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The aim of this study is to provide a class of state observers, based on differential neural networks, to approximate a class of advanced oxidation systems, based on the application of ozone high oxidant power and catalyst (the named catalytic ozonation). The study considers the design of a state observer for uncertain systems with the restrictions of the ozonation system, including the positivity of the states, as well as the control action. The observer includes a projection operator which is motivated by the state constraints. The learning laws of the proposed differential neural networks are obtained using a class of controlled state restricted Lyapunov functions. The detailed stability analysis proves the input to state stability with respect to the modeling error, as well as the bounded uncertainties of the ozonation system. The experimental confirmation of the state estimation is also presented. The experimental case considers the ozonation of a toxic organic contaminant (therephtalic acid) which is a regular pollutant of the plastic industry wastewater.

International audience; This study is devoted to the design of an adaptive discontinuous control based on differential neural networks (DNNs) for a class of uncertain homogeneous systems. The control is based on the universal approximation properties of artificial neural networks (ANNs) applied on a certain class of homogeneous nonlinear functions. The adaptation laws for the DNNs parameters are obtained with the application of the Lyapunov stability theory and the homogeneity properties of the approximated nonlinear system. The stability analysis of the closed loop system with the proposed controller is presented. The estimation error in the approximation of the uncertain homogeneous functions is considered in the stability analysis. The performance of the controller is illustrated by means of a numerical simulation of a homogeneous model.

In this paper, a non parametric identifier for homogeneous nonlinear systems affine in the input is proposed. The identification algorithm is based on the neural networks using sigmoidal activation functions. The learning algorithm is derived by means of Lyapunov function method and homogeneity theory. A numerical example demonstrates the performance of the proposed identifier.

The aim of this study was to design a discontinuous controller with adaptive gains, based on the sliding-mode theory. The adaptive controller solved the trajectory tracking problem for a class of systems with state constraints, specifically for a class of multi-articulated robot manipulator with a constraint work-space. The controller implemented a state dependent adaptive gain that grows in value when the trajectories approach the boundary of the set that characterized the states constraints. The design of the adaptive gain guaranteed the existence of a finite-time stable equilibrium point for a special sliding surface depending on the tracking trajectory error. The specific law used to adjust the gain was obtained by a Lyapunov-based stability analysis. Some numerical simulations proved that the sliding-mode controller showed a superior performance, measured by the mean square value of the tracking result, compared to the non-adaptive gain first order sliding-mode controller.

This paper introduces and evaluates a robust control algorithm based on sliding mode control theory, in which together with the use of the LMI methods the stabilization of an underactuated nonlinear system can be guaranteed. The obtained results are applied to a mechanical system which consists of two single gimbal control moment gyroscopes for triaxial attitude control of a gravity-gradient stabilized tethered satellite system. These objectives are investigated first using analytical methods and then verified by numerical simulations.

In this paper we present the problem of parameter estimation in continuous-time stochastic systems under coloured or correlated noises. The Least Squares Method (LSM) is a classical approach, but the estimation usually presents bias in stochastic systems. Here we combine this technique with a Kalman filter, that will minimize the noise effect, and will improve the estimation algorithm performance. The Instrumental Variable method will be implemented too, in order to analyse which method is more suitable for systems with coloured noises. The effectiveness of the proposed methods will be illustrated with a numerical example.

The authors suggest an algorithm for extremum seeking based on a random process optimization approach employing a gradient descent method with the synchronous detection technique. The problem consists on finding the minimum of a strongly convex function which is unknown but may be measured in any testing point subject to a noise perturbation. The suggested extremum seeking procedure is based on the estimated gradient obtained by the modified version of the Synchronous Detection Method. We have added a first order low-pass filter to the gradient estimator to attenuate the noise in the estimations. We prove the mean-squared convergence in probability of the suggested algorithm. To validate the contributions of the paper we present a numerical example.

This paper presents the results of the survey on the stabilization of the Triple-Link Inverted Pendulum as underactuated system. The mathematical model of the coupled electromechanical system is presented in the standard robotics format, where the geometry of its links is taken into account, further, the DC motor is considered. For the pursued aim, Attractive Ellipsoid Method is used in order to design robust stabilizing controller for electromechanical systems in a general form. In order to compare the performance for the suggested methodology, different robust Sliding Mode Control strategies are designed. The obtained algorithms are tested in numerical simulation.

This study solves a finite horizon optimal problem for linear systems with parametric uncertainties and bounded perturbations. The control solution considers the uncertain part of the system in the sub-optimal control solution by proposing a min-max problem solved by a dynamic neural programming approximate solution. The structure of the neural network was proposed to satisfy the charcateristics of the value function including possitiveness and continuity. The impact of the presence of bounded perturbation over the Hamiltonian maximization was analyzed in detail. The explicit learning law used to adjust the weights was obtained directly from the Hamilton-Jacobi-Bellman (HJB) approximate solution. The weights adjustment to the proposed algorithm is based on an on-line state dependent Riccati-like equation. A numerical simulation is presented to illustrate the results of the sub-optimal algorithm including its comparison against the classical linear regulator solved considering the non-perturbed system.

A classical bargaining situation involves two individuals who have the opportunity to collaborate for mutual benefit. In this paper we present a novel approach for computing the Nash bargaining equilibrium for controllable Markov chains games. We follow the solution introduced by Nash considering the disagreement point as the Nash equilibrium of the problem. For solving the bargaining process we consider the game formulation in terms of nonlinear programming equations implementing the regularized Lagrange method. For computing the equilibrium point we employ the extraproximal optimization approach. We present the convergence and rate of convergence of the method. Finally a numerical example for a two-person bargaining situation illustrates the effectiveness of the method.

The paper deals with the problem of state estimation of ”two-component” systems where the second vector-component may have unknown nonlinear Lipschitz-type dynamics and is subjected to stochastic perturbations of additive and multiplicative types. Both vector components governed by a system of stochastic differential equations with state dependent diffusion. The system is supposed to be quadratically stable in the mean-square sense. We consider a sliding mode observer with the gain parameter linearly depending on the norm of the output estimation error which is available during the process. The theoretical results are supported by numerical simulations.