Xinping Guan

Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays

This study introduces a guaranteed cost control method for nonlinear systems with time-delays which can be represented by Takagi-Sugeno (T-S) fuzzy models with time-delays. The state feedback and generalized dynamic output feedback approaches are considered. The generalized dynamic output feedback controller is presented by a new fuzzy controller architecture which is of dual indexed rule base. It considers both the dynamic part and the output part of T-S fuzzy model which guarantees that the controller without any delay information can stabilize time-delay T-S fuzzy systems. Based on delay-dependent Lyapunov functional approach, some sufficient conditions for the existence of state feedback controller are provided via parallel distributed compensation (PDC) first. Second, the corresponding conditions are extended into the generalized dynamic output feedback closed-loop system via so-called generalized PDC technique. The upper bound of time-delay can be obtained using convex optimization such that the system can be stabilized for all time-delays whose sizes are not larger than the bound. The minimizing method is also proposed to search the suboptimal upper bound of guaranteed cost function. The effectiveness of the proposed method can be shown by the simulation examples.

Robust backstepping control for a class of time delayed systems

In this note, the problem of robust output feedback control for a class of nonlinear time delayed systems is considered. The systems considered are in strict-feedback form. State observer is first designed, then based on the observed states the controller is designed via backstepping method. Both the designed observer and controller are independent of the time delays. Based on Lyapunov stability theory, we prove that the constructed controller can render the closed-loop system asymptotically stable. Simulation results further verify the effectiveness of the proposed approach.

Adaptive Fuzzy Output-Feedback Controller Design for Nonlinear Time-Delay Systems With Unknown Control Direction

In this paper, the robust-control problem is investigated for a class of uncertain nonlinear time-delay systems via dynamic output-feedback approach. The considered system is in the strict-feedback form with unknown control direction. A full-order observer is constructed with the gains computed via linear matrix inequality at first. Then, with the bounds of uncertain functions known, we design the dynamic output-feedback controller such that the closed-loop system is asymptotically stable. Furthermore, when the bound functions of uncertainties are not available, the adaptive fuzzy-logic system is employed to approximate the uncertain function, and the corresponding output-feedback controller is designed. It is shown that the resulting closed-loop system is stable in the sense of semiglobal uniform ultimate boundedness. Finally, simulations are done to verify the feasibility and effectiveness of the obtained theoretical results.

Robust Output Feedback Tracking Control for Time-Delay Nonlinear Systems Using Neural Network

In this paper, the problem of robust output tracking control for a class of time-delay nonlinear systems is considered. The systems are in the form of triangular structure with unmodeled dynamics. First, we construct an observer whose gain matrix is scheduled via linear matrix inequality approach. For the case that the information of uncertainties bounds is not completely available, we design an observer-based neural network (NN) controller by employing the backstepping method. The resulting closed-loop system is ensured to be stable in the sense of semiglobal boundedness with the help of changing supplying function idea. The observer and the controller designed are both independent of the time delays. Finally, numerical simulations are conducted to verify the effectiveness of the main theoretic results obtained

Technical communique: Robust controller design of a class of nonlinear time delay systems via backstepping method

The robust control problem is investigated for nonlinear time delay systems with triangular structure. The uncertain delay disturbances are bounded by nonlinear functions with unknown coefficients. Via the backstepping method, we construct a state feedback controller with the help of Razumikhin lemma. Based on Lyapunov stability theory, we show that the resulting closed-loop system is UUB stable.

Delay-Dependent Stability Analysis and Controller Synthesis for Discrete-Time T–S Fuzzy Systems With Time Delays

Based on a novel delay-dependent piecewise Lyapunov-Krasovskii functional (DPLKF), this paper presents delay-dependent stability analysis and synthesis methods for discrete-time Takagi-Sugeno (T-S) fuzzy systems with time delays. It is shown that the stability and stabilization with some required performance can be established for the closed loop control system if there exists a DPLKF and that the DPLKF and the corresponding controller can be obtained by solving a set of linear matrix inequalities (LMIs). New algorithms have also been developed to obtain the maximum value of the allowable constant delay and the suboptimal performance upper bound. An example is finally presented to demonstrate the efficiency and advantage of the proposed methods

Output Feedback Stabilization for Time-Delay Nonlinear Interconnected Systems Using Neural Networks

In this paper, dynamic output feedback control problem is investigated for a class of nonlinear interconnected systems with time delays. Decentralized observer independent of the time delays is first designed. Then, we employ the bounds information of uncertain interconnections to construct the decentralized output feedback controller via backstepping design method. Based on Lyapunov stability theory, we show that the designed controller can render the closed-loop system asymptotically stable with the help of the changing supplying function idea. Furthermore, the corresponding decentralized control problem is considered under the case that the bounds of uncertain interconnections are not precisely known. By employing the neural network approximation theory, we construct the neural network output feedback controller with corresponding adaptive law. The resulting closed-loop system is stable in the sense of semiglobal boundedness. The observers and controllers constructed in this paper are independent of the time delays. Finally, simulations are done to verify the effectiveness of the theoretic results obtained.

Adaptive Tracking Controller Design of Nonlinear Systems With Time Delays and Unknown Dead-Zone Input

This paper focuses on the tracking control problem for a class of nonlinear system with time delays and dead-zone input. The nonsymmetric dead-zone input case is considered without the knowledge of the dead zone parameters. The time delay uncertainties are bounded by a nonlinear function with unknown coefficients. By constructing a novel Lyapunov functional, we design a simple and smooth adaptive state feedback controller. It is shown that the solution of the resulting closed-loop error system converges to an adjustable region exponentially. Finally, numerical examples are included to show the effectiveness of the theoretical results.

Backstepping Control for Nonlinear Systems With Time Delays and Applications to Chemical Reactor Systems

The state feedback control problem is addressed for a class of nonlinear time-delay systems. The time delays appear in all state variables of the nonlinear system, which brings a challenging issue for controller design. With an introduced new Lyapunov-Krasovskii functional, we develop a novel control strategy. With the help of a backstepping method, we design a memoryless state feedback controller, which does not need the precise knowledge of time delays. It is rigorously proved that the closed-loop system is asymptotically stable. Chemical reactor plants are typical nonlinear systems with time delays. We apply the developed method to the control design of a two-stage chemical reactor with delayed recycle streams, and the simulation results verify the effectiveness of the main results.

Improving Automatic Detection of Defects in Castings by Applying Wavelet Technique

X-ray-based inspection systems are a well-accepted technique for identification and evaluation of internal defects in castings, such as cracks, porosities, and foreign inclusions. In this paper, some images showing typical internal defects in the castings derived from an X-ray inspection system are processed by some traditional methods and wavelet technique in order to facilitate automatic detection of these internal defects. An X-ray inspection system used to detect the internal defects of castings and the typical internal casting defects is first addressed. Second, the second-order derivative and morphology operations, the row-by-row adaptive thresholding, and the two-dimensional (2-D) wavelet transform methods are described as potentially useful processing techniques. The first method can effectively detect air-holes and foreign-inclusion defects, and the second one can be suitable for detecting shrinkage cavities. Wavelet techniques, however, can effectively detect the three typical defects with a selected wavelet base and multiresolution levels. Results indicate that 2-D wavelet transform is a powerful method to analyze images derived from X-ray inspection for automatically detecting typical internal defects in the casting