Xiaojun Ban

Design of polynomial fuzzy observer-controller with membership functions using unmeasurable premise variables for nonlinear systems

In this paper, the stability of polynomial fuzzy-model-based (PFMB) observer-control system is investigated via Lyapunov stability theory. The polynomial fuzzy observer with unmeasurable premise variables is designed to estimate the system states. Then the estimated system states are used for the state-feedback control of nonlinear systems. Although the consideration of the polynomial fuzzy model and unmeasurable premise variables enhances the applicability of the fuzzy-model-based (FMB) control strategy, it leads to non-convex stability conditions. Therefore, the refined completing square approach is proposed to derive convex stability conditions in the form of sum of squares (SOS) with less manually designed parameters. In addition, the membership functions of the polynomial observer-controller are optimized by the improved gradient descent method, which outperforms the widely applied parallel distributed compensation (PDC) approach according to a general performance index. Simulation examples are provided to verify the proposed design and optimization scheme.

A Gain-Scheduling Control Approach for Takagi–Sugeno Fuzzy Systems Based on Linear Parameter-Varying Control Theory

Due to the universal approximation capability of Takagi–Sugeno (T–S) fuzzy models for nonlinear dynamics, many control issues have been investigated based on fuzzy control theory. In this paper, a transformation procedure is proposed to convert fuzzy models into linear fractional transformation (LFT) models. Then, T–S fuzzy systems can be regarded as a special case of linear parameter-varying (LPV) systems which proved useful for nonlinear control problems. The newly established connection between T–S fuzzy models and LPV models provides a new perspective of the control problems for T–S fuzzy systems and facilitates the fuzzy control designs. Specifically, an output feedback gain-scheduling control design approach for T–S fuzzy systems is presented to ensure globally asymptotical stability and optimize H∞ performance of the closed-loop systems. The control synthesis problem is cast as a convex optimization problem in terms of linear matrix inequalities (LMIs). Two examples have been used to illustrate the efficiency of the proposed method.

Type-2 fuzzy logic control for underactuated truss-like robotic finger with comparison of a type-1 case1

Underactuated mechanical systems have their own difficulties within the control criterion. As a particular and complex underactuated mechanical system, underactuated truss-like robotic finger(UTRF) is studied by establishing its dynamic model. The control problems include high nonlinearity, model inaccuracy and uncertainties. Type-2 fuzzy logic control method is supposed to be a proper way to solve these problems, because fuzzy logic control itself does not depend on an accurate model of the controlled object, and type-2 fuzzy logic control is able to handle uncertainties. Based on a brief introduction on type-2 fuzzy logic systems, an interval type-2 fuzzy logic controller is designed for UTRF to accomplish the goal of stabilization in its equilibrium point. As an extension of the type-1 fuzzy, the performances of the proposed controller are compared with the type-1 one case to show the advantages of the type-2 fuzzy. Simulation results show that the designed interval type-2 fuzzy logic controller is correct and effective and has better performances than that of type-1 fuzzy control.

Gain-scheduling control of T-S fuzzy systems with actuator saturation

This paper presents a gain-scheduling output feedback control design method for T-S fuzzy systems with actuator saturation. Different from existing control design methods for T-S fuzzy systems, the basic idea of the proposed approach is to transform the T-S fuzzy model with saturation nonlinearity into the form of linear fractional transformation (LFT). Instead of commonly used fuzzy controllers, a gain-scheduled output feedback controller in the LFT form is introduced to stabilize the saturated T-S fuzzy system with guaranteed H∞ performance. The problem of establishing regional stability and performance of the closed-loop nonlinear system are tackled by using robust control techniques. As a result, the conservatism introduced by dealing with the quadratic terms of normalized fuzzy weighting functions can be avoided. The proposed controller synthesis problem is cast as a convex optimization in terms of linear matrix inequalities (LMIs) and can be solved efficiently. An example of balancing the inverted pendulum with bounded actuation is provided to illustrate the effectiveness of the proposed design method.

Gain scheduling output feedback control of linear plants with actuator saturation

Abstract From a gain-scheduling perspective, we will study the output feedback control problem for linear systems with some of control channels subject to actuator saturation. This includes the scenario of all actuator saturation as a special case. A feedback controller, expressed in the form of linear fractional transformation, is proposed to guarantee regional stability of the closed-loop system and provide disturbance/error attenuation measured in L 2 gain. The resulting synthesis condition is formulated as linear matrix inequalities (LMIs) and can be solved efficiently. Moreover, explicit formulas are derived to calculate controller gains, which reduces the computational cost compared to the method of directly solving the LMI-based condition. Numerical examples are provided to demonstrate the proposed saturation control approach.

LMI based control of a class of uncertain nonlinear systems with input rate saturation

Some systems suffer from not only input saturation but also input rate saturation due to special need or actuator limitation. This paper investigates the regulation control of a class of uncertain nonlinear systems with input rate saturation. By transformation, the rate saturation of input can be converted to the state and input constraints of certain linear systems. An LMI based method can then be introduced and improved to solve the transformed problem. The optimized state-feedback controller is robust to parametric uncertainties. It can guarantee the exponential stability of the original system without external disturbances, and can make the state trajectories exponentially converge to a defined region with external disturbances. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

A new design method of H ∞ state feedback gain-scheduling controller for T-S fuzzy systems

In this article, a new systematic synthesis method is proposed to design a full state feedback gain-scheduling controller for Takagi-Sugeno (T-S) fuzzy plants. Both the stability and H∞ performance of the closed-loop system are considered. More specifically, by using the information that the degree of membership function is constrained within the interval [0, 1], the T-S fuzzy plant is transformed into the form of linear fractional transformation (LFT). Within the framework of LFT, the problem of stability and H∞ performance for the T-S fuzzy system can be reformulated into a convex optimization problem which can be approached by solving a set of linear matrix inequalities. A numerical example is provided to illustrate the effectiveness of the proposed method.

Stability analysis for a type of T-S fuzzy control systems using integral quadratic constraints

Recently, the well-known circle criterion and Popov criterion are introduced to investigate the stability of a type of T-S fuzzy control systems. Although both the two corresponding stability conditions have elegant graphical interpretations, the relation of them is not well studied. In this paper, we try to explain the two conditions by a new unified stability condition, which is based on the integral quadratic constrains (IQCs). In addition, the proposed method is less conservative than the circle criterion and Popov criterion based methods. A numerical example is given to demonstrate how to use this criterion in analyzing the T-S fuzzy control systems.

Stability Analysis of a Type of T-S Fuzzy Control Systems Using Off-Axis Circle Criterion

Abstract In this paper, based on the off-axis circle criterion, a sufficient condition with a simple graphical explanation is derived to analyze the global asymptotic stability of a type of Takagi-Sugeno (T-S) fuzzy control systems in case of different constant reference inputs. Three numerical examples are given to demonstrate how to use the proposed method in analyzing the T-S fuzzy control systems.

Graphical L2-stability analysis of Takagi--Sugeno control systems in the frequency domain

In this paper, the upper bound of the L2-gain of the continuous-time SISO Takagi--Sugeno (T--S) fuzzy system is first graphically obtained in the frequency domain. Based on this upper bound of the L2-gain, the L2-stability of the above T--S fuzzy control system is next investigated by using the small gain theorem and circle criterion. Two sufficient conditions are derived, which can be employed to graphically investigate the L2-stability of certain kind of T--S fuzzy control system in the frequency domain. One numerical example is presented to illustrate how the L2-stability of the simplified continuous-time T--S fuzzy system can be graphically examined.