ABSTRACT
This article explores the observer-based feedback control problem for a nonlinear hyperbolic partial differential equations (PDEs) system. Initially, the polynomial fuzzy hyperbolic PDEs (PFHPDEs) model is established through the utilization of the fuzzy identification approach, derived from the nonlinear hyperbolic PDEs model. Various types of state estimation and controller design problems for the polynomial fuzzy PDEs system are discussed concerning the state estimation problem. To investigate the relaxed stability problem, Euler's homogeneous theorem, Lyapunov-Krasovskii functional with polynomial matrices (LKFPM), and the sum-of-squares (SOSs) approach are adopted. The exponential stabilization condition is formulated in terms of the spatial-derivative-SOSs (SD-SOSs). Additionally, a segmental algorithm is developed to find the feasible solution for the SD-SOS condition. Finally, a hyperbolic PDEs system and several numerical examples are provided to illustrate the validity and effectiveness of the proposed results.
ABSTRACT
In this article, a novel interval type-2 Takagi-Sugeno fuzzy c -regression modeling method with a modified distance definition is proposed. The modified distance definition is developed to describe the distance between each data point and the local type-2 fuzzy model. To improve the robustness of the proposed identification method, a modified objective function is presented. In addition, different from most previous studies that require numerous free parameters to be determined, an interval type-2 fuzzy c -regression model is developed to reduce the number of such free parameters. Furthermore, an improved ratio between the upper and lower weights is proposed based on the upper and lower membership function with each input data, and the ordinary least-squares method is adopted to establish the type-2 fuzzy model. The Box-Jenkins model and two numerical models are given to illustrate the effectiveness and robustness of the proposed results.
Subject(s)
Algorithms , Fuzzy Logic , Computer SimulationABSTRACT
This article addresses the H∞ stabilization problems for a class of nonlinear distributed parameter systems which is described by the first-order hyperbolic partial differential equations (PDEs). First, the first-order hyperbolic PDE systems are identified as a polynomial fuzzy PDE system and the polynomial fuzzy controller for the polynomial fuzzy PDE system is proposed. By utilizing the proposed homogeneous polynomial Lyapunov functional, Euler's homogeneous function theorem, and the proposed theorems, a spatial derivative sum-of-squares (SDSOS) exponential stabilization condition is proposed. In addition, a recursive algorithm for the SDSOS exponential stabilization condition is developed to find the feasible solution. Furthermore, in order to reduce the conservatism of the proposed results, a relaxed H∞ stabilization condition for the polynomial fuzzy PDE system is provided. Finally, the nonisothermal plug-flow reactor (PFR) is used to demonstrate the effectiveness and feasibility of the proposed method.
ABSTRACT
This article presents a novel path-following-method-based polynomial fuzzy control design. By examining the stabilization problem, the nonconvex stabilization criterion represented in terms of bilinear sum-of-squares (SOS) constraints is proposed to complement the existing convex stabilization criteria. Based on the polynomial Lyapunov function and considering the operation domain, the stabilization control is designed with a systematic region of attraction (ROA) analysis method. Since the proposed stabilization criterion remains in nonconvex form, the conservativeness caused by the transformation from nonconvex (bilinear SOS) constraints into convex (SOS) constraints can be avoided. Moreover, the restriction on the Lyapunov function candidates for the convex transformation in the literature does not exist in the proposed nonconvex stabilization criterion. The stabilization analysis for polynomial fuzzy control systems is concerned with the double fuzzy summation problem that can be treated as the copositivity problem. Therefore, the SOS-based copositive relaxation technique is applied for the proposed stabilization criterion. Since the proposed nonconvex stabilization criterion is represented in terms of bilinear SOS constraints, the path-following method is employed for solving the bilinear SOS problem. Finally, design examples are provided to demonstrate that the proposed nonconvex stabilization criterion complements the existing convex stabilization criteria.
ABSTRACT
In this paper, a detail design procedure of the real-time trajectory tracking for the nonholonomic wheeled mobile robot (NWMR) is proposed. A 9-axis micro electro-mechanical systems (MEMS) inertial measurement unit (IMU) sensor is used to measure the posture of the NWMR, the position information of NWMR and the hand-held device are acquired by global positioning system (GPS) and then transmit via radio frequency (RF) module. In addition, in order to avoid the gimbal lock produced by the posture computation from Euler angles, the quaternion is utilized to compute the posture of the NWMR. Furthermore, the Kalman filter is used to filter out the readout noise of the GPS and calculate the position of NWMR and then track the object. The simulation results show the posture error between the NWMR and the hand-held device can converge to zero after 3.928 seconds for the dynamic tracking. Lastly, the experimental results show the validation and feasibility of the proposed results.
ABSTRACT
The main theme of this paper is to present robust fuzzy controllers for a class of discrete fuzzy bilinear systems. First, the parallel distributed compensation method is utilized to design a fuzzy controller, which ensures the robust asymptotic stability of the closed-loop system and guarantees an H(infinity) norm-bound constraint on disturbance attenuation for all admissible uncertainties. Second, based on the Schur complement and some variable transformations, the stability conditions of the overall fuzzy control system are formulated by linear matrix inequalities. Finally, the validity and applicability of the proposed schemes are demonstrated by a numerical simulation and the Van de Vusse example.
