Victor Estrada-Manzo

Universidad Politécnica de Pachuca | UPP · Department of Mechatronics

This paper proposes a solution to design an observer for singular linear systems in terms of linear matrix inequalities whose solvability is verified in polynomial time. The observer under design shares the idea of a Luenberger one but adding the derivative of the outputs, which leads to the regularization of the error system. The direct Lyapunov m...

This work proposes a discrete-time output regulator for nonlinear descriptor systems. The approach consists in two parts: 1) the design of a convex nonlinear stabilizer computed by means of the so-called non-quadratic Lyapunov functions, 2) the design of a linear regulator computed through the so-called Francis equations for descriptor models; the...

El presente trabajo propone un regulador no lineal en tiempo discreto para sistemas no lineales tipo descriptor. El diseño está dividido en dos partes: 1) un estabilizador no lineal calculado por medio del método directo de Lyapunov y modelos convexos, 2) un regulador lineal calculado a través de las llamadas ecuaciones de Francis-Isidori-Byrnes pa...

A novel discontinuous observer design for nonlinear systems, whether stable or not, is presented in this paper; it removes former limitations on matching and minimum-phase conditions, Lipschitz bounds, and linearity of outputs. Based on a pair of diffeomorphisms an observer error system can be written whose nonlinear nominal model depends entirely...

This paper presents a trajectory-tracking controller of an inverted pendulum system on a self-balancing differential drive platform. First, the system modeling is described by considering approximations of the swing angles. Subsequently, a discrete convex representation of the system via the nonlinear sector technique is obtained, which considers t...

En este artículo, la robustez de la bien conocida técnica de par calculado es mejorada en dos aspectos: por un lado, la ley de control de bucle interno se hace depender exclusivamente de señales generadas por el usuario cuya precisión ya no se ve afectada por ruido o errores numéricos; por otro lado, la ley de control de bucle externo se hace depen...

This paper proposes a novel convex unknown input observer for simultaneously estimating system states and sensor faults in nonlinear systems. The observer design is based on the Lyapunov method and provides conditions in the form of linear matrix inequalities. The methodology allows handling a larger family of systems than previous approaches as it...

This paper presents a novel unknown input observer for nonlinear systems which, based on as much time derivatives of the output as its relative degree plus one, is able to asymptotically reconstruct both the state and the unknown input for a class of nonlinear systems. Design conditions are expressed as linear matrix inequalities thanks to a convex...

This note discusses common errors on using convex modelling and linear matrix inequalities for nonlinear control, a methodology that has become increasingly popular due to its systematicness and numerical implementability. Illustrations on common problems are made from existing literature: they are classified and discussed; advices are given to pre...

Discontinuous observer-based convex control of an underactuated rotatory system, better known as the Furuta pendulum, is the subject of this report. It is shown that a slight generalization of the traditional discontinuous observer design allows applying it to the referred plant. Since the observer gains are obtained via linear matrix inequalities...

This paper presents an alternative to design a static output feedback controllers for nonlinear descriptor systems. The methodology is based on the direct Lyapunov method, from which, after a convex rewriting of the original nonlinear systems, conditions in the form of linear matrix inequalities are obtained. The proposal is shown to be more relaxe...

This article presents a novel solution for adaptive output feedback of uncertain nonlinear systems; it uses nonlinear controller and observer structures to drive a time‐varying function as a Lyapunov one, thus guaranteeing asymptotic stability of the system states and observation error. Exact convex modeling of available terms and polytopic embeddi...

This paper is devoted to provide a numerical solution the nonlinear output regulation problem for descriptor systems. The control law under design is a nonlinear one, it consists on a nonlinear stabilizer combined with linear steady-state mapping as well as nonlinear steady-state input mapping; all of them are computed via linear matrix inequalitie...

This work proposes a proportional-integral fault estimation observer for nonlinear systems by means of convex structures. Unlike the traditional approaches that consider quadratic Lyapunov functions, this work employs nonquadratic ones. As a result, less conservative conditions in the form of linear matrix inequalities are obtained. Furthermore, an...

This paper presents an H∞ event-triggered state-feedback controller design for continuous-time nonlinear systems via convex optimization techniques. The proposal is based on an exact discretization and its quasi-linear parameter varying representation. Thus, two sets of design conditions in terms of linear matrix inequalities by means of both param...

This paper presents actuator fault detection of discrete-time nonlinear descriptor systems by means of nonlinear unknown input observers. The approach is based on the exact factorization of the estimation error in order to overcome the well-known problem of unmeasurable scheduling variables within the observation of convex models, thus avoiding the...

This paper presents a convex approach for nonlinear descriptor systems with multiple delays; it allows designing delayed nonlinear controllers such that the closed-loop system holds exponential estimates for convergence. The proposal takes advantage of an equivalent convex representation of the given descriptor model together with Lyapunov-Krasovsk...

En este artículo se realiza el diseño de observadores para sistemas descriptores no lineales en tiempo discreto mediante técnicas convexas. El enfoque se basa en una factorización exacta del error de observación recientemente aparecida, para superar el conocido problema de las variables de ponderación no medibles dentro del modelos convexos, evitan...

This work presents a methodology to choose the convex structure for nonlinear gains in approaches based on Takagi-Sugeno models. The proposal faces the problem of numerical complexity in LMI-based approaches within this area; it gives a finer convex structure for controller and observer matrices depending on two criteria: less number of LMI constra...

This paper proposes a comprehensive solution to persistent problems faced by nonlinear observer design via convex optimization techniques, namely, the construction of an exact error model and the handling of unmeasurable premises. Instead of using the differential mean value theorem, it is shown that the error system is always exactly amenable, via...

This paper proposes an identification-based nonlinear control scheme which casts the plant model as a recurrent high-order neural network. The model thus obtained consists on polynomials of a fixed number of nonlinearities, a fact that is exploited by transforming it into an exact tensor-product representation whose nested convex sums may increase...

This paper provides a novel solution for adaptive observer design based on a polytopic representation of the error system. Thanks to a recently appeared factorisation, the proposal is able to deal with fully nonlinear system matrices and nonlinear outputs while dropping conditions on Lipschitz bounds and persistence of excitation. Examples are prov...

This work presents an exact Takagi-Sugeno descriptor model of a recurrent high-order neural network arising from identification of a nonlinear plant. The proposed rearrangement allows exploiting the nonlinear characteristics of the neural model for H∞-optimal controller design whose conditions are expressed as linear matrix inequalities. Simulation...

This work deals with the design of nonlinear observers and their application to fault diagnosis and isolation. The methodology is based on convex optimization techniques; it considers the general problem of unmeasurable premises. Algebraic rearrangements and Taylor series are employed in order to obtain an adequate error system dynamics. Thus,the e...

This paper presents a static output feedback controller design for discrete-time nonlinear systems exactly represented by Takagi–Sugeno models. By introducing past states in the control law as well as in the Lyapunov function, more relaxed results are obtained. Different conditions in terms of linear matrix inequalities are provided. The proposed c...

Stability analysis of nonlinear singular systems, arising from differential algebraic equations, is addressed in this report, exploiting the fact that it belongs to the class of Positvstellensatz problems. By means of the direct Lyapunov method and a variety of convex descriptor forms, sufficient conditions in terms of linear matrix inequalities ar...

Concerned with descriptor systems, this paper extends recent results on nonquadratic controller design. The proposal employs an exact Takagi–Sugeno model of the descriptor redundancy form and a fully nonquadratic Lyapunov function. Based on these elements, a switching control law is proposed that achieves stabilization up to the modelling area by f...

This report is concerned with stability and stabilization of time-delay nonlinear nonsigular descriptor systems. Based-on a Lyapunov-Krasovskii functional and an exact convex representation of the system, conditions in the form of linear matrix inequalities are found that guarantee exponential estimates. The effectiveness of the proposed solutions...

The present paper introduces a simple model to study sitting control for persons with complete thoracic spinal cord injury. The system is obtained via Lagrangian techniques; this procedure leads to a nonlinear descriptor form, which can be written as a Takagi-Sugeno model. A first attempt to estimate the sitting control in disabled people is done v...

This paper deals with the admissibilisation with guaranteed H∞ performance of linear parameter-varying (LPV) discrete-time singular systems under gain-scheduled (GS) state-feedback control. In particular, we focus on systems with descriptor matrix of LPV form and unknown/unmeasurable disturbance input. To our best knowledge and despite its practica...

The present paper studies sitting control for persons with complete thoracic spinal cord injury by means of automatic control. The methodology begins by modeling sitting control, after a discretization of the nonlinear descriptor model is computed, then a Takagi-Sugeno model is obtained for further manipulations. The approach uses unknown input obs...

The present paper introduces a simple model to study sitting control for persons with complete thoracic spine cord injury. The system is obtained via Lagrangian techniques; this procedure leads to a nonlinear descriptor form, which can be written as a Takagi-Sugeno model. A first attempt to estimate the sitting control in disabled people is done vi...

Introduction Nous présentons une technique de modélisation pour estimer des paramètres du contrôle de la stabilité posturale en position assise chez les sujets souffrant de lésion médullaire. La position assise sans soutien dorsal est souvent pratiquée chez les personnes paraplégiques, que ce soit dans les activités quotidiennes ou lors des exercic...

This paper introduces a modelling approach to investigate seated postural stability for subject suffering a complete spine cord injury (SCI). A mechanical model, variation of the double inverted pendulum, is used to represent a subject in the sagittal plane moving back and forth his uppers limbs and head to maintain his stability. A non-linear desc...

This paper presents simulation and real-time results of a nonlinear control scheme for stabilization of the Furuta pendulum. Instead of the traditional state-space model, the proposal makes use of a convex exact rewriting of the nonlinear model in its descriptor form, which naturally arises in Lagrange-Euler dynamics. Convexity proves to be useful...

This paper introduces a simplified nonlinear model to study sitting control for persons with Spinal Cord Injury. The system obtained via Lagrangian techniques is defined with a nonlinear descriptor form and written under an exact Takagi-Sugeno model. In order to stabilize this class of system that includes a time-varying input delay, a state feedba...

People with complete thoracic spinal cord injury (SCI) cannot rely on any muscle activity below their injury level. Instead they can use their upper limbs and head in order to maintain the stability of the upper body as they are trained in rehabilitation. In order to understand how head and upper limbs participate in seated balance, and to extend c...

The present paper introduces a simple model to study sitting control for persons with complete thoracic spine cord injury. The system is obtained via Lagrangian techniques; this procedure leads to a nonlinear descriptor form, which can be written as a Takagi-Sugeno model. A first attempt to estimate the sitting control in disabled people is done vi...

The paper presents a new quadratic Lyapunov function for observer design for discrete-time nonlinear descriptor systems. The main idea is to represent the original nonlinear model as a Takagi- Sugeno one and then use Lyapunov's direct method to design the observer. The well-known Finsler's Lemma is used to design a non-Parallel-Distributed-Compensa...

The present paper provides a systematic way to generalize Takagi-Sugeno observer design for discrete-time nonlinear descriptor models. The approach is based on Finsler's lemma, which decouples the observer gains from the Lyapunov function. The results are expressed as strict LMI constraints. To obtain more degrees of freedom without altering the nu...

This thesis addresses the estimation and control for nonlinear descriptor systems. The developments are focused on a family of nonlinear descriptor models with a full-rank descriptor matrix. The proposed approaches are based on a Takagi-Sugeno (TS) descriptor representation of a given nonlinear descriptor model. This type of TS models is a generali...

This paper presents a static output feedback controller design for discrete-time nonlinear descriptor models. The conditions are given in terms of linear matrix inequalities (LMIs). The approach is based on the Takagi-Sugeno (T-S) representation of the nonlinear system and Finsler's Lemma. The proposed method exploits the discrete-time nature of th...

This chapter presents a systematic procedure to design observers for mechanical systems. In general, the state space representation of such systems can be naturally expressed as nonlinear descriptor models. The idea is to rewrite the original nonlinear model as a Takagi–Sugeno one and use Lyapunov’s direct method for observer design. This procedure...

The present paper deals with observer design for discrete-time nonlinear descriptor systems. Through Finsler's Lemma, we cut the link between the observer gains and the Lyapunov function, which relaxes existing conditions and introduces an extra degree of freedom. In addition, the results are expressed as LMI constraints. The effectiveness of the t...

Many physical systems are naturally represented by descriptor models. This paper is concerned with stabilization of discrete-time descriptor systems represented by Takagi-Sugeno fuzzy models. Two different approaches are presented based on non-quadratic Lyapunov functions. The results are expressed in terms of linear matrix inequalities. Numerical...

This paper considers observer design for nonlinear descriptor systems. We propose approaches based on Takagi–Sugeno (TS) models. An extended estimation vector is used in order to keep the descriptor structure of the observer. The design conditions are expressed as linear matrix inequalities. The proposed observer structure, via an intermediate vari...

The present paper provides a systematic way to generalize controller design for discrete-time nonlinear descriptor models. The controller synthesis is done using a Takagi-Sugeno representation of the descriptor models and linear matrix inequalities. We propose approaches to exploit the discrete-time nature of the problem by using delayed Lyapunov f...

The present paper deals with observer design for discrete-time nonlinear descriptor systems. Through Finsler's Lemma, we cut the link between the observer gains and the Lyapunov function, which relaxes existing conditions and introduces an extra degree of freedom. In addition, the results are expressed as LMI constraints. The effectiveness of the t...

This paper presents a relaxed approach for stabilization and H∞ disturbance rejection of continuous-time Takagi-Sugeno models in descriptor form. Based on Finsler's Lemma, the control law can be conveniently decoupled from a non-quadratic Lyapunov function. These developments include and outperform previous results on the same subject while preserv...

Trajectory tracking has been long ago set into a formal mathematical framework through the nonlinear output regulation theory. Results thereby derived have been hardly implemented in a systematic way due to their complexity, which forces the designer to lead with expressions which are not necessarily computationally tractable. Fuzzy regulation has...

Output regulation theory is a powerful tool for trajectory tracking of nonlinear systems which has led to extensive research for more than two decades, due to its mathematical insight, elegance, and effectiveness of solutions. Despite its success, regulation relies mainly on the designer's ability to fit the existence results and conditions for con...