20 results on '"Delay Systems"'
Search Results
2. Output feedback stabilization of stochastic high‐order nonlinear time‐delay systems with unknown output function
- Author
-
Wei Dong and Mengmeng Jiang
- Subjects
asymptotic stability ,control theory ,delay systems ,nonlinear control systems ,stochastic systems ,Control engineering systems. Automatic machinery (General) ,TJ212-225 - Abstract
Abstract This article considers the problem of output feedback stabilization for a class of stochastic high‐order nonlinear time‐delay systems with unknown output function. For stochastic high‐order nonlinear time‐delay systems, based on the Lyapunov stability theorem, by combining the addition of one power integrator and homogeneous domination method, the maximal open sector Δ of output function is given. As long as output function belongs to any closed sector included in Δ, an output feedback controller can be developed to guarantee the closed‐loop system globally asymptotically stable in probability.
- Published
- 2024
- Full Text
- View/download PDF
3. Intention inference‐based interacting multiple model estimator in photoelectric tracking
- Author
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Minxing Sun, Huabo Liu, Qianwen Duan, Junzhe Wang, Yao Mao, and Qiliang Bao
- Subjects
delay systems ,discrete time filters ,Kalman filters ,non‐linear estimation ,state estimation ,tracking ,Control engineering systems. Automatic machinery (General) ,TJ212-225 - Abstract
Abstract Aiming to improve the estimation and prediction accuracy of a target's position, this paper proposes a state estimation method for photoelectric tracking systems, based on the evaluation of the tracked target's motion intention. Traditional photoelectric tracking systems utilize external physical quantities such as the position, velocity, and acceleration of the target as the estimated states. While this method can output good results for pre‐modelled target positions, it struggles to maintain the accuracy when facing manoeuvering targets or complex motion patterns targets. Here, the relevant parameters of the tracked target's motion intention are directly estimated innovatively, like estimating the circling point position rather than the circular flying target's position and velocity. This approach enables recognizing the target's motion intention and leads to precise estimation, which specifically consists of an interacting multiple model approach, multiple unscented Kalman estimators, and a robust estimator. The effectiveness and stability of this estimator are validated through software simulations and experiments on a dual‐reflection mirror platform.
- Published
- 2024
- Full Text
- View/download PDF
4. Zero/low overshoot conditions based on maximally‐flatness for PID‐type controller design for uncertain systems with time‐delay or zeros
- Author
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Mehmet Canevi and Mehmet Turan Söylemez
- Subjects
continuous time systems ,damping ,delay systems ,feedback ,optimisation ,PI control ,Control engineering systems. Automatic machinery (General) ,TJ212-225 - Abstract
Abstract This paper extends the characteristic ratio approach using novel inequalities to ensure zero/low overshoot for linear‐time‐invariant systems with zeros. The extension provided by this paper is based on the maximally‐flatness property of a transfer function, where the square‐magnitude of the transfer function is ensured to be a low‐pass filter. In order to be able to design low‐order/fixed structure controllers, a partial pole‐assignment approach is used instead of the full pole‐assignment used in the Characteristic Ratio Assignment (CRA) method. The developed inequalities and additional stability conditions are combined into an optimization problem using time domain restrictions when necessary. Although the method given in the paper is general, particular inequalities are developed for PI and PI‐PD controller cases, due to their frequent use in industrial applications. Similarly, First‐Order‐Plus‐Delay‐Time (FOPDT) and Second‐Order‐Plus‐Delay‐Time (SOPDT) systems are considered specifically, since most of the practical systems can be approximated by one of these types. The study is extended to plants with uncertainties where a theorem is developed to decrease computation time dramatically. The benefits of the proposed methods are demonstrated by several examples.
- Published
- 2024
- Full Text
- View/download PDF
5. Structured invariant subspace and decomposition of systems with time delays and uncertainties.
- Author
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Phan‐Van, Huan and Gu, Keqin
- Subjects
- *
TIME delay systems , *LARGE scale systems , *INVARIANT subspaces , *DIFFERENTIAL-difference equations , *TIME-varying systems - Abstract
This article discusses invariant subspaces of a matrix with a given partition structure. The existence of a nontrivial structured invariant subspace is equivalent to the possibility of decomposing the associated system with multiple feedback blocks such that the feedback operators are subject to a given constraint. The formulation is especially useful in the stability analysis of time‐delay systems using the Lyapunov–Krasovskii functional approach where computational efficiency is essential in order to achieve accuracy for large scale systems. The set of all structured invariant subspaces are obtained (thus all possible decompositions are obtained as a result) for the coupled differential‐difference equations (DDE) associated with the DDE of retarded and neutral types, as well as systems with a time‐varying delay. It was shown that the known ad hoc methods of reducing the dimensions of delay channels can be considered as special cases of decomposition where one subsystem has trivial dynamics. The reduction of computational cost is demonstrated by a numerical example. For the general case, a recursive procedure is developed to obtain the set of all structured invariant subspaces. Based on this procedure, a method is presented to obtain a nontrivial structured invariant subspace that considers computational efficiency and increased possibility of terminating in a finite number of steps. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
6. Symmetries of differential delay systems with applications to observer design.
- Author
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Battilotti, Stefano
- Subjects
- *
TRANSFORMATION groups , *SYMMETRY , *DELAY differential equations - Abstract
In this paper we construct a general observer theory for differential delay systems based on different types of symmetries (exact symmetry or asymptotic symmetry), ending up with a certain number of semi‐global and global observers, with bounded or unbounded system's solutions. We introduce the notions of symmetry for a differential delay system, being inspired by well‐known definitions of symmetry for an ordinary or partial differential system, and variational symmetry for the associated variational differential delay system. We illustrate observer design procedures in details, by proving that the existence of a (variational asymptotic) symmetry with system's detectability in the first approximation have a central role in the design of a state observer. The symmetry is a one‐parameter group of transformations which maps the system into itself (exact symmetry) or into a different system (asymptotic symmetry), approximating the original one with better and better accuracy as the parameter of the symmetry is larger. The types of symmetries we consider here show an important contractive action on the state and input spaces for which the system's solutions are mapped into arbitrarily small neighbourhoods of the origin in which the transformed system can be well‐approximated by its linearization. The parameter of the symmetry may be constant (semiglobal observers) or updated on‐line by a state norm estimator (global observers). [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
7. Constrained control of multi‐input systems with distinct input delays.
- Author
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Abel, Imoleayo, Janković, Mrdjan, and Krstić, Miroslav
- Subjects
- *
ADMISSIBLE sets , *SYSTEM safety , *ROBUST control - Abstract
We consider the problem of enforcing safety in multi‐input systems with distinct input delays via the use of Control Barrier Functions (CBFs). For systems with input delay(s), a popular approach for enforcing safety is the combination of a CBF designed for the delay‐free system with state‐predictors that compensate the input delays. Typically, this comes with the assumption that the system does not violate safety constraints before all input delays have been compensated and the system is fully under control. In this paper, we introduce two control approaches that enforce safety before all input delays have been compensated, whenever it is possible to do so. We do this by utilizing a robust CBF formulation that treats longer‐delayed inputs as known disturbances when determining control effort for shorter delayed inputs. This formulation ensures that, whenever possible, a subset of input channels with shorter delays will be utilized for keeping the system in the admissible safe set before longer input delays have been compensated. The effectiveness of our approaches is demonstrated with two numerical examples. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
8. Intention inference‐based interacting multiple model estimator in photoelectric tracking.
- Author
-
Sun, Minxing, Liu, Huabo, Duan, Qianwen, Wang, Junzhe, Mao, Yao, and Bao, Qiliang
- Subjects
- *
TRACKING radar , *DISCRETE time filters , *INTENTION , *ACCELERATION (Mechanics) , *NONLINEAR estimation , *SIMULATION software - Abstract
Aiming to improve the estimation and prediction accuracy of a target's position, this paper proposes a state estimation method for photoelectric tracking systems, based on the evaluation of the tracked target's motion intention. Traditional photoelectric tracking systems utilize external physical quantities such as the position, velocity, and acceleration of the target as the estimated states. While this method can output good results for pre‐modelled target positions, it struggles to maintain the accuracy when facing manoeuvering targets or complex motion patterns targets. Here, the relevant parameters of the tracked target's motion intention are directly estimated innovatively, like estimating the circling point position rather than the circular flying target's position and velocity. This approach enables recognizing the target's motion intention and leads to precise estimation, which specifically consists of an interacting multiple model approach, multiple unscented Kalman estimators, and a robust estimator. The effectiveness and stability of this estimator are validated through software simulations and experiments on a dual‐reflection mirror platform. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
9. Zero/low overshoot conditions based on maximally‐flatness for PID‐type controller design for uncertain systems with time‐delay or zeros.
- Author
-
Canevi, Mehmet and Söylemez, Mehmet Turan
- Subjects
- *
UNCERTAIN systems , *TRANSFER functions , *CONTINUOUS time systems - Abstract
This paper extends the characteristic ratio approach using novel inequalities to ensure zero/low overshoot for linear‐time‐invariant systems with zeros. The extension provided by this paper is based on the maximally‐flatness property of a transfer function, where the square‐magnitude of the transfer function is ensured to be a low‐pass filter. In order to be able to design low‐order/fixed structure controllers, a partial pole‐assignment approach is used instead of the full pole‐assignment used in the Characteristic Ratio Assignment (CRA) method. The developed inequalities and additional stability conditions are combined into an optimization problem using time domain restrictions when necessary. Although the method given in the paper is general, particular inequalities are developed for PI and PI‐PD controller cases, due to their frequent use in industrial applications. Similarly, First‐Order‐Plus‐Delay‐Time (FOPDT) and Second‐Order‐Plus‐Delay‐Time (SOPDT) systems are considered specifically, since most of the practical systems can be approximated by one of these types. The study is extended to plants with uncertainties where a theorem is developed to decrease computation time dramatically. The benefits of the proposed methods are demonstrated by several examples. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
10. Controllability of the time-varying fractional dynamical systems with a single delay in control.
- Author
-
Vishnukumar, K. S., Sivalingam, S. M., Ahmad, Hijaz, and Govindaraj, V.
- Abstract
In this article, we explored the controllability of fractional dynamical systems with a single delay in the control function with the Caputo fractional derivative. It is the first work in which the author studies the controllability of a time-varying fractional dynamical system with a delay in the control function. We develop the necessary and sufficient criteria for the solution representation of controllability of time-varying fractional linear dynamical systems by utilizing the Grammian matrix. We use Schauder's fixed point theorem to establish sufficient conditions for the controllability of time-varying nonlinear fractional dynamical systems. With the help of successive approximation techniques, numerical examples validate the theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
11. Stability analysis of discrete‐time systems with a time‐varying delay via improved methods
- Author
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Hongjia Sha, Ju H. Park, Jun Chen, Mingbo Zhu, and Chengjie Nan
- Subjects
delay systems ,discrete time systems ,Lyapunov methods ,stability ,Control engineering systems. Automatic machinery (General) ,TJ212-225 - Abstract
Abstract This paper is concerned with the stability analysis of discrete‐time systems with a time‐varying delay. The conservatism and computation burden are two important factors to evaluate a stability condition. By taking the relationship of two reciprocally convex parts into consideration, a new combined matrix‐separation‐based inequality is proposed that involves only a few free matrices. Moreover, an improved matrix‐injection‐based transformation lemma with the parameter varying within a closed interval is proposed by introducing only one free matrix. By constructing an appropriate Lyapunov–Krasovskii functional and applying the improved methods, a relaxed stability condition is consequently obtained with a small number of decision variables. Two numerical examples are given to show the merits of the proposed methods.
- Published
- 2024
- Full Text
- View/download PDF
12. Fault estimation for nonlinear uncertain time‐delay systems based on unknown input observer
- Author
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Ataollah Azarbani, Ahmad Fakharian, and Mohammad Bagher Menhaj
- Subjects
delay systems ,fault diagnosis ,nonlinear dynamical systems ,Control engineering systems. Automatic machinery (General) ,TJ212-225 - Abstract
Abstract In this paper, a novel nonlinear unknown input observer is proposed in order to fault estimation for nonlinear uncertain systems with time delays. By the estimation of the faults, the features are detected such as shape, size occurrence time etc. The time delay is considered a constant and known parameter in the states. The disturbances are investigated in the states and outputs and also, and sensor and actuator faults are considered. The stability of the closed‐loop system is guaranteed by Lyapunov–Krasovskii theory and some feasible Linear matrix inequalities (LMI). The proposed method is simulated on a continuous‐stirred tank reactor (CSTR) with uncertainties and time delay. Simulation results show the appropriate efficiency of the proposed method.
- Published
- 2024
- Full Text
- View/download PDF
13. Stability analysis of discrete‐time systems with a time‐varying delay via improved methods.
- Author
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Sha, Hongjia, Park, Ju H., Chen, Jun, Zhu, Mingbo, and Nan, Chengjie
- Subjects
- *
DISCRETE-time systems , *TIME-varying systems , *DISCRETE systems - Abstract
This paper is concerned with the stability analysis of discrete‐time systems with a time‐varying delay. The conservatism and computation burden are two important factors to evaluate a stability condition. By taking the relationship of two reciprocally convex parts into consideration, a new combined matrix‐separation‐based inequality is proposed that involves only a few free matrices. Moreover, an improved matrix‐injection‐based transformation lemma with the parameter varying within a closed interval is proposed by introducing only one free matrix. By constructing an appropriate Lyapunov–Krasovskii functional and applying the improved methods, a relaxed stability condition is consequently obtained with a small number of decision variables. Two numerical examples are given to show the merits of the proposed methods. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
14. Fault estimation for nonlinear uncertain time‐delay systems based on unknown input observer.
- Author
-
Azarbani, Ataollah, Fakharian, Ahmad, and Menhaj, Mohammad Bagher
- Subjects
- *
UNCERTAIN systems , *NONLINEAR estimation , *LINEAR matrix inequalities , *TIME delay systems , *NONLINEAR dynamical systems , *NONLINEAR systems , *ADAPTIVE control systems - Abstract
In this paper, a novel nonlinear unknown input observer is proposed in order to fault estimation for nonlinear uncertain systems with time delays. By the estimation of the faults, the features are detected such as shape, size occurrence time etc. The time delay is considered a constant and known parameter in the states. The disturbances are investigated in the states and outputs and also, and sensor and actuator faults are considered. The stability of the closed‐loop system is guaranteed by Lyapunov–Krasovskii theory and some feasible Linear matrix inequalities (LMI). The proposed method is simulated on a continuous‐stirred tank reactor (CSTR) with uncertainties and time delay. Simulation results show the appropriate efficiency of the proposed method. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
15. Finite‐dimensional, output‐predictor‐based, adaptive observer for heat PDEs with sensor delay.
- Author
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Rafia, H., Benabdelhadi, A., Giri, F., Ouadi, H., and Chaoui, F. Z.
- Subjects
- *
MATHEMATICAL decoupling , *ORDINARY differential equations , *PARTIAL differential equations , *DETECTORS - Abstract
Summary: We are considering the problem of designing observers for heat partial differential equations (PDEs) that are subject to sensor delay and parameter uncertainty. In order to get finite‐dimensional observers, described by ordinary differential equations (ODE), we develop a design method based on the modal decomposition approach. The approach is extended so that both parameter uncertainty and sensor delay effects are compensated for. To cope more effectively with sensor delay, an output predictor is designed and the online provided output predictions are substituted to the future output values in the observer. To compensate for parameter uncertainty, we design a parameter estimator providing online parameter estimates, which are substituted to the unknown parameters in the observer. The parameter estimator design is made decoupled from the observer gain design by using an appropriate decoupling transformation. Using an analysis of the small‐gain‐theorem type, the whole (state and parameter) estimation error system is shown to be exponentially stable, under well‐defined conditions on the observer dimension, the sensor delay, and signal persistent excitation (PE). [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
16. Finite‐time tracking control for time‐delayed pure‐feedback systems with guaranteed performance.
- Author
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Dai, Yunfei, Wang, Yujuan, and Wang, Chao
- Subjects
- *
TIME delay systems , *CLOSED loop systems , *NONLINEAR systems , *CONTINUOUS functions , *PSYCHOLOGICAL feedback - Abstract
This article investigates the finite‐time tracking control problem with guaranteed performance for a class of nonlinear pure‐feedback systems subject to both time‐varying state delays and control input delays. Both the state delays and control input delays are assumed to be unknown yet bounded by some known constants. A new performance function is introduced that ensures the finite‐time convergence of tracking errors and guaranteed performance. The key to handling both the states and input delays lies in a novel construction of the Lyapunov–Krasovskii (LK) function, which also avoids the reconstruction of the LK function in stability analysis. In addition, a continuous package function is introduced, which allows the unknown nonlinear terms arising from the uncertain perturbation and the derivation of the LK function to be eliminated. Under the proposed method, the semi‐global uniform ultimate boundedness of all signals in the closed‐loop system can also be ensured. Simulation examples are provided to demonstrate the effectiveness of the proposed approach in this article. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
17. Robust stabilization of interval fractional‐order plants with an interval time delay by fractional‐order proportional integral derivative controllers.
- Author
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Ghorbani, Majid, Tepljakov, Aleksei, and Petlenkov, Eduard
- Subjects
- *
ROBUST stability analysis , *CLOSED loop systems , *TRANSFER functions , *INTEGRALS , *FACTORY orders - Abstract
This paper concentrates on presenting a reliable procedure to compute the stabilizing region of fractional‐order proportional integral derivative (FOPID) controllers for interval fractional‐order plants having an interval time delay. An interval fractional‐order plant is defined as a fractional‐order transfer function whose denominator and numerator coefficients are all uncertain and lie in specified intervals. Also, an interval time delay points to a delay term whose value varies in a specific interval. The D‐decomposition technique and the value set concept are employed to determine the stabilizing region of FOPID controllers. In this study, first, a theorem is presented to compute the boundary of the value sets of systems having interval time day. Then, a lemma is provided for robust stability analysis of the given closed‐loop control system. For a convenient use of the paper results, an algorithm is proposed to solve the problem of robustly stabilizing interval fractional‐order plants with an interval time delay using FOPID controllers. Finally, four examples are provided to illustrate the proposed procedure. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
18. Controllability of fractional dynamical systems having multiple delays in control with ψ‐Caputo fractional derivative.
- Author
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Panneer Selvam, Anjapuli and Govindaraj, Venkatesan
- Subjects
- *
CONTROLLABILITY in systems engineering , *DYNAMICAL systems , *NONLINEAR equations - Abstract
This study investigates the controllability problems for linear and nonlinear fractional control systems with multiple control delays in the context of the ψ$$ \psi $$‐Caputo fractional derivative. For the linear case, using the positive definiteness of the Gramian matrix, the necessary and sufficient conditions are obtained. For the nonlinear case, utilizing the iterative technique together with the completeness of the space, sufficient conditions for the existence of a solution are obtained. Just a few examples are included to make theoretical findings easier to grasp, and their respective graphs are plotted. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
19. Closed-form expressions for the pure time delay in terms of the input and output Laguerre spectra
- Author
-
Medvedev, Alexander and Medvedev, Alexander
- Abstract
The pure time delay operator is considered in continuous and discrete time under the assumption of the input signal being integrable (summable) with square. Then the input and the output signals are uniquely given by their Laguerre spectra. It is shown that a discrete convolution operator with polynomial Markov parameters constitutes a common description of the delay operator in the continuous and discrete case. Closed-form expressions for the delay value in terms of the output and input Laguerre spectra are derived. The expressions hold for any feasible value of the Laguerre parameter and can be utilized for e.g. building time-delay estimators that allow for non-persistent input. A simulation example is provided to illustrate the principle of Laguerre-domain time-delay modeling and analysis with perfect disturbance rejection.
- Published
- 2024
- Full Text
- View/download PDF
20. Inexact predictor feedback for multi-input nonlinear systems with distinct input delays.
- Author
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Fang, Qin and Zhang, Zhengqiang
- Subjects
- *
NONLINEAR systems , *EXPONENTIAL stability , *CLOSED loop systems , *HOPFIELD networks - Abstract
This paper presents a strategy of inexact predictor-feedback control for multi-input nonlinear systems with distinct delays. The controllers designed by an inexact predictor robustly compensate for the different delays. Different from exact predictor feedback, we propose a scheme that can achieve exponential stability of the system without accurately compensating for each delay and has the property of less complexity. For this purpose, we adopt a fixed constant as the prediction horizon, which is restricted to being within a sufficiently narrow range. Its function is to offset the partial effect of each delay. With a new Lyapunov-Krasovskii functional based on an infinite-dimensional backstepping transformation, we prove the global exponential stability of the closed-loop system. Finally, a numerical example is presented to verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
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