• Title, Summary, Keyword: Uncertain systems

### A Note on Positive Invariant Set for Linear Uncertain Discrete-Time Systems

• Matsumoto, H.;Otsuka, N.
• 제어로봇시스템학회:학술대회논문집
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• pp.571-574
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• 2005
• This paper gives some sufficient conditions for a given polyhedral set which is represented as a set of linear inequalities to be positive D-invariant for uncertain linear discrete-time systems in the case such that the systems matrices depend linearly on uncertain parameters whose ranges are given intervals. Further, the results will be applied to uncertain linear continuous systems in the sense of the above by using Euler approximation.

### A New Approach to Risk Comparison via Uncertain Measure

• Li, Shengguo;Peng, Jin
• Industrial Engineering and Management Systems
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• v.11 no.2
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• pp.176-182
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• 2012
• This paper presents a new approach to risk comparison in uncertain environment. Based on the uncertainty theory, some uncertain risk measures and risk comparison rules are proposed. Afterward the bridges are built between uncertain risk measures and risk comparison rules. Finally, several comparable examples are given.

### Comonotonic Uncertain Vector and Its Properties

• Li, Shengguo;Zhang, Bo;Peng, Jin
• Industrial Engineering and Management Systems
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• v.12 no.1
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• pp.16-22
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• 2013
• This paper proposes a new concept of comonotonicity of uncertain vector based on the uncertainty theory. In order to understand the comonotonicity of uncertain vector, some equivalent definitions are presented. Following the proposed concept, some basic properties of comonotonic uncertain vector are investigated. In addition, the operational law is given for calculating the uncertainty distributions of monotone functions of comonotonic uncertain variables. With the help of operational law, the comonotonic uncertain vector is applied to the premium pricing problems. At last, some numerical examples are given to illustrate the application.

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

• Chen, Su Huan;Song, Min;Chen, Yu Dong
• Structural Engineering and Mechanics
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• v.21 no.2
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• pp.185-204
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• 2005
• 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.

### Non-fragile Guaranteed Cost Control of Uncertain Nonlinear Systems with Time-varying Delays in State and Control Input (시변 시간 지연을 갖는 불확실한 비선형 시스템의 비약성 보장 비용 제어)

• Kim, Jae-Man;Choi, Yoon-Ho;Park, Jin-Bae
• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.3
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• pp.459-465
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• 2012
• In this paper, we present a non-fragile guaranteed cost control design method for uncertain nonlinear systems with time varying delays in state and control input, even though the controller gain is perturbed. The uncertain nonlinear term in the systems is norm bounded and the linear matrix inequality(LMI) optimization method is employed as a stability analysis of the systems. We design a robust controller and show the asymptotical stability of uncertain time-varying systems based on Lyapunov method. Also, we guarantee a specific level of performance of the systems. The simulations are carried out to demonstrate the effectiveness of the proposed method.

### Design of Adaptive Regulator for a Nonlinear Uncertain System (불확실성을 갖는 비선형 시스템의 적응 제어기 설계)

• Jin, Ju-Wha;Yu, Kyung-Tak;Son, Young-Ik;Seo, Jin-Heo
• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.2
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• pp.153-158
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• 1999
• We consider single-input nonlinear systems with unknown unmodelled time-varying parameters or disturbances which are bounded. The main goal is to identify classes of uncertain systems for which the control exist and to provide constructive design procedures. Assuming that the undisturbed nominal system ( ,g) is partially state feedback linearizable, that a strict triangularity condition, a linear parametrization condition, and {{{{ { G}_{r-1 } }}}} hold for the uncertain terms, and that some condition is satisfied in the transformed partially linear system, we design an adaptive regulating dynamic control. At first, we identify classes of nonlinear uncertain systems and give a systematic procedure for the design of a robust regulation for the nonlinear systems.

### Application of robust fault detection method for uncertain systms to diesel engine system (불확실성을 고려한 디젤엔진의 견실한 이상검출)

• 유경상;김대우;권오규
• 제어로봇시스템학회:학술대회논문집
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• pp.1419-1422
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• 1997
• This paper deals with the Appliation of robust fault detection problem in uncertain linear systems, having both model mismatch and noise. A robust fault detection method presented by Kwon et al.(1994) for SISO uncertain systems. Here we experimented this method to the diesel engine systems described by difference ARMA models. The model mismatch includes here linearization error as well as undermodeling. Comparisons are made with alternative fault detection method which do not account noise. The new method is shown to have good performance.

### Note on Robust Stabilization of Uncertain Input-delay Systems by Sliding Mode Control With Delay Compensation

• Yue, Dong;Won, Sangchul;Kwon, Ohmin
• Transactions on Control, Automation and Systems Engineering
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• v.4 no.3
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• pp.195-198
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• 2002
• In this note, we suggest a new matching condition and extend the stability analysis to the ultimate boundness of state $\chi$(t) for uncertain input-delay systems, using a sliding control with delay compensation.

### Robust Output-Tracking Control of Uncertain Takagi-Sugeno Fuzzy Systems

• 이호재;박진배;정근호;주영훈
• Proceedings of the Korean Institute of Intelligent Systems Conference
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• pp.315-318
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• 2003
• A systematic output-tracking control design technique for robust control of Takagi-Sugeno (T-S) fuzzy systems with norm-bounded uncertainties is developed. The uncertain T-S fuzzy system is first represented as a set of uncertain local linear systems. The tracking problem is then converted into the stabilization problem for a set of uncertain local linear systems thereby leading to a more feasible controller design procedure. A sufficient condition for robust asymptotic output tracking is derived in terms of a set of linear matrix inequalities (LMIs). A stability condition on the traversing time-instances is also established. The output tracking control simulation for a flexible-joint robot-arm model is demonstrated, to convincingly show the effectiveness of the proposed system modeling and controller design method.

### Uncertain Programming Model for Chinese Postman Problem with Uncertain Weights

• Zhang, Bo;Peng, Jin
• Industrial Engineering and Management Systems
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• v.11 no.1
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• pp.18-25
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• 2012
• IChinese postman problem is one of the classical combinatorial optimization problems with many applications. However, in application, some uncertain factors are frequently encountered. This paper employs uncertain programming to deal with Chinese postman problem with uncertain weight Within the framework of uncertainty theory, the concepts of expected shortest route, ${\alpha}$-shortest route, and distribution shortest route are proposed. After that, expected shortest model, and ${\alpha}$-shortest model are constructed. Taking advantage of properties of uncertainty theory, these models can be transf-ormed into their corresponding deterministic forms, which can be solved by classical algorithm..