On the interpretation and identification of dynamic Takagi-Sugenofuzzy models

Dynamic Takagi-Sugeno fuzzy models are not always easy to interpret, in particular when they are identified from experimental data. It is shown that there exists a close relationship between dynamic Takagi-Sugeno fuzzy models and dynamic linearization when using affine local model structures, which suggests that a solution to the multiobjective identification problem exists. However, it is also shown that the affine local model structure is a highly sensitive parametrization when applied in transient operating regimes. Due to the multiobjective nature of the identification problem studied here, special considerations must be made during model structure selection, experiment design, and identification in order to meet both objectives. Some guidelines for experiment design are suggested and some robust nonlinear identification algorithms are studied. These include constrained and regularized identification and locally weighted identification. Their usefulness in the present context is illustrated by examples

Optimal Control of Unknown Nonlinear System From Inputoutput Data

Optimal control designers usually require a plant model to design a controller. The problem is the controller\u27s performance heavily depends on the accuracy of the plant model. However, in many situations, it is very time-consuming to implement the system identification procedure and an accurate structure of a plant model is very difficult to obtain. On the other hand, neuro-fuzzy models with product inference engine, singleton fuzzifier, center average defuzzifier, and Gaussian membership functions can be easily trained by many well-established learning algorithms based on given input-output data pairs. Therefore, this kind of model is used in the current optimal controller design. Two approaches of designing optimal controllers of unknown nonlinear systems based on neuro-fuzzy models are presented in the thesis. The first approach first utilizes neuro-fuzzy models to approximate the unknown nonlinear systems, and then the feasible-direction algorithm is used to achieve the numerical solution of the Euler-Lagrange equations of the formulated optimal control problem. This algorithm uses the steepest descent to find the search direction and then apply a one-dimensional search routine to find the best step length. Finally several nonlinear optimal control problems are simulated and the results show that the performance of the proposed approach is quite similar to that of optimal control to the system represented by an explicit mathematical model. However, due to the limitation of the feasible-direction algorithm, this method cannot be applied to highly nonlinear and dimensional plants. Therefore, another approach that can overcome these drawbacks is proposed. This method utilizes Takagi-Sugeno (TS) fuzzy models to design the optimal controller. TS fuzzy models are first derived from the direct linearization of the neuro-fuzzy models, which is close to the local linearization of the nonlinear dynamic systems. The operating points are chosen so that the TS fuzzy model is a good approximation of the neuro-fuzzy model. Based on the TS fuzzy model, the optimal control is implemented for a nonlinear two-link flexible robot and a rigid asymmetric spacecraft, thus providing the possibility of implementing the well-established optimal control method on unknown nonlinear dynamic systems

Stabilizing Fuzzy Control via Output Feedback

The chapter presents new conditions suitable in design of stabilizing static as well as dynamic output controllers for a class of continuous-time nonlinear systems represented by Takagi-Sugeno models. Taking into account the affine properties of the TS model structure, and applying the fuzzy control scheme relating to the parallel-distributed output compensators, the sufficient design conditions are outlined in the terms of linear matrix inequalities. Depending on the proposed procedures, the Lyapunov matrix can be decoupled from the system parameter matrices using linear matrix inequality techniques or a fuzzy-relaxed approach can be applied to make closed-loop dynamics faster. Numerical examples illustrate the design procedures and demonstrate the performances of the proposed design methods

非線形システムに対する制御系設計と外乱抑制のための積分型リアプノフ関数アプローチ

電気通信大学202

Nouveaux schémas de commande et d'observation basés sur les modèles de Takagi-Sugeno

This thesis addresses the estimation and controller design for continuous-time nonlinear systems. The methodologies developed are based on the Takagi-Sugeno (TS) representation of the nonlinear model via the sector nonlinearity approach. All strategies intend to get more relaxed conditions.The results presented for controller design are split in two parts. The first part is about standard TS models under control schemes based on: 1) a quadratic Lyapunov function (QLF); 2) a fuzzy Lyapunov function (FLF); 3) a line-integral Lyapunov functions (LILF); 4) a novel non-quadratic Lyapunov functional (NQLF). The second part concerns to TS descriptor models. Two strategies are proposed: 1) within the quadratic framework, conditions based on a general control law and some matrix transformations; 2) an extension to the nonquadratic approach based on a line-integral Lyapunov function (LILF) using non-PDC control law schemes and the Finsler’s Lemma; this strategy offers parameter-dependent linear matrix inequality (LMI) conditions instead of bilinear matrix inequality (BMI) constraints for second-order systems. On the other hand, the problem of the state estimation for nonlinear systems via TS models is also addressed considering: a) the particular case where premise vectors are based on measured variables and b) the general case where premise vectors can be based on unmeasured variables. Several examples have been included to illustrate the applicability of the obtained results.Cette thèse aborde l'estimation et la conception de commande de systèmes non linéaires à temps continu. Les méthodologies développées sont basées sur la représentation Takagi-Sugeno (TS) du modèle non linéaire par l'approche du secteur non-linéarité. Toutes les stratégies ont l'intention d'obtenir des conditions plus détendu. Les résultats présentés pour la conception de commande sont divisés en deux parties. La première partie est environ sur les modèles TS standard au titre des schémas de commande basés sur: 1) une fonction de Lyapunov quadratique (QLF); 2) une fonction de Lyapunov floue (FLF); 3) une fonction de Lyapunov intégrale de ligne (LILF); 4) un nouveau fonctionnelle de Lyapunov non-quadratique (NQLF). La deuxième partie concerne des modèles TS descripteurs. Deux stratégies sont proposées: 1) dans le cadre quadratique, des conditions basées sur une loi de commande général et quelques transformations de matrices; 2) une extension de l'approche non quadratique basée sur LILF utilisant un schéma de commande non-PDC et le lemme du Finsler; cette stratégie offre conditions sur la forme d’inégalité matricielles linéaires (LMI) dépendant des paramètres au lieu des contraintes sur la forme d’inégalité matricielles bilinéaires (BMI) pour les systèmes de second ordre. D'autre part, le problème de l'estimation de l'état pour les systèmes non linéaires via modèles TS est également abordé considérant: a) le cas particulier où les vecteurs prémisses sont basées sur les variables mesurées et b) le cas général où les vecteurs prémisse peuvent être basés sur des variables non mesurées. Plusieurs exemples ont été inclus pour illustrer l'applicabilité des résultats obtenus