Imperfect Premise Matching based Fuzzy Control with Passive Constraints for Discrete Time-Delay Multiplicative Noised Stochastic Nonlinear Systems

Cheung-Chieh Ku,Wen-Jer Chang,Chun-Hung Lin,Yao-Chung Chang 제어·로봇·시스템학회 2013 International Journal of Control, Automation, and Vol.11 No.3

This paper investigates a fuzzy controller design method for discrete-time nonlinear stochastic time-delay systems which are presented by the Takagi-Sugeno (T-S) fuzzy model with multiplicative noises. Utilizing the proposed design method, the fuzzy controller can be carried out via not only state feedback scheme but also output feedback scheme. Both of them are accomplished by the concept of imperfect premise matching (IPM). For discussing the stabilization problem, the Lyapunov-Krasovskii function and passivity theory are applied to derive the sufficient conditions. Moreover, the discrete Jensen inequality is employed to decrease the conservatism of the proposed method. Finally, a numerical example for the control of a nonlinear time-delay pendulum system is provided to show the effectiveness and usefulness of the proposed design method.

Robust H∞ Control of Uncertain Stochastic Systems with Time-varying Interval Delays

Cheung-Chieh Ku,Guan-Wei Chen 제어·로봇·시스템학회 2018 International Journal of Control, Automation, and Vol.16 No.1

A robust delay-dependent stability criterion for discrete-time uncertain stochastic systems is proposed to achieve asymptotical stability and H∞ performance in this paper. Based on modeling approaches, Linear Parameter Varying (LPV) system with multiplicative noise term is built to represent uncertain stochastic systems. Moreover, state and input delays are considered as two individual time-varying interval cases for general effect. Employing a novel Lyapunov-Krasovskii function, Jensen inequality and transform technology, some relaxed sufficient conditions are derived into Linear Matrix Inequality (LMI) forms to apply convex optimization algorithm. Through solving the derived conditions, Gain-Scheduled (GS) controller can be designed such that robust asymptotical stability and H∞ performance of closed-loop system are achieved in the mean square. At last, two numerical examples are provided to demonstrate applicability and effectiveness of this paper.

Gain-Scheduled Controller Design for Discrete-Time Linear Parameter Varying Systems with Multiplicative Noises

Cheung-Chieh Ku,Guan-Wei Chen 제어·로봇·시스템학회 2015 International Journal of Control, Automation, and Vol.13 No.6

In this paper, two technologies to design gain-scheduled controller are proposed for discretetime Linear Parameter Varying (LPV) systems with multiplicative noises. In the considered systems, the time-varying parameters are proposed to describe the uncertainties. And, the added multiplicative noise term is applied to describe the stochastic behaviors of the system. Furthermore, the gainscheduled design scheme is applied to deal with the stabilization problem of the LPV systems with multiplicative noises. Through the parameter-independent and parameter-dependent Lyapunov functions, the corresponding sufficient conditions are derived to discuss the stability and stabilization problems of the system. In order to apply the convex optimization algorithm, the derived sufficient conditions are converted into Linear Matrix Inequality (LMI) problems. Based on the proposed design technologies, gain-scheduled controllers are designed such that the considered system is asymptotically stable in the mean square. Finally, two numerical examples are applied to demonstrate the application and effectiveness of the proposed design technologies of this paper.

Detecting multimuon jets from the Higgs boson exotic decays in the Higgs portal framework

Chang, Jung,Cheung, Kingman,Hsu, Shih-Chieh,Lu, Chih-Ting American Physical Society 2017 Physical review. D Vol.95 No.3

<P>A muon jet (mu-jet) is a very special feature that consists of a cluster of collimated muons from the decay of a fast-moving light particle of mass about O(1 GeV). We will use this feature to search for very light particles from rare decays of the Higgs boson. For such a small angular separation of muons which might come from a long-lived particle, both ATLAS and CMS could have the displaced-vertexing-reconstruction capability. We use two simple models of the Higgs portal type to explore the possibilities of event topologies with two 2 mu-jets, one 2 mu-jet and one 4 mu-jet, and two 4 mu-jets in the final state at LHC-14. We also summarize existing constraints on these models.</P>

A Relaxed Observer-based Control for LPV Stochastic Systems Subject to H∞ Performance

Guan-Wei Chen,Cheung-Chieh Ku 제어·로봇·시스템학회 2020 International Journal of Control, Automation, and Vol.18 No.4

A relaxed observer-based control problem of the disturbed Linear Parameter Varying (LPV) stochastic systems is addressed in this paper. For the control problem, some sufficient conditions are derived via a Lyapunov function whose positive definite matrix is not required as the diagonal case. Besides, a general H∞ performance index is proposed to constrain the effect of external disturbance on the state and estimation error. Furthermore, a lemma is proposed to eliminate the oscillation caused by determining performance level of state and estimation error. Another lemma is developed via extending projection lemma to convert the derived conditions into strict Linear Matrix Inequality (LMI) form. By using convex optimization algorithm, all feasible solutions can be obtained by a single-step calculation to establish an observer-based Gain-Scheduled (GS) controller. Based on the designed controller, the asymptotical stability and H∞ performance of the LPV stochastic systems can be guaranteed in the sense of mean square. Finally, two examples are provided to demonstrate the effectiveness and applicability of the proposed method.

Robust Fuzzy Control for Discrete Perturbed Time-Delay Affine Takagi-Sugeno Fuzzy Models

Wen-Jer Chang,Wei-Han Huang,Cheung-Chieh Ku 제어·로봇·시스템학회 2011 International Journal of Control, Automation, and Vol.9 No.1

The purpose of this paper is to study the stability analysis and controller synthesis principles of Discrete Perturbed Time-Delay Affine (DPTDA) Takagi–Sugeno (T–S) fuzzy models. In general, the T–S fuzzy model is a weighted sum of some linear subsystems via fuzzy membership functions. This paper considers fuzzy rules include both linear nominal parts and uncertain parameters in the time-delay affine T–S fuzzy model. For DPTDA T–S fuzzy models, the T–S fuzzy control scheme is used to confront the H∞ performance constraints. Some sufficient conditions are derived on robust H∞ disturbance attenuation in which both robust stability and a prescribed performance are required to be achieved. In order to find suitable fuzzy controllers, the Iterative Linear Matrix Inequality (ILMI) algorithm is employed to solve these sufficient conditions. At last, a numerical simulation for the nonlinear truck-trailer system is given to show the applications of the present design approach.

Passive Fuzzy Controller Design via Observer Feedback for Stochastic Takagi-Sugeno Fuzzy Models with Multiplicative Noises

Wen-Jer Chang,Liang-Zhi Liu,Cheung-Chieh Ku 제어·로봇·시스템학회 2011 International Journal of Control, Automation, and Vol.9 No.3

This paper investigates the fuzzy control problem of a class of nonlinear continuous-time stochastic systems with achieving the passivity performance. A model-based observer feedback fuzzy control utilizing the concept of so-called parallel distributed compensation (PDC) is employed to stabilize the class of nonlinear stochastic systems that are represented by the Takagi-Sugeno (T-S) fuzzy models. Based on the Lyapunov criteria, the Linear Matrix Inequality (LMI) technique is used to synthesize the observer feedback fuzzy controller design such that the closed-loop system satisfies stability and passivity constraints, simultaneously. Finally, a numerical example is given to demonstrate the applicability and effectiveness of the proposed design method.

Complex Performance Control Using Sliding Mode Fuzzy Approach for Discrete-Time Nonlinear Systems via T-S Fuzzy Model with Bilinear Consequent Part

Wen-Jer Chang,Feng-Ling Hsu,Cheung-Chieh Ku 제어·로봇·시스템학회 2017 International Journal of Control, Automation, and Vol.15 No.4

In this paper, a stabilization problem for the discrete nonlinear system with external disturbance, multiplicativenoises and multiple constraints has been discussed in accordance with the definition of Lyapunov stability. Based on fuzzy modeling approach, the overall fuzzy model of a nonlinear plant is transformed into a class of linearsystems. Applying a Sliding Mode Fuzzy Control (SMFC) scheme, the designed controller causes the closed-loopsystem converging to the sliding surface and achieving the required control performance. For the control performance,the concepts of stability, individual state variance and passivity constraints are introduced for the slidingmode fuzzy control system. To apply convex optimal programming algorithm, some sufficient conditions derivedin this paper are reduced to Linear Matrix Inequality (LMI) problem. At last, two simulation examples are proposedto demonstrate the applicability and usefulness of the proposed design method. One of the examples is to discussthe conservatism of this paper. Another is to show that the discrete truck-trailer system controlled by sliding modefuzzy controller can achieve stability constraints, individual state variance constraints and passivity constraints.

Robust Decentralized Fuzzy Control for Large-scale Descriptor Systems With Decay Rate Constraint

Che-Lun Su,Wen-Jer Chang,Cheung-Chieh Ku 제어·로봇·시스템학회 2023 International Journal of Control, Automation, and Vol.21 No.12

This study addresses the control problem of a nonlinear large-scale descriptor system (LSDS) through the use of a decentralized proportional-plus-derivative state feedback fuzzy (DPDF) control strategy. The TakagiSugeno (T-S) fuzzy modeling technique, which is widely used by researchers, is used to describe the nonlinear LSDS as a set of linear subsystems with interconnections. Based on the constructed T-S fuzzy LSDS, a DPDF feedback method is proposed to address the limitations of the descriptor matrix of the T-S fuzzy LSDS and to solve the regular and impulse-free problems of systems while providing a more convenient and effective approach for discussing system stability. Additionally, the Lyapunov theory is chosen to analyze the stability conditions. This study uses a quadratic Lyapunov function to provide sufficient criteria to ensure the decay rate performance of the LSDS, which can be transformed into linear matrix inequality (LMI) form. The proposed method is demonstrated through several examples to showcase its effectiveness.