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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. [ABSTRACT FROM AUTHOR]

The aim of this study was to design an adaptive control strategy based on recurrent neural networks (RNNs). This neural network was designed to obtain a non-parametric approximation (identification) of discrete-time uncertain nonlinear systems. A discrete-time Lyapunov candidate function was proposed to prove the convergence of the identification error. The adaptation laws to adjust the free parameters in the RNN were obtained in the same stability analysis. The control scheme used the states of the identifier, and it was developed fulfilling the necessary conditions to establish a behavior comparable with a quasi-sliding mode regime. This controller does not use the regular form of the switching function that commonly appears in the sliding mode control designs. The Lyapunov candidate function to design the controller and the identifier simultaneously requires the existence of positive definite solutions of two different matrix inequalities. As consequence, a class of separation principle was proven when the RNN-based identifier and the controller were designed by the same analysis. Simulations results were designed to show the behavior of the proposed controller solving the tracking problem for the trajectories of a direct current (DC) motor. The performance of the proposed controller was compared with the solution obtained when a classical proportional derivative controller and an adaptive first-order sliding mode controller assuming poor knowledge of the plant. In both cases, the proposed controller showed superior performance when the relation between the tracking error convergence and the energy used to reach it was evaluated. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This study introduces a method for designing stable learning laws of Long Short-Term Memory (LSTM) networks working as a non-parametric identifier of nonlinear systems with uncertain models. The strategy applies the concept of stability for discrete-time systems in the sense of Lyapunov to prove that origin is a practical stable equilibrium point for the identification error. The laws consider a general class of sigmoidal functions placed at the different gates of a LSTM structure (long and short memory). The design of the learning laws uses a matrix inequality framework to obtain the rate gains associated with the evolution of the weights. Numerical results show the designed learning laws for the non-parametric identifier based on a LSTM approximation tested on two classes of nonlinear systems: the first one describes the ozone-based degradation of organic contaminants, and the second one represents the dynamics of a Van Der Poll oscillator. The LSTM identifier is compared against a classical Lyapunov-based recurrent neural network. This comparison demonstrates how the proposed algorithm approximates the trajectories of both systems with a smaller mean squared error, which serves as an indicator of the benefits obtained with these new learning laws. [ABSTRACT FROM AUTHOR]

This study aims to develop stable learning laws (in the sense of Lyapunov) for a general class of multilayer recurrent neural network (RNN) non-parametric identifier. The application of control Lyapunov functions in the discrete-time domain ensures the ultimate boundedness for the identification error enforcing it to reach a boundary set related to the power of parametric uncertainties and the modeling error. This work presents a general algorithm to design RNNs with n layers: one input layer, n - 2 hidden layers, and one output layer. Numerical simulations support the theoretical results showing the advantages of increasing the number of layers in an RNN structure. A first example identifies the unknown states of the Van Der Pol oscillator. Then, a second example demonstrates the behavior of an RNN in a third-order system with high nonlinear dynamics describing an ozonation system of a single contaminant. For both cases, the application of the developed learning laws succeeds in estimating the uncertain dynamics. Moreover, the numerical simulations show how the identification error decreases as the number of layers increases. [ABSTRACT FROM AUTHOR]

Summary: This study aims to design a robust state feedback controller for uncertain and perturbed linear systems with state constraints described by a polytope. This novel design incorporates the use of a composite barrier Lyapunov function (CBLF) and the convex hull of a set of ellipsoids inscribed in the given polytopic constraint set. The CBLF is used to ensure that this convex hull is an invariant set for the perturbed system states. Then, an optimization scheme is implemented to maximize the size of this invariant set to use it as a safe set. This is a set of initial conditions ensuring that the system solutions conform to the constraints for any subsequent time instant. Additionally, a minimal ultimate bound for the states is calculated to ensure asymptotic convergence to a region as close to the origin as possible. This region is characterized by a second convex hull of ellipsoids using the well‐known attractive ellipsoid method and the CBLF. Numerical simulations illustrate and compare the obtained results against a similar approach, considering the classical quadratic Lyapunov function, instead of the CBLF. [ABSTRACT FROM AUTHOR]

Accurate and fast estimation of single-phase grid voltage phase and frequency has the potential to improve the performances of various control and monitoring techniques used in electric power systems. This letter applies an adaptive sliding mode observer for frequency and phase estimation. The observer is simple, easy to tune, and suitable for real-time implementation. The proposed adaptive observer can be considered as an alternative to a phase-locked loop (PLL) with better performance. dSPACE-based experimental results are given to show the effectiveness and performance improvement of the proposed approach with respect to two other advanced PLL techniques, namely, pseudolinear enhanced PLL and second-order generalized integrator-frequency locked loop. [ABSTRACT FROM AUTHOR]

This manuscript proposes the design of a speech synthesis algorithm based on measured electroencephalographic (EEG) signals previously classified by a class of neural network with continuous dynamics. A novel multilayer differential neural network (MDNN) classifies a database with the EEG studies of 20 volunteers. The database contains information described by input-output pairs corresponding to EEG signals and a corresponding word imagined by the volunteer. The suggested MDNN estimates the unknown relationship between the information instances and suggests the most-likely word that the user wants mentioning. The proposed MDNN satisfactory classifies over 95% a set of words obtained from the suggested EEG study in which, the users have to watch four different geometric figures on a screen. [ABSTRACT FROM AUTHOR]

This article solves the tracking trajectory problem of teleoperated robotic systems with different workspaces. The overall robotic system satisfies a regular master–slave structure with a delta-robot as the master device and a planar manipulator attached to a Cartesian robot with five degrees of freedom (DOFs) as the slave device. A forward kinematics analysis describes the workspace for the delta-robot and the five-DOFs manipulator. A coordinate transformation based on sigmoidal functions establishes the relation between the workspaces for both robotic devices. The obtained transformation yields a feasible workspace for the slave robot. Then, an inverse kinematics analysis provides the desired reference trajectories. The tracking trajectory control implements a robust strategy based on Barrier Lyapunov functions. The barrier controller does not allow the slave robot to reach non-attainable configurations. State-dependent gains characterized the obtained controller taking into account the different workspaces for each device. Numerical results describe the suggested controller applied in a virtual teleoperated robot and a real robotic system platform. The obtained results confirm the improvements (measured in terms of the mean square error and the l 2 norm of the applied controls) of the proposed controller against a traditional state feedback realization. Furthermore, the results show that the trajectories of the slave robot do not leave the valid workspace. • Output feedback control for teleoperated manipulators under state constraints. • Adaptive control formulation based on logarithmic barrier Lyapunov functions. • Super-twisting differentiator implementation to obtain the tracking error derivative. • Experimental evaluations on a manipulator (slave) and a Delta robot (master). [ABSTRACT FROM AUTHOR]