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This work presents the development of a multilevel electromagnetic actuation system that controls the shape of a flexible rotatory robotic structure. An array of electromagnets is used as the set of actuators that regulate the position of permanent magnets within the flexible device. The primary outcome of this study is the design and experimental validation of the multilevel rotating device. In addition, the theoretical description of the system motion under electromagnetic actuation is formulated using Euler-Lagrange and electromagnetic theories. Given the developed model, a theoretical study leads to designing an adaptive control that considers motion restrictions in the flexible device. The controller aims to modify the current applied to the electromagnets, which changes the interaction forces between the electromagnet and the permanent magnets in the robotic flexible structure. A set of numerical simulations confirms the proposed controller's effectiveness compared to the traditional state feedback approach that does not consider the state restrictions, which is implemented in devices that also operate under an electromagnetic approach. Furthermore, an experimental version of the flexible device allows for testing of the developed controller. The experimental results show the suitability of the proposed control to generate non-oscillatory controlled motion during the regulation of the flexible mechanic device shape., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 International Society of Automation. Published by Elsevier Ltd. All rights reserved.)

In this research project, a closed-chain robotic active ankle orthosis with six degrees of freedom is designed, constructed, numerically valued, instrumented, and experimentally validated. The mechanical arrangement to implement the orthosis corresponds to a six-legged Stewart platform. An adaptive gain control strategy with state constraints based on a state-dependent gains control (that behaves as a diverging function as the states approach the state restrictions) operates the device's motion. The convergence to an invariant positive set centered at the origin of the tracking error space is validated using the stability analysis based on the second method of Lyapunov, with the implementation of a state barrier Lyapunov-like function. The ultimate boundedness of the tracking error is proven with an endorsed gains adjustment method leading to a reachable minimum size of the ultimate bound. Hence, the impact of the state constraints and the formal reason for applying the controller on the suggested orthosis are all established. The orthosis is also controlled using a conventional state feedback strategy to assess the tracking error for an external disturbance and contrast its performance with the proposed control approach. The technology is tested on a few carefully chosen volunteers, successfully limiting the range of motion within a pre-defined region based on the scope of movement reported by patients with ankle illnesses discovered in the literature. Based on a unique mechatronic device, the created system offers a fresh approach to treating this class of impairments., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024. Published by Elsevier Ltd.)

This study presents the design of an adaptive event-driven controller for solving the trajectory tracking problem of a composite robotic device made up of a three-dimensional Cartesian and a parallel Delta robot. The proposed composite device has a mathematical model satisfying a standard Lagrangian structure affected by modeling uncertainties and external perturbations. The adaptive gain of the controller is considered to enforce the convergence of the tracking error while the state bounds are satisfied. The barrier Lyapunov function addresses the preconceived state constraints for both robotic devices by designing a time-varying gain that guarantees the ultimate boundedness of the tracking error under the effect of external perturbations. The event-driven approach considers that the Cartesian robot is moving into a predefined invariant zone near to the origin. In contrast, the delta robot can complete the tracking problem once the end-effector is inside the given zone. The suggested controller was evaluated using a virtual representation of the composite robotic device showing better tracking performance (while the restrictions are satisfied) than the performances obtained with the traditional linear state feedback controllers. Analyzing the mean square error and its integral led to confirming the benefits of using the adaptive barrier control., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 ISA. Published by Elsevier Ltd. All rights reserved.)

Motion restrictions in robotic devices may introduce complex requirements for any closed-loop control design, mainly when the robot joints must track reference trajectories that force the end-effector to perform planned motions. This study summarizes the comprehensive technical design of an adaptive state feedback controller for multi-link robotic manipulators that consider the effect of position and velocity restrictions on the tracking trajectory control approach. The proposed design is less conservative than other methods because of the explicit inclusion of state restrictions in the control gain dynamics. A logarithm barrier Lyapunov function class supports the design of the adaptive gain for the manipulator. Sufficient conditions based on a Riccati equation simplify the implementation of the adaptive controller with gains depending on the distance between the current state and the restriction sets. Numerical simulations show the advantages of the proposed controller with adaptive gains concerning a similar adaptive controller that does not consider the restrictions and a proportional-integral-derivative form. An implementation for the motion control of a robotic arm is presented to demonstrate the development by implementing the proposed gain, which confirms the suggested improvements enforced by the proposed controller. The performed comparison shows the advantages of the suggested adaptive gain control form, inducing better tracking of reference trajectories and smaller control energy applications., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 ISA. Published by Elsevier Ltd. All rights reserved.)

Electromagnetic actuation results suitable for wireless driven motion, where the estimation of the force between magnetic elements is usually required. This force can lead to states where the magnetic-mechanical system remains fixed, requiring constraints to avoid the transgression of these states, and Barrier Lyapunov Functions (BLF) are useful for this purpose. This work presents an adaptive controller with BLF in a magnetic pendulum with state restrictions. It employs fixed electromagnets to induce motion on a pendulum with a permanent magnet as its bob. The force between the magnetic elements is obtained through approximation functions. A new implementation strategy for the control gains introduces the effect of state restrictions on the control action based on a control BLF. Results are analyzed in both simulations and experimental stages, which prove the advantages of employing BLF controllers in mechanical systems that require the avoidance of specific boundaries., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 ISA. Published by Elsevier Ltd. All rights reserved.)

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., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 ISA. Published by Elsevier Ltd. All rights reserved.)

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., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2021 ISA. Published by Elsevier Ltd. All rights reserved.)

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., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2021 ISA. Published by Elsevier Ltd. All rights reserved.)

This study describes the design, instrumentation and control of an exoskeleton for lower limb children rehabilitation with nine degrees of freedom. Three degrees of freedom in each leg exert the movements of hip, knee and ankle in the sagittal plane, and three control the drive track system composed by a caterpillar-like robot. The control scheme presents a model free decentralized output feedback adaptive high-order sliding mode control to solve the trajectory tracking problem in each degree of freedom of the exoskeleton. A high order sliding mode differentiator estimates the unmeasured states and, by means of a dynamical state extension, it approximates the unknown dynamical model of the exoskeleton. A second-order adaptive sliding mode controller based on the super-twisting algorithm drives the exoskeleton articulations to track the proposed reference trajectories, inducing an ultimate boundedness for the tracking error. Numerical and experimental simulation results demonstrate the effect of the adaptive gain on the super-twisting control design. Such evaluations confirmed the superior tracking performance forced by the adaptive law for the controller with a smaller chattering amplitude and smaller mean tracking error., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020 ISA. Published by Elsevier Ltd. All rights reserved.)

The aim of this study was to design and evaluate a prototype of a snake-like endoscopic manipulator robot (SLEMR) and its corresponding automatic controller based on the first order sliding mode theory. The SLEMR was controlled with a set of actuators made of shape memory alloys (SMA). The SLEMR device was constructed with a sequential arrangement of links interconnected by a two degree-of-freedom joint. A parallel agonist-antagonist configuration of actuators was implemented to move each joint. The physical relation between temperature and elongation in SMA forced the execution of the movement in the joint. Elongation-temperature model of the SMA actuator served to get a feasible bound of velocity for each joint. Each pair of SMA actuators was controlled by a first order sliding mode controller. This control design solved the tracking trajectory problem for each joint in the SLEMR because of its robustness against uncertainties and external perturbations. The control action was projected into a feasible implementable set of pulse-width modulated signals which was used to regulate the temperature of the corresponding SMA actuator. The controller designed in this study was experimentally validated in a SLEMR made up by a tridimensional printing technique. The control strategy induced the successful trajectory tracking for all the joints in the SLEMR simultaneously. This characteristic of the control design also enforces the tracking of a reference position by the tip of the final link of the SLEMR. An image acquisition system was used to determine the position of the final actuator in the SLEMR. The effectiveness of the controller proposed in this study was confirmed by the evaluation of the tracking error of the final actuator which approached to a bounded region (less than 1.0 mm) near the origin in a finite-time (0.5 s)., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020 ISA. Published by Elsevier Ltd. All rights reserved.)

The main goal of this study is developing an adaptive controller which can solve the trajectory tracking for a class of quadcopter unmanned aerial system (UAS), namely a quadrotor. The control design introduces a new paradigm for adaptive controllers based on the implementation of a set of differential neural networks (DNNs) in the consequence section of a Takagi-Sugeno (T-S) fuzzy inference system. This dynamic fuzzy inference structure was used to approximate the UAS description. The particular form of interaction between neural networks and fuzzy inference systems proposed in the present work received the name of dynamic neural fuzzy system (DNFS). An adaptive controller based on this DNFS form was the main solution attained in this study. This DNFS controller was focused on the estimation and compensation of the uncertain section of the Quadrotor dynamics and then, forced the UAS to perform a hover flight while the tracking of desired angular positions succeeded, which results in tracking a desired trajectory in the X-Y plane. The control design methodology supported on the Lyapunov stability theory guaranteed ultimate boundedness of the estimation and tracking errors simultaneously. Several experimental tests in an outdoor environment by using a real Quadrotor platform was performed by using an RTK-GPS (Real Time Kinematic) system to determine the position of the vehicle in the X-Y plane. The experimental results confirmed the superior performance of the proposed algorithm based on the combination of DNNs and T-S techniques with respect to classical robust controllers., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020 ISA. Published by Elsevier Ltd. All rights reserved.)

The aim of this study is to design and implement a virtual reality bicycle system based on a functional-based mechatronic design approach. The development of virtual reality technologies with haptic systems demands a proper integration of the involved disciplines to provide immerse experiences for users. The proposed design approach provides a formal manner to gather the subsystems in the mechatronic device. The developed system is divided in a Virtual Reality System (VRS) and a Physical System (PS) for the design process. The former includes an interactive virtual environment in which an Avatar is animated using a simple kinematic bicycle model. The latter includes an adapted mountain bicycle with haptic feedback mechanisms to interact with the user and to produce the corresponding inputs for the bicycle model. Both systems are integrated by a control behavior system that works under two operation modes, where the user carries out virtual tours and gets feedbacks from a stereoscopic display system, audio cues, and haptic mechanisms. A multibody simulation validates the consistency and the integration of the physical system. In addition, a set of experimental results show the performance of instrumentation elements, control strategies, and feedback mechanisms, to provide the user with an immersive experience in the virtual environment. A brief survey was carried out to assess the opinion of users about the virtual bicycle tours, providing feedback for future improvements. The different designed modules and sub-systems allow modifying and enhancing the VRS without major modifications of the PS, or allow enhancing the physical platform without affecting the functionality of the virtual environment., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2019 ISA. Published by Elsevier Ltd. All rights reserved.)

This article summarizes the comprehensive design of an adaptive control that solves the trajectory tracking of a four-rotor unmanned aerial vehicle supplied by an own-designed grasping device. The controller design uses the regular proportional-derivative (PD) structure which is common to solve regulation, as well as tracking problems for robotic systems. The PD structure needs the estimation of the time-derivative to be exerted on-line. The super-twisting algorithm served to operate as a decentralized estimator of the derivatives for the tracking errors. The controller gains were adjusted by the differential laws aimed to track attainable reference trajectories. The adaptive strategy adjusts the controller gains enforcing the convergence of both the estimation and the tracking errors. A numerical example showed the observer/controller performance. A comparison with a classic non-adaptive PD controller confirms the effectiveness on the tracking task by the proposed design. In addition, a set of virtual numerical evaluations using the parameters of a real quadcopter system confirmed the performance benefits of the adaptive controller based on the PD structure aided with the estimation of the velocity obtained by the observer., (Copyright © 2019. Published by Elsevier Ltd.)

In this paper, an adaptive disturbance estimation-based control of a class of uncertain feedback linearizable systems with the presence of, both, external perturbations as well as non-modeled dynamics is considered. The aim of the control design was to solve the tracking trajectory problem for a class of output-based linearizable uncertain systems. An adaptive scheme is proposed for developing a state estimator of the uncertain dynamics. The estimation of both, the states and the uncertain dynamics is attained despite the limited knowledge of the plant and the information contained in the output signal. The uncertain section in the linearized system was approximated by a class of time-dependent combination of the system states. The observer implemented a parametric identifier to obtain the time varying parameters associated to the estimation of the uncertain section. This method ensured the adequate estimation process of the uncertainties/perturbations, measured in terms of the mean square error. Simultaneously, an adaptive gain associated to the observer adjusts its trajectories to provide the ultimate boundedness of the estimation error. Once the states of the uncertain system are obtained, a feedback controller rejects actively the perturbations that affect the system by a compensation scheme. Two numerical examples were developed to show the observer-based control performance., (Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.)

This study addresses the problem of designing an output-based controller to stabilize multi-input multi-output (MIMO) systems in the presence of parametric disturbances as well as uncertainties in the state model and output noise measurements. The controller design includes a linear state transformation which separates uncertainties matched to the control input and the unmatched ones. A differential neural network (DNN) observer produces a nonlinear approximation of the matched perturbation and the unknown states simultaneously in the transformed coordinates. This study proposes the use of the Attractive Ellipsoid Method (AEM) to optimize the gains of the controller and the gain observer in the DNN structure. As a consequence, the obtained control input minimizes the convergence zone for the estimation error. Moreover, the control design uses the estimated disturbance provided by the DNN to obtain a better performance in the stabilization task in comparison with a quasi-minimal output feedback controller based on a Luenberger observer and a sliding mode controller. Numerical results pointed out the advantages obtained by the nonlinear control based on the DNN observer. The first example deals with the stabilization of an academic linear MIMO perturbed system and the second example stabilizes the trajectories of a DC-motor into a predefined operation point., (Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.)

Most of the research in sliding mode theory has been carried out to in continuous time to solve the estimation and control problems. However, in discrete time, the results in high order sliding modes have been less developed. In this paper, a discrete time super-twisting-like algorithm (DSTA) was proposed to solve the problems of control and state estimation. The stability proof was developed in terms of the discrete time Lyapunov approach and the linear matrix inequalities theory. The system trajectories were ultimately bounded inside a small region dependent on the sampling period. Simulation results tested the DSTA. The DSTA was applied as a controller for a Furuta pendulum and for a DC motor supplied by a DSTA signal differentiator., (Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.)

This study addressed the problem of robust control of a biped robot based on disturbance estimation. Active disturbance rejection control was the paradigm used for controlling the biped robot by direct active estimation. A robust controller was developed to implement disturbance cancelation based on a linear extended state observer of high gain class. A robust high-gain scheme was proposed for developing a state estimator of the biped robot despite poor knowledge of the plant and the presence of uncertainties. The estimated states provided by the state estimator were used to implement a feedback controller that was effective in actively rejecting the perturbations as well as forcing the trajectory tracking error to within a small vicinity of the origin. The theoretical convergence of the tracking error was proven using the Lyapunov theory. The controller was implemented by numerical simulations that showed the convergence of the tracking error. A comparison with a high-order sliding-mode-observer-based controller confirmed the superior performance of the controller using the robust observer introduced in this study. Finally, the proposed controller was implemented on an actual biped robot using an embedded hardware-in-the-loop strategy., (Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.)

This paper deals with a switching robust tracking feedback design for a corona-effect ozone generator. The generator is considered as a switched systems in the presence of bounded model uncertainties as well as external perturbations. Three nonlinear dynamic models under arbitrary switching mechanisms are considered assuming that a sample-switching times are known. The stabilization issue is achieved in the sense of a practical stability. We apply the newly elaborated (extended) version of the conventional attractive ellipsoid method (AEM) for this purpose. The same analysis was efficient to obtain the minimal size of region where the tracking error between the trajectories of the ozone generator and reference states converges. The numerically implementable sufficient conditions for the practical stability of systems are derived based on bilinear matrix inequalities (BMIs)., (Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.)

Designing a proportional derivative (PD) controller has as main problem, to obtain the derivative of the output error signal when it is contaminated with high frequency noises. To overcome this disadvantage, the supertwisting algorithm (STA) is applied in closed-loop with a PD structure for multi-input multi-output (MIMO) second order nonlinear systems. The stability conditions were analyzed in terms of a strict non-smooth Lyapunov function and the solution of Riccati equations. A set of numerical test was designed to show the advantages of implementing PD controllers that used STA as a robust exact differentiator. The first numerical example showed the stabilization of an inverted pendulum. The second example was designed to solve the tracking problem of a two-link robot manipulator., (Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.)

2,4-Dichlorophenoxyacetic acid (2,4-D) is usually used as a refractory model compound that requires a prolonged reaction time for mineralization. In this study, we found that nickel oxide (NiO) significantly improved 2,4-D degradation and mineralization in reaction with ozone. Other metal oxides, such as titania, silica and alumina, were also tested in this reaction, so that, the mineralization degree was almost the same for all of them (ca. 25%), whereas NiO showed more than 60% in 1h. These outstanding results led us to study in more depth the role of NiO as catalyst in the degradation of 2,4-D. For instance, the optimum NiO loading amount was 0.3 g L(-1). The catalytic ozonation showed a high stability after three reaction cycles. With the aim of identifying the surface species responsible for the high activity of NiO, besides knowing the byproducts during the degradation of 2,4-D, XPS and HPLC were mainly used as analytical tools. According to the results, the mineralization of 2,4-D was directly influenced by the adsorbed chlorate organic compounds and oxalate group onto NiO. Therefore, NiO plays a true role as a catalyst forming surface compounds which are subsequently decomposed causing an increase in the mineralization efficiency. In addition, it was possible to identify several degradation byproducts (2,4-diclorophenol, glycolic, fumaric, maleic and oxalic acids) that were included in a rational reaction pathway. It was proposed that 2,4-D elimination in presence of NiO as catalyst is a combination of processes such as: conventional ozonation, indirect mechanism (OH) and surface complex formation., (Copyright © 2013 Elsevier B.V. All rights reserved.)

In the present work the degradation of the lignin and its derivatives in the residual water of a paper industry by simple ozonation was investigated. The remediation of lignin was realized using the combination of the pre-treatment with chemical precipitation, using concentrated sulfuric acid (97.1%) at the pH 1 and 3, and of the simple ozonation of the filtered residual water at the pH 1, 3, 8 and 12. Since the high residues content (the initial chemical oxygen demand (COD) is 70,000 mg/L) in the experiments the diluted samples (1:10) were used. The previous precipitation has showed a significant effect on the reduction of the COD (77%) and color (96.1%). The sludge precipitated contents sulfolignin, which in the reaction with sulfuric acid was formed. In ozonation of the filtered residual water during 25 min at the pH 1, 3, 8 and 12 the follows by-products were formed: fumaric, maleic, malonic and formic acids. The biodegradability of the treated water in ozonation increases up 0.067-0.29. The effect of the precipitation and the ozonation conditions on the decolorization kinetics was evaluated.

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.