Xinchun Jia

Fuzzy

This paper investigates the fuzzy tracking control problem for a class of nonlinear networked control systems (NCSs) with a prescribed H infin tracking performance. Such NCSs consist of a nonlinear controlled plant, a tracked plant, sensors, a controller, and an actuator. A Takagi-Sugeno fuzzy model is employed to represent the nonlinear controlled plant in the NCSs, and a tracked plant is described by a linear stable reference model. In transmission, both network-induced delay and packet losses are considered. By the parallel distributed compensation technique, a novel tracking model of the nonlinear NCSs is first established. Based on Lyapunov stability theory, a control design method that guarantees the prescribed H infin tracking performance of the nonlinear NCSs is developed in terms of linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of our result.

H_{\infty}

This paper is concerned with network-based output tracking control for a T-S fuzzy system. An event-triggered communication scheme, under which the threshold depends on the latest successfully transmitted sampled-data, is introduced to reduce network resource utilization. Taking the event-triggered communication scheme and the asynchronous operation between the fuzzy system and the fuzzy controller, the resulting system is modeled as an asynchronous threshold-error-dependent system with an interval time-varying delay. A new delay-dependent criterion for L 2 -gain tracking performance of the asynchronous system is derived by applying the deviation bounds of asynchronous normalized membership functions. Based on this performance criterion, some criteria on the existence of the fuzzy tracking controller are established. A co-design algorithm is presented to obtain the control gains and the event-triggering parameters simultaneously. An example is given to illustrate the effectiveness of the proposed method.

Tracking Control for Nonlinear Networked Control Systems in T–S Fuzzy Model

This paper investigates network-based output tracking control for a T-S fuzzy system that can not be stabilized by a nondelayed fuzzy static output feedback controller, but can be stabilized by a delayed fuzzy static output feedback controller. By intentionally introducing a communication network that produces proper network-induced delays in the feedback control loop, a stable and satisfactory tracking control can be ensured for the T-S fuzzy system. Due to the presence of network-induced delays, the fuzzy system and the fuzzy tracking controller operate in an asynchronous way. Taking the asynchronous operation and network-induced delays into consideration, the network-based tracking control system is modeled as an asynchronous T-S fuzzy system with an interval time-varying delay. A new delaydependent criterion for L2-gain tracking performance is derived by using the deviation bounds of asynchronous normalized membership functions and a complete Lyapunov-Krasovskii functional. Applying a particle swarm optimization technique with the feasibility of the derived criterion, a novel design algorithm is presented to determine the minimum L2-gain tracking performance and control gains simultaneously. The effectiveness of the proposed method is illustrated by performing network-based output tracking control of a Duffing-Van der Pols oscillator.

Network-based output tracking control for T-S fuzzy systems using an event-triggered communication scheme

Abstract This paper investigates the positive effects of packet dropouts on network-based H ∞ control for a linear system that cannot be stabilized by a non-delayed static output feedback controller, but can be stabilized by a delayed static output feedback controller. By intentionally inserting a lossy network between the system and the controller, and embedding a logical packet-selecting algorithm that produces some packet dropouts in the actuator module, the networked control system is modeled as a system with an interval time-delay, which is stable with some nonzero time-varying delay, but is unstable without a time-delay. By constructing a complete Lyapunov–Krasovskii functional and discretizing both the lower bound and the upper bound of the interval delay, some new delay-dependent criteria for H ∞ performance and controller design are derived in terms of linear matrix inequalities. It is shown through an example that (i) proper packet dropouts can produce a stable control effect; (ii) utilizing the discretization of the lower delay bound can reduce the conservatism of the H ∞ performance criterion; and (iii) the proposed design result is effective in achieving satisfactory H ∞ control performance.

Network-Based Output Tracking Control for a Class of T-S Fuzzy Systems That Can Not Be Stabilized by Nondelayed Output Feedback Controllers

This paper considers H∞ tracking control for a class of network-based T-S fuzzy systems with available asynchronous constraints on membership functions. Using a fuzzy controller associated with available sampled-data of both premise variables and feedback states, the network-based control system is equivalent to an asynchronous T-S fuzzy system with an interval time-varying sawtooth delay. Notice that the routine relaxation methods in traditional T-S fuzzy systems can not be used for stability analysis and controller design of the asynchronous fuzzy system since common product terms of membership functions can not be grouped. Instead, a new relaxation method is proposed by using asynchronous constraints on fuzzy membership functions to introduce some free weighting matrices. By using the proposed relaxation method and a new discontinuous Lyapunov-Krasovskii functional, some criteria on H∞ tracking performance analysis and controller design are derived. Compared with the existing results, the derived criteria are of less conservatism and allow the existence of a network-based fuzzy controller with different gains, which can ensure a better H∞ tracking performance. The effectiveness of the proposed method is illustrated by an example.

Investigating the positive effects of packet dropouts on network-based H∞ control for a class of linear systems

This paper is concerned with network-based static output feedback tracking control for a class of systems that can not be stabilized by a static output feedback controller without a time-delay, but can be stabilized by a delayed static output feedback controller. For such systems, a stable and satisfactory tracking control can be achieved by intentionally introducing bounded network-induced delays in the feedback loop. A new discontinuous complete Lyapunov-Krasovskii functional is constructed to derive a criterion on H∞ tracking performance analysis. Using a particle swarm optimization technique with feasibility of the derived criterion, a novel design algorithm is proposed to search the minimum H∞ tracking performance and corresponding feedback gains. An illustrative example is given to show the effectiveness of the proposed method.

Tracking control for network-based T-S fuzzy systems with asynchronous constraints

This paper investigates network-based H∞ fuzzy control for a self-balancing two-wheeled inverted pendulum via a T-S fuzzy model. Due to the insertion of a communication network between the pendulum and a fuzzy controller, the fuzzy control is implemented in an asynchronous way. Unlike the existing works, asynchronous constraints on fuzzy membership functions are introduced in deriving some delay-dependent criteria for H∞ performance analysis and controller design. A numerical example shows that the proposed method using asynchronous constrains can stabilize the pendulum and achieve a better H∞ performance.

Network-based static output feedback tracking control for a class of systems using the positive effects of network-induced delays

This paper proposes a new approach to investigate the fault-tolerant control problem for Takagi-Sugeno fuzzy systems with actuator faults. The fault is considered to be time-varying and has a lower and upper bounds. By using the fault partitioning idea, a new fuzzy fault-tolerant control model is formulated, in which the actuator faults has several fault modes with fault parameters, and the switching among them is governed by a finite-state Markov chain with partly unknown transition probabilities. Then a fault-partitioning-dependent stability criterion is derived by combining the stability theory of Markov jump systems and the convex combination technique. The fault tolerant controller is designed in terms of linear matrix inequalities, which guarantees the faulty system is stochastically stable. A numerical example is given to illustrate the effectiveness of the proposed methods.

Network-based H ∞ fuzzy control for a self-balancing two-wheeled inverted pendulum

Abstract This paper deals with absolute stability of uncertain Lur’e systems with time-varying delay. By introducing a Lyapunov–Krasovskii functional related to a second-order Bessel–Legendre inequality, some absolute stability criteria are derived for the system under study. Different from some existing approaches, a remarkable feature of this paper is that the time-derivative of the Lyapunov–Krasovskii functional is estimated by a linear function rather than a quadratic function on the time-varying delay, thanks to the introduction of four extra vectors. As a result, the resulting absolute stability criteria are of less conservatism than some existing ones, which is demonstrated through three examples.

Fault-tolerant control for T-S fuzzy systems with actuator faults: A fault partitioning approach

Abstract This paper addresses the networked H∞ filtering problem for time-delay systems with quadratically inner-bounded nonlinearities, where the different output sub-vectors of the systems are sampled respectively by sensor groups with different sampling periods (i.e., multirate sampling or MRS). The multirate sampled data are transmitted to a filter through multiple communication channels with network-induced packet dropouts and time-varying transmission delays. Considering MRS’s asynchronous behavior, we propose a matching mechanism to synchronize the successfully transmitted sampled data of the nonlinear system and the sampled data of a filter. Based on the matched sampled data, two types of new continuous-time filters are presented to estimate the objective signal of the nonlinear system. In view of the fact that the lifting technique may fail to model the nonlinear system, the resultant filtering error systems are modeled as continuous-time nonlinear systems with several sawtooth delays. By the Lyapunov-Krasovskii functional approach, some sufficient conditions are obtained to ensure that the filtering error systems are stable with a prescribed H∞ performance level, and the design methods of the two filters are given. Finally, a numerical example shows the effectiveness of our proposed methods.