Ivan Salgado

Nonlinear discrete time neural network observer

State estimation for uncertain systems affected by external noises has been recognized as an important problem in control theory for either discrete and continuous plants. This paper deals with the state observation problem when the discrete-time dynamic model of a plant is partially unknown and it is affected by some sort of uncertainties and external perturbations. Recurrent Neural Networks (RNN) have shown several advantages to treat many different control and state estimation problems. In this paper, a new discrete-time Luenberger-like observer using the structure of a RNN is proposed. The class of discrete-time nonlinear system just has the input-output pairs as available information. The neural observer is training off-line using a class of least mean square method for matrix parameters. Lyapunov theory is employed to obtain the upper bounds for the weights dynamics as well for the estimation error and the learning laws to ensure the convergence of the observer. Simulation results using the van der Pol oscillator as data generator are presented to demonstrate the effectiveness of the proposed neural observer.

Control of discrete time systems based on recurrent Super-Twisting-like algorithm.

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.

Super-twisting sliding mode differentiation for improving PD controllers performance of second order systems.

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.

Discrete time recurrent neural network observer

State estimation for uncertain systems affected by external noises is an important problem in control theory. This paper deals with the state observation problem when the dynamic model of a plant contains uncertainties or is completely unknown and it is oriented to discrete time nonlinear systems because most of the existent results have been developed for continous time systems. The recurrent neural network (RNN) have shown his advantages to deal with this class problem. The Lyapunov second method is applied to generate a new learning law, containing an adaptive adjustment rate, implying the stability condition for the free parameters of the neural-observer. A numerical example is given using the RNN in the estimation of a mathematical model of HIV infection with three states.

Robust synchronization of master-slave chaotic systems using approximate model: An experimental study

Robust synchronization of master slave chaotic systems are considered in this work. First an approximate model of the error system is obtained using the ultra-local model concept. Then a Continuous Singular Terminal Sliding-Mode (CSTSM) Controller is designed for the purpose of synchronization. The proposed approach is output feedback-based and uses fixed-time higher order sliding-mode (HOSM) differentiator for state estimation. Numerical simulation and experimental results are given to show the effectiveness of the proposed technique.

Quasi-minimal active disturbance rejection control of MIMO perturbed linear systems based on differential neural networks and the attractive ellipsoid method

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.

Robust observer-based controller design for state constrained uncertain systems: attractive ellipsoid method

ABSTRACT This study focuses in the output feedback stabilisation of constrained linear systems affected by uncertainties and noisy output measurements. The system states are restricted inside a given polytope and a classical Luenberger observer is used to reconstruct the unmeasurable states from output observations. Based on the observed states, a state feedback is proposed as the control input. The stability analysis and the control design are done using an extended version of the attractive ellipsoid method (AEM) approach. To avoid the violation of state constraints, this work proposes a barrier Lyapunov function (BLF) based analysis. The control parameters are obtained throughout the solution of some optimisation problems such that the BLF ensures an approximation of the constraints by a maximal ellipsoidal set and the AEM provides the characterisation of a minimal ultimately bounded set for the closed-loop system solutions. Numerical simulations show the advantages using the BFL-AEM methodology against classical sub-optimal controllers in academic second order and third order examples. Then, the proposed control strategy is applied over a Buck DC-DC converter. In all the cases, the method proposed here prevails over the other controllers.

Adaptive Unknown Input Estimation by Sliding Modes and Differential Neural Network Observer

In this paper, a differential neural network (DNN) implemented as a robust observer estimates the dynamics of perturbed uncertain nonlinear systems affected by exogenous unknown inputs. In the first stage, the identification error converges into a neighborhood around the origin. Then, the second-order sliding mode supertwisting algorithm implemented as a robust exact differentiator reconstructed the unknown inputs. The approach proposed in this paper can be applied in the case of full access to the state vector (identification problem) and in the case of partial access to the state vector (estimation problem). In the second case, the nonlinear system under study must have well-defined full relative degree with respect to the unknown input. Numerical examples showed the effectiveness of the proposed algorithm. The first example tested the DNN working as an identifier into a mathematical model describing the dynamics of a spatial minisatellite. The second example (with a DNN implemented as an observer) tested the methodology of this paper over a single link flexible robot manipulator represented in a canonical (Brunovsky) form. In both examples, the mathematical models served as data generators in the testing of the neural networks. Even when not exact mathematical description of both models was used in the input estimation, the accuracy obtained with the DNN is comparable with the case of applying a high-order differentiator with complete knowledge of the plant.

Active disturbance rejection control based on differential neural networks

This study addresses the problem of designing an output model reference control for non-linear systems in the presence of parametric disturbances/uncertainties in the state model and output noise measurements. A state observer based on a differential neural network (DNN) estimates the unknown states and the unknown disturbance simultaneously. The control design includes the estimated disturbance to provide a better tracking performance. The second result optimizes the gains of the controller and observer in order to obtain a reduced convergence zone for the tracking error based on the attractive ellipsoid method approach (AEM). Numerical results point out the advantages obtained by the nonlinear control based on the DNN observer when it is compared with a classical Luenberger structure.

Two-layer dynamic neural field learning law basec on controlled Lyapunov functions

The aim of this study was to develop a dynamic neural field (DNF) model to capture the essential non-linear characteristics of neural activity along several millimeters of visual cortex in response to local flashed stimuli. A two-layer DNF model was assessed to describe the response of both excitation and inhibitory layers of neurons. This particular structure of neurons interconnection was analyzed as a coupled system of non-linear integro-differential equations. This representation transformed the regular distributed form of DNF into an interconnected nonlinear model. A non-parametric modeling strategy yields to design the adjustment laws for the DNF weights. The algorithm used to adjust the weights considered self interconnections for each layer as well as external stimulus. The concept of controlled Lyapunov function served as the main tool to design a stable learning method for DNF. This algorithm was implemented in a class of hybrid computational model that served to execute the modeling of physiological response associated to visual external stimuli. The DNF model designed in this study can consider just the excitation response of specific neuron circuits without considering the presence of inhibitory response. This condition extends the number of electrophysiological trials where the adjusted DNF model can be evaluated. The learning method was evaluated with the information from a database that contains information coming from a selective visual attention experiment where the external stimuli appeared briefly in any of five squares arrayed horizontally above a central fixation cross. The degree of correlation (above 0.95) between signals measured at the brain cortex and the response of the DNF justified the application of the method proposed in this study.