Stability analysis for affine fuzzy system based on fuzzy Lyapunov functions

An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local model. Thus, the stability analysis method of the homogeneous fuzzy system can be used for reference. Stability conditions are derived in terms of linear matrix inequalities based on the fuzzy Lyapunov functions and the modified common Lyapunov functions, respectively. The results demonstrate that the stability result based on the fuzzy Lyapunov functions is less conservative than that based on the modified common Lyapunov functions via numerical examples. Compared with the method which does not expand the consequent part, the proposed method is simpler but its feasible region is reduced. Finally, in order to expand the application of the fuzzy Lyapunov functions, the piecewise fuzzy Lyapunov function is proposed, which can be used to analyze the stability for triangular or trapezoidal membership functions and obtain the stability conditions. A numerical example validates the effectiveness of the proposed approach.

Stabilization design for continuous-time Takagi-Sugeno fuzzy systems based on new relaxed conditions

This paper deals with the problem of stabilization design for a class of continuous-time Takagi-Sugeno（T-S）fuzzy systems.New stabilization conditions are derived based on a relaxed approach in which both fuzzy Lyapunov functions and staircase membership functions are used.Through the staircase membership functions approximating the continuous membership functions of the given fuzzy model,the information of the membership functions can be brought into the stabilization design of the fuzzy systems,thereby significantly reducing the conservativeness in the existing stabilization conditions of the T-S fuzzy systems.Unlike some previous fuzzy Lyapunov function approaches reported in the literature,the proposed stabilization conditions do not depend on the time-derivative of the membership functions that may be the main source of conservatism when considering fuzzy Lyapunov functions analysis.Moreover,conditions for the solvability of the controller design are written in the form of linear matrix inequalities,but not bilinear matrix inequalities,which are easier to be solved by convex optimization techniques.A simulation example is given to demonstrate the validity of the proposed approach.

A Novel Control Algorithm for Interaction Between Surface Waves and A Permeable Floating Structure

An analytical solution is undertaken to describe the wave-induced flow field and the surge motion of a permeable platform structure with fuzzy controllers in an oceanic environment.In the design procedure of the controller,a parallel distributed compensation（PDC） scheme is utilized to construct a global fuzzy logic controller by blending all local state feedback controllers.A stability analysis is carried out for a real structure system by using Lyapunov method.The corresponding boundary value problems are then incorporated into scattering and radiation problems.They are analytically solved,based on separation of variables,to obtain series solutions in terms of the harmonic incident wave motion and surge motion.The dependence of the wave-induced flow field and its resonant frequency on wave characteristics and structure properties including platform width,thickness and mass has been thus drawn with a parametric approach.From which mathematical models are applied for the wave-induced displacement of the surge motion.A nonlinearly inverted pendulum system is employed to demonstrate that the controller tuned by swarm intelligence method can not only stabilize the nonlinear system,but has the robustness against external disturbance.

New approaches to relaxed stabilization conditions and H-infinity control designs for T-S fuzzy systems

This paper focuses on the problem of fuzzy control for a class of continuous-time T-S fuzzy systems. New methods of stabilization design and H-infinity control are derived based on a relaxed approach in which both fuzzy Lyapunov functions and staircase membership functions are used. Through the staircase membership functions approx- imating the continuous membership functions of the given fuzzy model, the membership functions can be brought into the design conditions of fuzzy systems, thereby significantly reducing the conservativeness in the recent fuzzy controller design methods. Unlike some previous fuzzy Lyapunov function approaches reported in the literatures, the proposed design techniques of stabilization and H-infinity control do not depend on the time-derivative of the membership functions that may be pointed out as the main source of conservatism when considering fuzzy Lyapunov functions analysis. Moreover, conditions for the solvability of the controller design given here are written in the form of linear matrix inequalities, but not bilinear matrix inequalities, which are easier to be solved by convex optimization techniques. Simulation examples are given to demonstrate the validity and applicability of the proposed approaches.

Fuzzy adaptive tracking control within the full envelope for an unmanned aerial vehicle

Motivated by the autopilot of an unmanned aerial vehicle（UAV） with a wide flight envelope span experiencing large parametric variations in the presence of uncertainties, a fuzzy adaptive tracking controller（FATC） is proposed. The controller consists of a fuzzy baseline controller and an adaptive increment, and the main highlight is that the fuzzy baseline controller and adaptation laws are both based on the fuzzy multiple Lyapunov function approach, which helps to reduce the conservatism for the large envelope and guarantees satisfactory tracking performances with strong robustness simultaneously within the whole envelope. The constraint condition of the fuzzy baseline controller is provided in the form of linear matrix inequality（LMI）, and it specifies the satisfactory tracking performances in the absence of uncertainties. The adaptive increment ensures the uniformly ultimately bounded（UUB） predication errors to recover satisfactory responses in the presence of uncertainties. Simulation results show that the proposed controller helps to achieve high-accuracy tracking of airspeed and altitude desirable commands with strong robustness to uncertainties throughout the entire flight envelope.