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In this paper, the tracking problem for discrete-time switched systems subject to actuator saturation and exogenous input is considered. The considered class of systems encompasses discrete-time systems subject to asymmetric saturation or time-varying saturation. Using switched Lyapunov functions and L2-gain analysis, a one-step method is proposed to design the controller and the anti-windup compensator. Some sufficient conditions are derived to guarantee local asymptotic stability and L2-performance of the closed-loop system in terms of linear matrix inequalities (LMI). To illustrate the advantages of the proposed scheme, comparisons with existing schemes are provided. At last, the effectiveness of the proposed scheme is illustrated on the velocity tracking problem of a heavy train with asymmetric saturation constraints.

This paper investigates the steering fault detection problem for autonomous ground vehicles (AGVs). Using an observer-based approach, a new fuzzy fault detector for steering actuator is designed for safety concern. To this end, a two degrees-of-freedom (2-DOF) nonlinear vehicle model is adopted to represent the nonlinear dynamics of AGVs. Since it is not easy to measure the lateral velocity in practice, this model is then represented in a specific Takagi-Sugeno (TS) fuzzy form with nonlinear consequents. In contrast to the conventional TS fuzzy modeling, it allows separating the unmeasured premise variables in the local nonlinear consequent, which enables a more effective way to deal with the challenging issue of unmeasured premise variables. Moreover, to minimize the effect of disturbances on system performance and maximize that of actuator faults on the generated residual, both H∞ disturbance attenuation index and H_fault sensitivity index are taken into account in a finite-frequency domain. The conditions to design fault detection TS fuzzy observer are derived using Lyapunov stability method. The design procedure can be reformulated as an optimization problem under linear matrix inequalities, efficiently solved by standard numerical solvers. Simulation results are given to verify the fault detection performance of the proposed method.

In this report we illustrate that nonlinear control and observer design can be described as a Positivstellensatz problem, we consider a quadratic candidate function to stabilize nonlinear systems that have been modeled via the nonlinear sector methodology as an exact convex representation. New shape-independent conditions for satisfying positiveness in double sums are established based on the concept of copositivity. The conditions obtained are compared with previous approaches found in the literature via a numerical example.

This paper deals with the control design for freight trains, with the objective to reduce coupler failures and issues that might arise from low wheel-track adhesion. Since train cars are not equipped with position sensors, a cascade of observers is used to obtain finite-time estimations of in-train forces that cause coupler strain and adhesion level estimation. The controller is then aware of high amplitudes of in-train forces and of low adhesion situations, and adjusts the control signal accordingly, using LMI-based anti-windup technique. Simulation results show the benefits of the proposed approach.

For the control design of freight trains, the estimation of in-train forces is crucial to avoid safety issues caused by the possible failure of car couplers under excessive stress. However, the in-train forces and the relative positions of adjacent train cars are not directly measurable. To address this issue, this paper designs estimators of train car positions and in-train forces using only locomotive-based measurements. Using the multi-point train model, a cascade structure of robust sliding mode differentiators is developed. It provides finite-time estimation of train car positions and in-train forces. Simulation results illustrate the feasibility of the proposed approach.

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 constraints or more decision variables while keeping the same number of LMIs in traditional approaches. The advantages of the proposal are illustrated via numerical examples.

International audience; This paper extends the well-known computed-torque control technique for trajectory tracking in parallel robotic manipulators, which belong to the class of nonlinear systems under algebraic restrictions. The proposed methodology is based on Euler-Lagrange modelling which, once the closed-loop kinematic chain is taken into account, leads to a system of differential algebraic equations requiring proper initialisation while controlled. The control scheme is illustrated for an ankle therapy device known as the motoBOTTE, where post-stroke patients are subject to reeducation routines corresponding to different trajectories of the parallel manipulator.

Pontryagin’s Minimum Principle is a way of solving hybrid powertrain optimal energy management. This paper presents an improvement of a classical implementation. The core of this improvement consists in relaxing the tolerance on some intermediate steps of the algorithm in order to reduce the number of iterations and thereby reducing the number of operations required to compute an optimal solution. The paper describes both a classical implementation of Pontryagin’s Minimum Principle as well as the improved version. Numerical simulations are conducted on an academic example to demonstrate the benefits of the proposed approach.

Brain&ndash, computer interfaces (BCIs) have been proven to be useful for stroke rehabilitation, but there are a number of factors that impede the use of this technology in rehabilitation clinics and in home-use, the major factors including the usability and costs of the BCI system. The aims of this study were to develop a cheap 3D-printed wrist exoskeleton that can be controlled by a cheap open source BCI (OpenViBE), and to determine if training with such a setup could induce neural plasticity. Eleven healthy volunteers imagined wrist extensions, which were detected from single-trial electroencephalography (EEG), and in response to this, the wrist exoskeleton replicated the intended movement. Motor-evoked potentials (MEPs) elicited using transcranial magnetic stimulation were measured before, immediately after, and 30 min after BCI training with the exoskeleton. The BCI system had a true positive rate of 86 &plusmn, 12% with 1.20 &plusmn, 0.57 false detections per minute. Compared to the measurement before the BCI training, the MEPs increased by 35 &plusmn, 60% immediately after and 67 &plusmn, 60% 30 min after the BCI training. There was no association between the BCI performance and the induction of plasticity. In conclusion, it is possible to detect imaginary movements using an open-source BCI setup and control a cheap 3D-printed exoskeleton that when combined with the BCI can induce neural plasticity. These findings may promote the availability of BCI technology for rehabilitation clinics and home-use. However, the usability must be improved, and further tests are needed with stroke patients.

International audience; This document presents an approach for nonlinear control design in singular systems by combining Lyapunov's direct method with exact convex structures. The conditions obtained are given in terms of linear matrix inequalities, the methodology proposed is illustrated by applying the nonlinear sector methodology to the mathematical model of a parallel robot for stabilizing it in a desired set point.

International audience; This chapter proposes a new control approach for the turbocharged air system of a gasoline engine. To simplify the control implementation task, static lookup tables (LUTs) of engine data are used to estimate the engine variables in place of complex dynamical observer and/or estimators. The nonlinear control design is based on the concept of robust feedback linearization which can account for the modeling uncertainty and the estimation errors induced by the use of engine lookup tables. The control feedback gain can be effectively computed from a convex optimization problem. Two control strategies have been investigated for this complex system: drivability optimization and fuel reduction. The effectiveness of the proposed control approach is clearly demonstrated with an advanced engine simulator.

This paper deals with T–S fuzzy model with nonlinear consequent parts that has shown to reduce the number of fuzzy rules and decrease modeling error comparing with conventional T–S with linear consequent parts. To further increase the benefits of using such model, many novelties in analyzing and applying it are introduced here. Canceling the nonlinear part of subsystems by fuzzy feedback linearization, using a novel fuzzy non-quadratic Lyapunov function and new relaxation methods for further reduction of conservativeness and maximizing the region of attractions are all discussed in this paper. Numerical examples illustrate the effectiveness of the proposed method.

IF=2.894; International audience; Descriptor models are naturally obtained from the Euler–Lagrange modeling approach to mechanical systems. Since the underlying system is nonlinear, global stabilization and/or tracking is possible only in a limited number of cases. Therefore, we develop conditions for local stabilization and tracking of discrete-time descriptor systems represented by Takagi–Sugeno fuzzy models, using both quadratic and nonquadratic Lyapunov functions. An estimate of the region of attraction is also obtained. The conditions are illustrated on a numerical example and in tracking control for a robot arm.

This paper is dedicated to the implementation process of advanced Takagi-Sugeno controllers. The considered application is the control of the throttle of a gasoline engine running at idle speed. In order to design a model-based control, a model is first obtained and identified with an engine test bench. Since it involves nonlinearities, a Takagi-Sugeno representation is expressed. Due to the complexity of the model, a simple TS controller cannot be obtained after applying the Lyapunov methodology. Then, an advanced non-PDC controller has to be considered. LMI conditions are obtained through the direct Lyapunov direct method. However, the real-time matrix inversion involved in the non-PDC structure makes the implementation difficult or impossible. An alternative controller is then designed to have similar performances without any matrix inversion. Then, the controller is implemented in the industriallike Electronic Control Unit of the engine test bench. Experimental results are provided to illustrate the efficiency of the proposed advanced Takagi-Sugeno controller.

IF=8.759; International audience; This paper is concerned with the reduction of conservatism on stabilization conditions of discrete-time Takagi-Sugeno fuzzy models via delayed nonquadratic Lyapunov functions. A fruitful approach recently appeared in the literature, which, despite its benefits, dramatically increases the number of linear matrix inequalities needed to synthesize a controller. The two sets of sufficient conditions hereby proposed tackle this numerical problem while reducing conservatism and increasing the stabilization domain of existing conditions in literature, as illustrated in several examples.

This paper is devoted to the development of a new saturated non-parallel distributed compensation control law for disturbed Takagi-Sugeno fuzzy systems subject to both control input and state constraints. In order to cover a large range of real-world applications, both L 2 and L ∞ disturbances are considered which result in two different control design procedures. A parameter-dependent version of the generalized sector condition is effectively exploited in a fuzzy Lyapunov control framework to handle the control input saturation. Moreover, the proposed control method is based on the concept of robust invariant set which is able to provide an explicit characterization of the estimated domain of attraction of the closed-loop system. Different optimization algorithms are also proposed to deal with the trade-off between different closed-loop requirements in a local control context. The design conditions are expressed in terms of linear matrix inequalities which can be solved efficiently with available solvers. The numerical examples illustrate how the proposed methodology leads to less conservative results as well as less computational complexity when compared to very recent works in the literature.

This paper is devoted to developing a novel approach to deal with constrained continuous-time nonlinear systems in the form of Takagi-Sugeno fuzzy models. Here, the disturbed systems are subject to both input and state constraints. The one-step design method is used to simultaneously synthesize the dynamic output feedback controller and its anti-windup strategy. A parameter-dependent version of the generalized sector condition is used together with Lyapunov stability theory to derive linear matrix inequality design conditions. Based on this result and for different design specifications, the synthesis of an anti-windup based dynamic output feedback controller is expressed on the form of convex optimization problems. A physically motivated example is given to illustrate the effectiveness of the proposed method.

This paper aims to present a methodology to control the position of the clutch actuator. The objective is to improve the position reference tracking in order to get better performances and accuracy on the clutch slip control. The originality of this work is to use a model that takes into account the nonlinear characteristic of the stiffness of the clutch diaphragm. Instead of robustness approach, the nonlinearity is managed using the quasi-LPV Takagi-Sugeno representation and, additionally, because the nonlinearity is switching, the developed control law is, consequently, a nonlinear switching one. Moreover, in order to use unmeasured values in the controller, such as the current of the electric motor, a Takagi-Sugeno switching observer is designed. Some simulation results highlight the efficiency of the proposed approach.

This paper considers local stability analysis of discrete-time Takagi-Sugeno fuzzy systems, for which classically in the TS literature only global stability is considered. Using a common quadratic and nonquadratic Lyapunov function, respectively, LMI conditions are developed to establish local stability of an equilibrium point. An estimate of the region of attraction of this point is also determined. The developed conditions are illustrated on a numerical example.

International audience; The motoBOTTE is a robot designed for assistive rehabilitation. The identification of a mathematical model for the system is shown; then we design and implement a nonlinear control law for tracking a reference signal. The nonlinear controller design is achieved by combining an exact convex representation with the direct method of Lyapunov. Results are given in terms of linear matrix inequalities (LMI); simulation and real-time results are shown as well.

IF=2.675; International audience; In many real time applications, information of transmitted torque is a mandatory input of the embedded control strategies. In the most of cases, the use of a physical torque sensor (strain gauge) is compromised by cost and bulk reasons and the torque is not measured. Unfortunately, the need of an embedded torque measurement is a general real time application problem and can only be solved through an accurate embeddable estimation method. This issue is especially common in automotive industry concerning the powertrain management for example.A virtual strain gauge based on an unknown input Takagi–Sugeno discrete observer designed in the angular domain and a shaft angular deformation estimation method is proposed as a universal torque estimator. The static torque estimation is ensured rebuilding the shaft torsion angle by a virtual tooth adding method into the encoder sensors disposed at each edge of the shaft. The observer performs the dynamic part of the transmitted torque through a mass-spring model structure of the shaft.The virtual strain gauge has been applied on real torque estimation issues in automotive application such as the engine and the clutch torque estimation. Simulation and real time results have permitted to validate the feasibility, the versatility and the accuracy of the virtual strain gauge.

This paper is dedicated to the control of the air-fuel ratio in a gasoline engine. The use of the crank-angle domain handles the variable transport delay, which is the main challenge when controlling air-fuel ratio. The Takagi-Sugeno methodology is considered to deal with the nonlinearities in the model. The control law is obtained using an extended state that includes the delayed variables. Simulations confirm the feasibility of the method and highlight the efficiency of the proposed air-fuel ratio controller.

IF=7.671; International audience; Many of the recent advances on control and estimation of systems described by Takagi-Sugeno (TS) fuzzy models are based on matrix inversion, which could be a trouble in the case of real-time implementation. This paper is devoted to the development of alternative solutions to this matrix inversion problem in the discrete-time case. Two different methods are proposed: The first one relies on replacing the matrix inversion by multiple sums and the second methodology is based on an estimation of the matrix inversion by an observer structure. For the first methodology, a new class of controllers and observers are introduced which are called, respectively, the counterpart of an advanced TS-based (CATS) controller and the replica of an advanced TS-based (RATS) observer. Instead of relaxations for the linear matrix inequalities conditions, an original use of the membership functions is presented. In the second methodology, it is proposed the estimation-based control law for approximating TS-based (ECLATS) controller that uses a fuzzy state observer. The Lyapunov theory is used to ensure stability conditions for either the closed-loop system as well as the estimation error. Numerical examples and comparisons highlight the efficiency of the procedures that can be used to replace any inverted matrix in any advanced fuzzy controller or observer. Finally, advantages and drawbacks of the proposed method are discussed.

Purpose – The purpose of this paper is to deal with the stabilization of the continuous Takagi Sugeno (TS) fuzzy models using their discretized forms based on the decay rate performance approach. Design/methodology/approach – This approach is structured as follows: first, a discrete model is obtained from the discretization of the continuous TS fuzzy model. The discretized model is obtained from the Euler approximation method which is used for several orders. Second, based on the decay rate stabilization conditions, the gains of a non-PDC control law ensuring the stabilization of the discrete model are determined. Third by keeping the values of the gains, the authors determine the values of the performance criterion and the authors check by simulation the stability of the continuous TS fuzzy models through the zero order hold. Findings – The proposed idea lead to compare the performance continuous stability results with the literature. The comparison is, also, taken between the quadratic and non-quadratic cases. Originality/value – Therefore, the originality of this paper consists in the improvement of the continuous fuzzy models by using their discretized models. In this case, the effect of the discretization step on the performances of the continuous TS fuzzy models is studied. The usefulness of this approach is shown through two examples.

This paper considers the stabilisation of switching nonlinear models by switching between the subsystems. We assume that arbitrary switching between two subsystems is possible once a subsystem has been active for a predefined number of samples. We use a Takagi–Sugeno representation of the models and a switching Lyapunov function is employed to develop sufficient stability conditions. If the conditions are satisfied, we construct a switching law that stabilises the system. The application of the conditions is illustrated in several examples.

In automation control system applications, the transmitted engine and clutch torque are unavoidable information for the control strategies. For example, these information are required to engine control, hybrid vehicle and automated transmission management. An angular domain discrete observer is proposed to estimate the transmitted torque from incremental encoders which are already implemented on the vehicle. Some simulation results of transmitted clutch torque estimation are presented as instantaneous brake engine torque and clutch torque estimation on real data. This proposed torque estimation method based on shaft angular deformation permits to obtain accurate results in different automotive applications.