization uses the tracking error as well as its estimated derivative, which is calculated using a variant of adaptive super-twisting algorithm operating as robust differentiator. The proposed CNTSM is numerically evaluated on a two-link RM with uncertain inertia and Coriolis matrices. Simulation and experimental results evidence the efficiency of the CNTSM controller demonstrating a better tracking performance while the full-state constraints are satisfied in counterpart with the classical non-singular terminal sliding mode which is not able to keep such restrictions.

Anodizing of Hydrogenated Titanium and Zirconium Films.

Magnetron-sputtered thin films of titanium and zirconium, with a thickness of 150 nm, were hydrogenated at atmospheric pressure and a temperature of 703 K, then anodized in boric, oxalic, and tartaric acid aqueous solutions, in potentiostatic, galvanostatic, potentiodynamic, and combined modes. A study of the thickness distribution of the elements in fully anodized hydrogenated zirconium samples, using Auger electron spectroscopy, indicates the formation of zirconia. The voltage- and current-time responses of hydrogenated titanium anodizing were investigated. In this work, fundamental possibility and some process features of anodizing hydrogenated metals were demonstrated. In the case of potentiodynamic anodizing at 0.6 M tartaric acid, the increase in titanium hydrogenation time, from 30 to 90 min, leads to a decrease in the charge of the oxidizing hydrogenated metal at an anodic voltage sweep rate of 0.2 V·s-1. An anodic voltage sweep rate in the range of 0.05-0.5 V·s-1, with a hydrogenation time of 60 min, increases the anodizing efficiency (charge reduction for the complete oxidation of the hydrogenated metal). The detected radical differences in the time responses and decreased efficiency of the anodic process during the anodizing of the hydrogenated thin films, compared to pure metals, are explained by the presence of hydrogen in the composition of the samples and the increased contribution of side processes, due to the possible features of the formed oxide morphologies.

Peculiar Porous Aluminum Oxide Films Produced via Electrochemical Anodizing in Malonic Acid Solution with Arsenazo-I Additive.

The influence of arsenazo-I additive on electrochemical anodizing of pure aluminum foil in malonic acid was studied. Aluminum dissolution increased with increasing arsenazo-I concentration. The addition of arsenazo-I also led to an increase in the volume expansion factor up to 2.3 due to the incorporation of organic compounds and an increased number of hydroxyl groups in the porous aluminum oxide film. At a current density of 15 mA·cm-2 and an arsenazo-I concentration 3.5 g·L-1, the carbon content in the anodic alumina of 49 at. % was achieved. An increase in the current density and concentration of arsenazo-I caused the formation of an arsenic-containing compound with the formula Na1,5Al2(OH)4,5(AsO4)3·7H2O in the porous aluminum oxide film phase. These film modifications cause a higher number of defects and, thus, increase the ionic conductivity, leading to a reduced electric field in galvanostatic anodizing tests. A self-adjusting growth mechanism, which leads to a higher degree of self-ordering in the arsenazo-free electrolyte, is not operative under the same conditions when arsenazo-I is added. Instead, a dielectric breakdown mechanism was observed, which caused the disordered porous aluminum oxide film structure.

Optical Properties of Porous Alumina Assisted Niobia Nanostructured Films-Designing 2-D Photonic Crystals Based on Hexagonally Arranged Nanocolumns.

Three types of niobia nanostructured films (so-called native, planarized, and column-like) were formed on glass substrates by porous alumina assisted anodizing in a 0.2 M aqueous solution of oxalic acid in a potentiostatic mode at a 53 V and then reanodizing in an electrolyte containing 0.5 M boric acid and 0.05 M sodium tetraborate in a potentiodynamic mode by raising the voltage to 230 V, and chemical post-processing. Anodic behaviors, morphology, and optical properties of the films have been investigated. The interference pattern of native film served as the basis for calculating the effective refractive index which varies within 1.75-1.54 in the wavelength range 190-1100 nm. Refractive index spectral characteristics made it possible to distinguish a number of absorbance bands of the native film. Based on the analysis of literature data, the identified oxide absorbance bands were assigned. The effective refractive index of native film was also calculated using the effective-medium models, and was in the range of 1.63-1.68. The reflectance spectra of all films show peaks in short- and long-wave regions. The presence of these peaks is due to the periodically varying refractive index in the layers of films in two dimensions. FDTD simulation was carried out and the morphology of a potential 2-D photonic crystal with 92% (wavelength 462 nm) reflectance, based on the third type of films, was proposed.

Porous Alumina Films Fabricated by Reduced Temperature Sulfuric Acid Anodizing: Morphology, Composition and Volumetric Growth.

The volumetric growth, composition, and morphology of porous alumina films fabricated by reduced temperature 280 K galvanostatic anodizing of aluminum foil in 0.4, 1.0, and 2.0 M aqueous sulfuric acid with 0.5-10 mA·cm-2 current densities were investigated. It appeared that an increase in the solution concentration from 0.4 to 2 M has no significant effect on the anodizing rate, but leads to an increase in the porous alumina film growth. The volumetric growth coefficient increases from 1.26 to 1.67 with increasing current density from 0.5 to 10 mA·cm-2 and decreases with increasing solution concentration from 0.4 to 2.0 M. In addition, in the anodized samples, metallic aluminum phases are identified, and a tendency towards a decrease in the aluminum content with an increase in solution concentration is observed. Anodizing at 0.5 mA·cm-2 in 2.0 M sulfuric acid leads to formation of a non-typical nanostructured porous alumina film, consisting of ordered hemispheres containing radially diverging pores.

Robust min-max optimal control design for systems with uncertain models: A neural dynamic programming approach.

The design of an artificial neural network (ANN) based sub-optimal controller to solve the finite-horizon optimization problem for a class of systems with uncertainties is the main outcome of this study. The optimization problem considers a convex performance index in the Bolza form. The dynamic uncertain restriction is considered as a linear system affected by modeling uncertainties, as well as by external bounded perturbations. The proposed controller implements a min-max approach based on the dynamic neural programming approximate solution. An ANN approximates the Value function to get the estimate of the Hamilton-Jacobi-Bellman (HJB) equation solution. The explicit adaptive law for the weights in the ANN is obtained from the approximation of the HJB solution. The stability analysis based on the Lyapunov theory yields to confirm that the approximate Value function serves as a Lyapunov function candidate and to conclude the practical stability of the equilibrium point. A simulation example illustrates the characteristics of the sub-optimal controller. The comparison of the performance indexes obtained with the application of different controllers evaluates the effect of perturbations and the sub-optimal solution.

Extraproximal method application for a Stackelberg-Nash equilibrium calculation in static hierarchical games.

A regularized version of the extraproximal method is suggested for finding the Stackelberg-Nash equilibrium in a multiparticipant static game. There exist two levels of hierarchy in decision making: The first one consists of a leader decision, and the second one is formed by the decisions of the (N - 1) followers. The followers react to the leader's announced strategy by playing according to the Nash equilibrium concept, selecting among themselves that whose equilibrium is most favorable or unfavorable for the leader. Here, applying the extraproximal technique, the Stackelberg-Nash equilibrium is attained. The convergence of the suggested procedure is analyzed. Simulation results illustrate the feasibility of this method.

Application of the differential neural network observer to the kinetic parameters identification of the anthracene degradation in contaminated model soil.

In this work a new technique dealing with differential neural network observer (DNNO), which is related with differential neural networks (DNN) approach, is applied to estimate the anthracene dynamics decomposition and to identify the kinetic parameters in a contaminated model soil treatment by simple ozonation. To obtain the experimental data set, the model soil (sand) is combined with an initial anthracene concentration of 3.24mg/g and treated by ozone (with the ozone initial concentration 16mg/L) during 90min in a reactor by the "fluid bed" principle. The anthracene degradation degree was controlled by UV-vis spectrophotometry and HPLC techniques. Based on the HPLC data, the obtained results confirm that anthracene may be decomposed completely in the solid phase by simple ozonation during 20min and by-products of ozonation are started to be destroyed after 30min of treatment. In the ozonation process the ozone concentration in the gas phase at the reactor outlet is registered by an ozone detector. The variation of this parameter is used to obtain the summary characteristic curve of the anthracene ozonation (ozonogram). Then, using the experimental decomposition dynamics of anthracene and the ozonogram, the proposed DNNO is trained to reconstruct the anthracene decomposition and to estimate the anthracene ozonation constant using the DNN technique and a modified Least Square method.