Intelligent Digital Redesign for Uncertain Nonlinear Systems Using Power Series

성화창(Hwa Chang Sung),박진배(Jin Bae Park),고성현(Sung Hyun Go),주영훈(Young Hoon Joo) 한국지능시스템학회 2005 한국지능시스템학회논문지 Vol.15 No.7

분 논문은 복합 상태 공간에서의 퍼지 기반 제어기를 이용한 지능형 디지털 재설계의 전 역적 접근 방안에 대해 재안하고자 한다. 이산화를 통한 제어기 설계에 있어서 불확실성이 포함된 실시간 비선형 시스템에 대해 보다 효율적이고 안정적인 접근을 위해 TS 퍼지 모델이 사용되었다. 그리고 전 역적 접근을 위핸 방안으로서 문제를 볼록 최적화 관점으로 변환 후, 에라가 가질 수 있는 놈의 영역을 최소화 하여 상태 접합을 이루고자 하였다. 또한 power series를 사용함으로써 불확실성이 포함된 비선형 시스템을 보다 더 정확하게 분석하였다. 샘플링 기간이 충분히 작다면, 불확실 비선형 시스템의 실시간 시스템으로의 전환이 충분한 이유를 가지게 된다. 전 역적 접근을 통한 디지털로 제어된 시스템은 선형 행렬 부등식 형태로 바꾸어 시스템의 안정성을 보장하고자 하였다. 마지막으로 TS 퍼지 모델로 분석된 혼돈 Lorenz system에 적용함으로써 제안된 방법의 안정성과 효율성을 보장받게 된다. This paper presents intelligent digital redesign method of global approach for hybrid state space fuzzy-model-based controllers. For effectiveness and stabilization of continuous-time uncertain nonlinear systems under discrete-time controller, Takagi-Sugeno(TS) fuzzy model is used to represent the complex system. And global approach design problems viewed as a convex optimization problem that we minimize the en-or of the norm bounds between nonlinearly interpolated linear operators to be matched. Also, by using the power series, we analyzed nonlinear system's uncertain parts more precisely. When a sampling period is sufficiently small, the conversion of a continuous-time structured uncertain nonlinear system to an equivalent discrete-time system have proper reason. Sufficiently conditions for the global state-matching of the digitally controlled system are formulated in terms of linear matrix inequalities (LMIs). Finally, a TS fuzzy model for the chaotic Lorentz system is used as an example to guarantee the stability and effectiveness of the proposed method.

Reliability Analysis of Unrepairable Systems with Uncertain Lifetimes

Ying Liu,Xiaozhong Li,Congcong Xiong 보안공학연구지원센터 2015 International Journal of Security and Its Applicat Vol.9 No.12

The topic of unrepairable system is an important content in system reliability theory. There are many reasons cannot be repaired, some because of technical reasons, cannot repair, some because of economic reasons, not worth to repair, and some because of making repairable system simplification. So it is essential to pay attention to unrepairable systems. In this paper, the lifetimes of unrepairable systems are considered as uncertain variables. Based on that, the fundamental mathematical models of series systems, parallel systems, series-parallel systems and parallel-series systems are established, respectively. Furthermore, we make reliability analysis of above four unrepairable systems, respectively. Some numerical examples are also given for illustration.

Robustness analysis of vibration control in structures with uncertain parameters using interval method

Chen, Su Huan,Song, Min,Chen, Yu Dong Techno-Press 2005 Structural Engineering and Mechanics, An Int'l Jou Vol.21 No.2

Variations in system parameters due to uncertainties may result in system performance deterioration. Uncertainties in modeling of structures are often considered to ensure that control system is robust with respect to response errors. Hence, the uncertain concept plays an important role in vibration control of the engineering structures. The paper discusses the robustness of the stability of vibration control systems with uncertain parameters. The vibration control problem of an uncertain system is approximated by a deterministic one. The uncertain parameters are described by interval variables. The uncertain state matrix is constructed directly using system physical parameters and avoided to use bounds in Euclidean norm. The feedback gain matrix is determined based on the deterministic systems, and then it is applied to the actual uncertain systems. A method to calculate the upper and lower bounds of eigenvalues of the close-loop system with uncertain parameters is presented. The lower bounds of eigenvalues can be used to estimate the robustness of the stability the controlled system with uncertain parameters. Two numerical examples are given to illustrate the applications of the present approach.

Intelligent Digital Redesign of Uncertain Nonlinear Systems : Global approach

성화창(Hwachang Sung),주영훈(Younghoon Joo),박진배(Jinbae Park),김도완(Dowan Kim) 한국지능시스템학회 2005 한국지능시스템학회 학술발표 논문집 Vol.15 No.2

This paper presents intelligent digital redesign method of global approach for hybrid state space fuzzy-model-based controllers. For effectiveness and stabilization of continuous-time uncertain nonlinear systems under discrete-time controller, Takagi-Sugeno(TS) fuzzy model is used to represent the complex system. And global approach design problems viewed as a convex optimization problem that we minimize the error of the norm bounds between nonlinearly interpolated linear operators to be matched. Also by using the power series, we analyzed nonlinear system's uncertain parts more precisely. When a sampling period is sufficiently small, the conversion of a continuous-time structured uncertain nonlinear system to an equivalent discrete-time system have proper reason. Sufficiently conditions for the global state-matching of the digitally controlled system are formulated in terms of linear matrix inequalities (LMIs). Finally, we prove the effectiveness and stabilization of the proposed intelligent digital redesign method by applying the chaotic Lorentz system.

Tracking Control Design for a Bilinear Control System With Unstable and Uncertain Internal Dynamics Using Adaptive Backstepping

Khozin Mu’tamar,Janson Naiborhu,Roberd Saragih,Dewi Handayani 제어·로봇·시스템학회 2024 International Journal of Control, Automation, and Vol.22 No.9

A non-minimum phase system has unstable zero internal dynamics. Even though the system’s output has stabilised, the state variables of the internal dynamics continue to grow indefinitely. Uncertain parameters in the internal dynamics make their behaviour even more unpredictable. In this article, we solve the tracking problem for a bilinear control system with unstable internal dynamics and uncertain parameters using adaptive backstepping. The bilinear control system is transformed using input–output feedback linearisation to normal form. The unstable internal dynamics containing uncertain parameters are first stabilised using the external dynamics as a virtual control. The external dynamics are then stabilised using other state variables in the external dynamics; the final system uses the actual control function. Numerical simulations are performed to demonstrate the proposed control’s technical implementation and performance. A robustness test is conducted analytically and numerically to understand the control function’s tolerance to uncertain parameters. The simulation results show that the control function successfully solves tracking problems in non-minimum phase systems. Using the integral absolute error criterion, we also determine the range of uncertain parameter values for which the control function works satisfactorily.

Optimal Guaranteed Cost Tracking of Uncertain Nonlinear Systems Using Adaptive Dynamic Programming with Concurrent Learning

Dengguo Xu,Qinglin Wang,Yuan Li 제어·로봇·시스템학회 2020 International Journal of Control, Automation, and Vol.18 No.5

In this paper, based on adaptive dynamic programming (ADP) with concurrent learning, the problem of optimal guaranteed cost tracking is studied for a class of uncertain continuous-time nonlinear systems. First, the original uncertain system and a reference system are combined into an augmented uncertain system, and the performance index is transformed into the corresponding augmented form. Afterwards, the solution of the optimal control problem consisting of the nominal augmented system with the modified performance index is proven to be the optimal guaranteed cost tracking control law of the original uncertain system. Moreover, a concurrent learning tuning algorithm based on ADP is presented to approximate the solution of corresponding Hamilton-Jacobi-Bellman (HJB) equation, which relaxes the condition of persistent excitation (PE). A neural network-based approximate optimal guaranteed cost tracking design is developed not only to ensure tracking error convergence to zero for alladmissible uncertainties but also to achieve the minimal guaranteed cost. Finally, two simulation examples are considered to verify the effectiveness of the theoretical results.

An Alternative State Estimation Filtering Algorithm for Temporarily Uncertain Continuous Time System

( Pyung Soo Kim ) 한국정보처리학회 2020 Journal of information processing systems Vol.16 No.3

An alternative state estimation filtering algorithm is designed for continuous time systems with noises as well as control input. Two kinds of estimation filters, which have different measurement memory structures, are operated selectively in order to use both filters effectively as needed. Firstly, the estimation filter with infinite memory structure is operated for a certain continuous time system. Secondly, the estimation filter with finite memory structure is operated for temporarily uncertain continuous time system. That is, depending on the presence of uncertainty, one of infinite memory structure and finite memory structure filtered estimates is operated selectively to obtain the valid estimate. A couple of test variables and declaration rule are developed to detect uncertainty presence or uncertainty absence, to operate the suitable one from two kinds of filtered estimates, and to obtain ultimately the valid filtered estimate. Through computer simulations for a continuous time aircraft engine system with different measurement memory lengths and temporary model uncertainties, the proposed state estimation filtering algorithm can work well in temporarily uncertain as well as certain continuous time systems. Moreover, the proposed state estimation filtering algorithm shows remarkable superiority to the infinite memory structure filtering when temporary uncertainties occur in succession.

An H_∞ Output Feedback Control for Uncertain Singularly Perturbed T-S Fuzzy Systems

류석환,오설동,Yoo, Seog-Hwan,Wu, Xue-Dong Korean Institute of Intelligent Systems 2009 한국지능시스템학회논문지 Vol.19 No.6

This paper deals with an $H_{\infty}$ output feedback controller design for uncertain singularly perturbed T-S fuzzy systems. Integral quadratic constraints are used to describe various kinds of uncertainties of the plant. It is shown that the $H_{\infty}$ norm of the uncertain singularly perturbed fuzzy system is less than $\gamma$ for a sufficiently small $\varepsilon$ > 0 if the $H_{\infty}$ norms of both the slow and fast subsystem are less than $\gamma$. Using this fact, we develop a linear matrix inequality based design method which is independent of the singular perturbation parameter $\varepsilon$. A numerical example is provided to demonstrate the efficacy of the proposed design method.

An H<SUB>∞</SUB> Output Feedback Control for Uncertain Singularly Perturbed T-S Fuzzy Systems

Seog-Hwan Yoo(류석환),Wu Xuedong(오설동) 한국지능시스템학회 2009 한국지능시스템학회논문지 Vol.19 No.6

This paper deals with an H∞ output feedback controller design for uncertain singularly perturbed T-S fuzzy systems. Integral quadratic constraints are used to describe various kinds of uncertainties of the plant. It is shown that the H∞ norm of the uncertain singularly perturbed fuzzy system is less than γ for a sufficiently small ε>0 if the H∞ norms of both the slow and fast subsystem are less than γ. Using this fact, we develop a linear matrix inequality based design method which is independent of the singular perturbation parameter ε. A numerical example is provided to demonstrate the efficacy of the proposed design method.

Robust Stabilization of Constrained Uncertain Linear Systems using Feedforward Control based on High-gain Disturbance Observer

Mun Chae Yoon,Jung-Su Kim,Juhoon Back 제어로봇시스템학회 2015 제어로봇시스템학회 국제학술대회 논문집 Vol.2015 No.10

This paper proposes a robust stabilizing control for constrained uncertain linear systems by combining a disturbance observer (DOB) and state feedback controller. To this end, a state feedback controller is designed for the nominal system and then a disturbance observer based feedforward control is added in order to reject uncertainties. In doing so, the DOB and state feedback controller are united in a way that the combined control satisfies the input constraints and closed loop stability is guaranteed. Simulation results are given to show that the proposed control scheme successfully stabilizes the uncertain systems.