A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Unknown input observer for Takagi-Sugeno implicit models with unmeasurable premise variables

Recent years have seen a great deal of interest in implicit nonlinear systems, which are used in many different engineering applications. This study is dedicated to presenting a new method of fuzzy unknown inputs observer design to estimate simultaneously both non-measurable states and unknown inputs of continuous-time nonlinear implicit systems defined by Takagi-Sugeno (T-S) models with unmeasurable premise variables. The suggested observer is based on the singular value decomposition approach and rewritten the continuous-time T-S implicit models into an augmented fuzzy system, which gathers the unknown inputs and the state vector. The exponential convergence condition of the observer is established by using the Lyapunov theory and linear matrix inequalities are solved to determine the gains of the observer. Finally, the effectiveness of the suggested method is then assessed using a numerical application. It demonstrates that the estimated variables and the unknown input converge to the real variables accurately and quickly (less than 0.5 s)

Robust unknown input observer for state and fault estimation in discrete-time Takagi-Sugeno systems

In this paper, a robust unknown input observer (UIO) for the joint state and fault estimation in discrete-time Takagi-Sugeno (TS) systems is presented. The proposed robust UIO, by applying the H-infinity framework, leads to a less restrictive design procedure with respect to recent results found in the literature. The resulting design procedure aims at achieving a prescribed attenuation level with respect to the exogenous disturbances, while obtaining at the same time the convergence of the observer with a desired bound on the decay rate. An extension to the case of unmeasurable premise variables is also provided. Since the design conditions reduce to a set of linear matrix inequalities that can be solved efficiently using the available software, an evident advantage of the proposed approach is its simplicity. The final part of the paper presents an academic example and a real application to a multi-tank system, which exhibit clearly the performance and effectiveness of the proposed strategy.Postprint (author's final draft

Simultaneous Parameters Identification and State Estimation based on Unknown Input Observer for a class of LPV Systems

International audienceA novel unknown input observer structure for parameters and state estimation is proposed to enhance the performance of the estimator. In this paper, we suggest how a failed matching condition in a nonlinear unknown input observer can be recovered by using time delayed measurement to solve the inversing problem. Based on delayed outputs, an augmented system is constructed from which the parameters of the model and the system states can be simultaneously estimated. The augmented nonlinear model is transformed into a Takagi Sugeno (TS) form. Sufficient conditions for the existence of the estimator are given in terms of linear matrix inequalities (LMIs). Using the obtained information on the unknown input observer, unknown parameters are identified. Finally, the feasibility and the effectiveness of the suggested approach is demonstrated on examples

Fuzzy control turns 50: 10 years later

In 2015, we celebrate the 50th anniversary of Fuzzy Sets, ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in FSS, see [1]. Ten years is at the same time a long period and short time thinking to the inner dynamics of research. This paper, presented for these 50 years of Fuzzy Sets is taking into account both thoughts. A first part presents a quick recap of the history of fuzzy control: from model-free design, based on human reasoning to quasi-LPV (Linear Parameter Varying) model-based control design via some milestones, and key applications. The second part shows where we arrived and what the improvements are since the milestone of the first 40 years. A last part is devoted to discussion and possible future research topics.Guerra, T.; Sala, A.; Tanaka, K. (2015). Fuzzy control turns 50: 10 years later. Fuzzy Sets and Systems. 281:162-182. doi:10.1016/j.fss.2015.05.005S16218228

Robust fault detection for vehicle lateral dynamics: Azonotope-based set-membership approach

© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksIn this work, a model-based fault detection layoutfor vehicle lateral dynamics system is presented. The majorfocus in this study is on the handling of model uncertainties andunknown inputs. In fact, the vehicle lateral model is affectedby several parameter variations such as longitudinal velocity,cornering stiffnesses coefficients and unknown inputs like windgust disturbances. Cornering stiffness parameters variation isconsidered to be unknown but bounded with known compactset. Their effect is addressed by generating intervals for theresiduals based on the zonotope representation of all possiblevalues. The developed fault detection procedure has been testedusing real driving data acquired from a prototype vehicle.Index Terms— Robust fault detection, interval models,zonotopes, set-membership, switched uncertain systems, LMIs,input-to-state stability, arbitrary switching.Peer ReviewedPostprint (author's final draft

Contribution à la commande des systèmes non linéaires : application à la machine synchrone à réluctance variable

N ombreux sont les problèmes en ingénierie nécessite l’estimation de l’état d’un système via un observateur. Cependant, la modélisation et la synthèse de l’observateur deviennent des taches difficiles pour des systèmes non linéaires. Face à ces difficultés, l’approche multimodèle peut être mise à profit. Les travaux de recherche présentés dans cette thèse portent sur l’estimation d’état des systèmes non linéaires représentés par des multimodèles flous de type Takagi-Sugeno couplé. Cette représentation est obtenue grâce à l’utilisation de la décomposition en secteurs non linéaire qui nous permettant de réécrire le nouveau système sous forme de polytopes sans perte d’information. Cette forme est ensuite utile pour la synthèse d’un observateur robuste vis-à-vis des entrées inconnues afin de reconstruire les états du système et les entrées inconnues. Après une brève introduction à l’approche multimodèle, le problème de l’estimation d’état des systèmes non linéaires décrits par les multimodèles flous couplés est abordé. Ensuite, nous présentons des algorithmes pour synthétiser des observateurs d’état robustes face à des entrées inconnues. Nous avons utilisé deux types d’observateurs à gains proportionnel-intégral et à gains multi-intégral. Finalement, nous appliquons ces approches au modèle d’une machine synchrone à réluctance variable

A Reduced-Order TS Fuzzy Observer Scheme with Application to Actuator Faults Reconstruction

This paper focuses on the principle for designing reduced-order fuzzy-observer-based actuator fault reconstruction for a class of nonlinear systems. The problem addressed can be indicated as an approach for a kind of reduced-order fuzzy observer design with special gain matrix structure that depends on a given matching condition specification. Using the Lyapunov theory, the stability conditions are obtained and expressed in terms of linear matrix inequalities, and the conditions for asymptotic estimation of actuator faults are derived. Simulation results illustrate the observer design procedure and demonstrate the actuator fault reconstruction effectiveness and performance

Advanced control designs for output tracking of hydrostatic transmissions

The work addresses simple but efficient model descriptions in a combination with advanced control and estimation approaches to achieve an accurate tracking of the desired trajectories. The proposed control designs are capable of fully exploiting the wide operation range of HSTs within the system configuration limits. A new trajectory planning scheme for the output tracking that uses both the primary and secondary control inputs was developed. Simple models or even purely data-driven models are envisaged and deployed to develop several advanced control approaches for HST systems