Thierry Marie Guerra

LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form

This paper presents the stabilization analysis for a class of nonlinear systems that are represented by a Takagi and Sugeno (TS) discrete fuzzy model (Takagi and Sugeno IEEE Trans. Systems Man Cybern. 15(1)(1985)116). The main result given here concerns their stabilization using new control laws and new nonquadratic Lyapunov functions. New relaxed conditions and linear matrix inequality-based design are proposed that allow outperforming previous results found in the literature. Two examples are also provided to demonstrate the efficiency of the approaches.

Control of a parallel hybrid powertrain: optimal control

Control strategies for hybrid powertrains are algorithms that choose the power split between the engine and motor of a hybrid vehicle in order to minimize the fuel consumption and/or emissions. The goal of this paper is to propose an efficient tool to evaluate minimal fuel consumption that is achievable in simulation. Several approaches have been proposed, using heuristics (Delprat et al. 1999) or dynamic programming (Brahma et al., 2000; Rimaux et al., 1999). One drawback of these approaches is the huge amount of time required to obtain solutions. The approach described here is based on optimal control theory (Lewis & Syrmos, 1995) and avoids this drawback. Moreover, it can be easily applied to a large family of parallel arrangements.

Perspectives of fuzzy systems and control

Although fuzzy control was initially introduced as a model-free control design method based on the knowledge of a human operator, current research is almost exclusively devoted to model-based fuzzy control methods that can guarantee stability and robustness of the closed-loop system. State-of-the-art techniques for identifying fuzzy models and designing model-based controllers are reviewed in this article. Attention is also paid to the role of fuzzy systems in higher levels of the control hierarchy, such as expert control, supervision and diagnostic systems. Open issues are highlighted and an attempt is made to give some directions for future research.

Equivalent consumption minimization strategy for parallel hybrid powertrains

Hybrid vehicles use at least two energy sources for their propelling. Usually an electric motor is used with an IC engine. Hybrid vehicles are expected to be less polluting and to have a lower fuel consumption than conventional vehicles. This paper presents an algorithm which chooses the power split between the motor and the engine in order to minimize the fuel consumption. First of all, the prototype built at the LAMIH is presented, then the equivalent consumption minimization strategy is described. First results show that a 17.5% of fuel reduction can be achieved for the CEN speed cycle.

Nonquadratic Stabilization Conditions for a Class of Uncertain Nonlinear Discrete Time TS Fuzzy Models: A New Approach

The discrete-time uncertain nonlinear models are considered in a Takagi-Sugeno form and their stabilization is studied through a non- quadratic Lyapunov function. The classical conditions consider a one- sample variation, here, the main results are obtained considering k samples variation, i.e., Deltak V(x(t)) = V(x(t + k)) - V(x(t)). The results are shown to always include the classical cases, and several examples illustrate the effectiveness of the approach.

Adaptive fuzzy control of a class of MIMO nonlinear systems

This paper presents two indirect adaptive fuzzy control schemes for a class of uncertain continuous-time multi-input multi-output nonlinear dynamic systems. Within these schemes, fuzzy systems are employed to approximate the plants unknown nonlinear functions and robustifying control terms are used to compensate for approximation errors. By using a regularized matrix inverse, a stable well-defined adaptive controller is firstly investigated. Then, in order to obtain an adaptive controller not depending upon any parameter initialization conditions and to relax the requirement of bounding parameter values, a second adaptive controller is proposed. All parameter adaptive laws and robustifying control terms are derived based on Lyapunov stability analysis so that, under appropriate assumptions, semi-global stability and asymptotic convergence to zero of tracking errors can be guaranteed. Simulations performed on a two-link robot manipulator illustrate the approach and exhibit its performance.

Adaptive fuzzy control of a class of SISO nonaffine nonlinear systems

This paper presents a direct adaptive fuzzy control scheme for a class of uncertain continuous-time single-input single-output (SISO) nonaffine nonlinear dynamic systems. Based on the implicit function theory, the existence of an ideal controller, that can achieve control objectives, is firstly shown. Since the implicit function theory guarantees only the existence of the ideal controller and does not provide a way for constructing it, a fuzzy system is employed to approximate this unknown ideal control law. The adjustable parameters in the used fuzzy system are updated using a gradient descent adaptation algorithm. This algorithm is designed in order to minimize a quadratic cost function of the error between the unknown ideal implicit controller and the used fuzzy control law. The stability analysis of the closed-loop system is performed using a Lyapunov approach. In particular, it is shown that the tracking error converges to a neighborhood of zero. The effectiveness of the proposed adaptive control scheme is demonstrated through the simulation of a simple nonaffine nonlinear system.

Simulation and assessment of power control strategies for a parallel hybrid car

Abstract The aim of this paper is to propose a power control strategy for hybrid electrical vehicles. This strategy uses a fuel consumption criterion with battery charge sustaining. It is based on an instantaneous minimization of the equivalent fuel flow. Two comparisons are performed to evaluate the proposed strategy. The first one uses the loss minimization strategy of Seiler and Schröder [1], which appears to be realistic and efficient for real-time control. This strategy is also based on an instantaneous optimization and allows the battery state of charge to be taken into account. The second comparison is made with an optimal solution found for a given driving schedule. Although not realistic for real-time control, this solution is derived through a global optimization algorithm, the well-known simulated annealing method.

Generalized Nonquadratic Stability of Continuous-Time Takagi–Sugeno Models

This paper provides generalized nonquadratic stability conditions for continuous-time nonlinear models in the Takagi-Sugeno (TS) form obtained by sector-nonlinearity approach. Should global quadratic stability fail for a given nonlinear model, the proposed approach allows the obtaining of progressively better estimations of the stability domain via local asymptotic conditions in the form of linear-matrix inequalities (LMIs), which are efficiently solved by convex optimization techniques. Illustrative examples are presented to emphasize the broadening capabilities of the new stability analysis.

LMI Solution for Robust Static Output Feedback Control of Discrete Takagi–Sugeno Fuzzy Models

This paper deals with the stabilization problem of discrete-time Takagi-Sugeno (T-S) fuzzy systems via static output controller (SOFC). The proposed method uses the descriptor approach to study this problem and leads to strict linear matrix inequality (LMI ) formulation. In contrast with the existing results, the method allows coping with multiple output matrices, as well as uncertainties. Moreover, the new proposed method can lead to less conservative results by introducing slack variables and considering multiple Lyapunov matrices. A robust SOFC for uncertain T-S fuzzy models is also derived in strict LMI terms. Numerical examples are given to illustrate the effectiveness of the proposed design results.