Existence and nonexistence of solutions to nonlinear gradient elliptic systems involving (p(x),q(x))-Laplacian operators

In this article, we establish the existence of nontrivial solutions by employing the fibering method introduced by Pohozaev. We also generalize the well-known Pohozaev and Pucci-Serrin identities to a (p(x),q(x))-Laplacian system. A nonexistence result for a such system is then proved

Robust Saturated Control Based Static Output Feedback for Steering Control of the Autonomous Vehicle via Non Quadratic Lyapunov Function

International audienceThis chapter presents a robust nonlinear H∞ Static Output Feedback control (SOF) design for steering control of the autonomous vehicle under actuator saturation, external disturbances, and taking into account the unavailability of the sideslip angle. The Takagi-Sugeno (T-S) approach is used to model both the lateral and lane keeping dynamics of autonomous vehicles. Based on the non-quadratic Lyapunov approach, a static output Feedback controller based on non-compensation parallel distributed technic the H∞ stabilization conditions without saturation are developed. Then, a polytopic representation of the actuator saturation is investigated to express the robust non-qudratiquc stabilisation conditions of Vehicle lateral dynamic control with input constraints in term of LMIs. Finally, the simulation results show that the proposed controllers can stabilize the closed-loop system and present great lane-keeping and external disturbance rejection performances

Fuzzy reference model H∞H_{\infty} integral fuzzy maximum power tracking of WECS based-on DFIG

International audienceThis paper presents a new fuzzy control design for maximum power point tracking (MPPT) of wind energy conversion systems (WECS) using a doubly fed induction generator (DFIG) based on H∞ optimal control. In the first place, a new nonlinear reference model is developed for describing the optimal dynamic of the doubly fed induction generator (DFIG). In the second place, the nonlinear dynamic behaviour of the real system and its reference model are represented by a Takagi-Sugeno (TS) fuzzy model. Then, using a fuzzy proportional integral state feedback controller, a novel MPPT strategy for DFIG-based wind energy conversion systems is investigated. The H∞ criteria performance is used to design a robust fuzzy proportional integral state controller under varying wind speed. The H∞ stabilisation conditions are generated and given in terms of linear matrix inequalities (LMI). The estimation of the largest set invariance conditions are proposed as a LMI convex optimization problem. Finally, simulation results show that the proposed fuzzy integral state controller gives a good disturbance rejection and MPPT rapid convergence in the presence of wind's gusts

SOS-Based Robust Control Design Subject to Actuator Saturation for Maximum Power Point Tracking of Photovoltaic System

International audienceThis chapter presents a robust maximum power point tracking (MPPT) control design for a standalone photovoltaic (PV) system subject to actuator saturation via polynomial Tackagi-Seguno (T-S) Fuzzy model based control approach. In order to optimize the installation cost, an output feedback controller is designed which reduce the number of sensors of current and voltage required. In addition, the problem of input saturation (duty cycle) is addressed by using constrained control approach. The stabilization conditions subject to H∞ performance of the closed-loop system are derived and solved in terms of linear matrix inequalities (LMI’s) and sum of squares (SOS) optimization problems. Simulation results are provided to show the effectiveness of the proposed controllers

H∞ Static Output Feedback Control for Path Tracking of Autonomous Vehicles with input constraints

This paper presents a robust nonlinear H ∞ Static Output Feedback control (SOF) design for steering control of the autonomous vehicle with input constraint, external disturbances, and the unavailability of the sideslip angle. To deal with the actuator saturation, a polytopic representation has been used. Then, based on a Takagi-Sugeno (T-S) model of the vehicle lateral dynamics in its discrete-time form and using a non-quadratic fuzzy Lyapunov function, stabilization conditions have been derived in terms of Linear Matrix Inequalities (LMIs). Finally, the robustness and the advantages of the proposed approach are demonstrated through different tests

Adaptive fuzzy observer based non-quadratic control for nonlinear system subject to actuator faults and saturation

International audienceThis paper provides a new non-quadratic stabilization conditions based on adaptive fuzzy observer for a class of Takagi-Sugeno (T-S) fuzzy systems subject to external disturbances and both actuator faults and saturation. Firstly, an observer based fault tolerant control (FTC) is proposed, not only to estimate both system states and actuator faults but also to compensate for the actuator faults and to stabilize the faulty system with input constraints. The saturation effect is transformed into dead-zone nonlinearity and the generalized sector bound condition is used to estimate the attraction domain. To less the conservatism of the quadratic Lyapunov technique, a proper integral structure based on the non-quadratic function is investigated. The H∞ criteria is considered and the robust stabilization conditions of the faulty closed-loop system are expressed as a linear matrix inequalities (LMIs) optimization problem. Finally, the robustness and the advantages of the proposed approach are demonstrated through a mixed CSTR and a numerical example

Tracking Power Photovoltaic System with Robust Polynomial Output Feedback Control Strategy

International audienceThis paper proposes a new robust stabilization conditions for Maximum Power Point Tracking (MPPT) control of photovoltaic (PV) systems based on polynomial fuzzy systems. In this scheme, an output feedback controller is exploited to reduce the number of needed sensors. The stabilization conditions are formulated in terms of sum-of-squares (SOS) conditions, which can be solved efficiently by using semidefinite program-ming (SDP) tool. The efficiency of the proposed controller is demonstrated through the simulation results

Fuzzy control for Electric Power Steering System with assist motor current input constraints

Friction and disturbances of the road are the main sources of nonlinearity in the Electric Power Steering (EPS) System. Consequently, conventional linear controllers design based on a simplified linear model of the EPS system will result in poor dynamic performance or system instability. On the other hand, a brush-type DC motor is more used in EPS control with an input current that is limited in practice. The control laws designed without taking into account the saturation effect may have undesirable consequences on the system stability. In this paper, a Takagi-Sugeno (T-S) fuzzy is used to represent the nonlinear behavior of an EPS system, and stabilization conditions for nonlinear EPS system with both constrained and saturated control input cases are proposed in terms of linear matrix inequalities (LMI). Simulation results show that both the saturated and constrained controls can stabilize the resulting closed-loop EPS system and provide a stable driving in the presence of nonlinear friction, disturbance of the road and actuator saturation

Fuzzy Control of DC-DC Converters with Input Constraint

This paper proposes a method for designing fuzzy control of DC-DC converters under actuator saturation. Because linear control design methods do not take into account the nonlinearity of the system, a T-S fuzzy model and a controller design approach is used. The designed control not only handles the external disturbance but also the saturation of duty cycle. The input constraint is first transformed into a symmetric saturation which is represented by a polytopic model. Stabilization conditions for the state feedback system of DC-DC converters under actuator saturation are established using the Lyapunov approach. The proposed method has been compared and verified with a simulation example

H ∞ fuzzy proportional integral state feedback controller of photovoltaic systems under asymmetric actuator constraints

International audienceThis paper presents a new strategy for a robust maximum power point (MPP) tracking fuzzy controller for photovoltaic (PV) systems subject to actuator asymmetric saturation. A DC-DC boost converter is used to connect a PV panel with an output load. The output voltage of the DC-DC boost converter can be adjusted by duty ratio that is limited between 0 and 1. The aim of our control design is to track the MPP under atmospheric condition changes and the presence of the asymmetric saturation of the duty ratio. To minimize tracking error and disturbance effect, the dynamic behaviour of a PV system and its reference model are described by using Takagi–Sugeno fuzzy models. Then, a constrained control based on a fuzzy PI state feedback controller is proposed. The H∞ control approach is used in control design and stability conditions of the closed-loop system are formulated and solved in terms of linear matrix inequalities. Finally, simulation results are given to show the tracking performance of the control design