Optimal and stable fuzzy controllers for nonlinear systems based on an improved genetic algorithm

Dept. of Electron. & Inf. Eng., Hong Kong Polytech. Univ., Kowloon, China
IEEE Transactions on Industrial Electronics (Impact Factor: 6.5). 03/2004; DOI: 10.1109/TIE.2003.821898
Source: IEEE Xplore

ABSTRACT This paper addresses the optimization and stabilization problems of nonlinear systems subject to parameter uncertainties. The methodology is based on a fuzzy logic approach and an improved genetic algorithm (GA). The TSK fuzzy plant model is employed to describe the dynamics of the uncertain nonlinear plant. A fuzzy controller is then obtained to close the feedback loop. The stability conditions are derived. The feedback gains of the fuzzy controller and the solution for meeting the stability conditions are determined using the improved GA. In order to obtain the optimal fuzzy controller, the membership functions are further tuned by minimizing a defined fitness function using the improved GA. An application example on stabilizing a two-link robot arm will be given.

  • [Show abstract] [Hide abstract]
    ABSTRACT: This study investigates the stability of parameter-dependent polynomial-fuzzy-model-based (PDPFMB) control systems. A parameter-dependent polynomial fuzzy model is proposed to represent a non-linear plant. A parameter-dependent polynomial fuzzy controller is then employed to stabilise the non-linear plant. The stability of PDPFMB control systems is investigated using the sum-of-squares (SOS) technique based on a parameter-dependent Lyapunov function candidate. With the consideration of the information of system parameters, parameter-dependent SOS-based stability conditions are obtained to determine the system stability and polynomial feedback gains. A feasible solution to the stability conditions can be obtained numerically using the third-party Matlab toolbox SOSTOOLS. Unlike the membership functions, as the system parameters are not single signed functions, the traditional analysis approach obtaining the stability conditions cannot be applied. Instead, the membership functions and system parameters are considered as symbolic variables for the construction of the parameter-dependent SOS-based stability conditions. A simulation example is given to demonstrate the merits of the proposed approach.
    IET Control Theory and Applications 07/2012; 6(11):1645 - 1653. · 1.72 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: This paper considers the problem of multiobjective fuzzy control design for a class of nonlinear spatially distributed processes (SDPs) described by parabolic partial differential equations (PDEs), which arise naturally in the modeling of diffusion-convection-reaction processes in finite spatial domains. Initially, the modal decomposition technique is applied to the SDP to formulate it as an infinite-dimensional singular perturbation model of ordinary differential equations (ODEs). An approximate nonlinear ODE system that captures the slow dynamics of the SDP is thus derived by singular perturbations. Subsequently, the Takagi-Sugeno fuzzy model is employed to represent the finite-dimensional slow system, which is used as the basis for the control design. A linear matrix inequality (LMI) approach is then developed for the design of multiobjective fuzzy controllers such that the closed-loop SDP is exponentially stable, and an L2 performance bound is provided under a prescribed H∞ constraint of disturbance attenuation for the slow system. Furthermore, using the existing LMI optimization technique, a suboptimal fuzzy controller can be obtained in the sense of minimizing the L2 performance bound. Finally, the proposed method is applied to the control of the temperature profile of a catalytic rod.
    IEEE Transactions on Industrial Informatics 11/2012; 8(4):860-868. · 8.79 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: This study proposes a new category of fuzzy-observer-based controllers to stabilise non-linear plants based on the fuzzy-model-based control approach. A fuzzy observer is proposed to estimate the system states of the non-linear plant and a fuzzy-observer-based controller using the estimated system states for feedback compensation is proposed to close the feedback loop for the control process. It does not require that the fuzzy observer and fuzzy-observer-based controller have to share the same premise membership functions and the same number of rules of the Takagi-Sugeno fuzzy model. A membership-function-dependent stability analysis approach is proposed to investigate the stability of the fuzzy-observer-based control system based on the Lyapunov method. A set of bilinear matrix inequalities (BMIs) is obtained to guarantee the system stability and control synthesis. To find a feasible solution of the BMI-based stability conditions, a solution-searching algorithm, which combines global searching algorithm and convex programming techniques, is proposed. A simulation example is provide to demonstrate its capability of relaxing control design flexibility and effectiveness.
    IET Control Theory and Applications 03/2013; 7(5):663-672. · 1.72 Impact Factor