23 results
Search Results
2. Adaptive event-triggering distributed filter of positive Markovian jump systems based on disturbance observer.
- Author
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Lin, Fengyu, Zhang, Junfeng, Jia, Xianglei, and Zhou, Xiaoyue
- Subjects
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MARKOVIAN jump linear systems , *POSITIVE systems , *ADAPTIVE filters , *LINEAR programming , *LYAPUNOV functions , *STOCHASTIC programming - Abstract
This paper presents an adaptive event-triggered filter of positive Markovian jump systems based on disturbance observer. A new adaptive event-triggering mechanism is constructed for the systems. A positive disturbance observer is designed for the systems to estimate the disturbance. A distributed output model of each subsystem of positive Markovian jump systems is introduced. Then, an adaptive event-triggering distributed filter is designed by employing stochastic copositive Lyapunov functions. All presented conditions are solvable in terms of linear programming. Under the designed disturbance observer and the distributed filter, the corresponding error system is stochastically stable. The filter design approach is also developed for discrete-time positive Markovian jump systems. The contribution of the paper lies in that: (i) A new adaptive event-triggering mechanism is established for positive systems, (ii) A positive disturbance observer is designed for the disturbance of positive Markovian jump systems, and (iii) The designed distributed filter can guarantee the stochastic stability of the error while existing filters in literature only achieve the stochastic gain stability of the error. Finally, two examples are given to illustrate the effectiveness of the proposed design. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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3. Novel consensus framework on discrete-time positive multi-agent systems.
- Author
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Zhang, Junfeng, Lin, Fengyu, Jia, Xuan, and Du, Baozhu
- Subjects
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MULTIAGENT systems , *POSITIVE systems , *LINEAR programming , *LYAPUNOV functions - Abstract
This paper investigates the consensus of discrete-time positive multi-agent systems. A framework on the consensus of positive multi-agent systems is constructed. By introducing a finite point and a self-feedback term, a novel consensus protocol is proposed to drive all states to common nonnegative finite values. An improved error model is established for positive multi-agent systems. Based on the consensus error model, the consensus of the agents is transformed into the stability of the error systems. Under the proposed consensus protocol and the new consensus error model, the consensus of agents is realized. A copositive Lyapunov function is chosen to derive the consensus of the multi-agent systems. Such a consensus approach is extended for time-delay multi-agent systems. All positivity and consensus conditions can be solved by virtue of linear programming. The main novelties of this paper lie in that: (i) A novel consensus error model is established, (ii) A finite value consensus is achieved, and (iii) Linear programming-based conditions are presented for the consensus design. Finally, two illustrated examples are given to verify the validity of the theoretical findings. • A novel consensus error model is established for PMASs. • A finite value consensus is achieved under the presented consensus framework. • Linear programming and copositive Lyapunov function are chosen as the computation and analysis approaches. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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4. Output feedback [formula omitted] control of positive Markov jump systems: A dynamic event-triggered method.
- Author
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Yin, Kai and Yang, Dedong
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MARKOVIAN jump linear systems , *DYNAMICAL systems , *LINEAR programming , *LYAPUNOV functions , *COMPUTER simulation - Abstract
The output feedback l 1 control problems of positive Markov jump systems(PMJSs) are studied using event-triggered method in this paper. Firstly, two novel dynamic output event-triggered control strategies(DOETCS) are proposed for continuous-time PMJSs as well as discrete-time PMJSs, which can reduce the event-triggered frequency and save network resources. Then, by constructing multiple linear copositive Lyapunov functions, two sufficient conditions about positivity and stochastic stability with l 1 -gain performance are presented for the continuous-time closed-loop PMJSs and the discrete-time closed-loop PMJSs. Simultaneously, two desired output feedback l 1 controllers and two DOETCS are also co-designed to stabilize the PMJSs in continuous and discrete cases, respectively. All the conditions obtained in this paper are in the form of linear programming(LP). Further more, the influence of parameters in the novel DOETCS on the event-triggered frequency is investigated in detail in the section of numerical simulation. Finally, two numerical examples are provided to verify the effectiveness of the proposed design schemes. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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5. An auxiliary approach to interval observer design for linear systems with disturbances.
- Author
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Li, Liwei, Zhang, Tu, Shen, Mouquan, and Park, Ju H.
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LINEAR systems , *LINEAR programming , *ADAPTIVE fuzzy control , *LYAPUNOV stability , *KALMAN filtering - Abstract
An auxiliary filtering system approach is adopted in this paper to treat the interval observer design for linear systems with state and output disturbances. By augmenting the filtering system along with the disturbances boundaries, interval observer is built under the unknown input observer framework. Relying on the Lyapunov stability method and H ∞ technique, the existence of the interval observer is formulated into strict linear matrix inequalities instead of the combination of linear programming and linear matrix inequalities. Compared with the existing result, the proposed method could render tighter state intervals from simulation studies. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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6. Event-triggered controller design for positive T-S fuzzy systems with random time-delay.
- Author
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Zhang, Di and Du, Baozhu
- Subjects
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FUZZY systems , *CLOSED loop systems , *LINEAR programming , *MARKOV processes , *LYAPUNOV functions - Abstract
This paper is concerned with the design of event-triggered controller for positive Takagi-Sugeno (T-S) fuzzy systems with a random time-delay. The random time-delay is described as a Markov process. A controller switched at different event-triggered instant is proposed. By constructing a new event-triggered instant-dependent linear co-positive Lyapunov function, the design criteria of event-triggered controller is derived to ensure the positivity and stability of the closed-loop system. These criteria can be solved by linear programming (LP) technique. A positive lower bound on the inter-execution time is ensured, which means that there is Zeno-free phenomenon. Finally, the simulation has demonstrated the effectiveness and merit of the proposed results. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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7. Dissipative PID control for uncertain positive Roesser system under the try-once-discard protocol.
- Author
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Zhang, Na and Liang, Jinling
- Subjects
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POSITIVE systems , *CLOSED loop systems , *PID controllers , *LINEAR programming , *TELECOMMUNICATION systems , *ADAPTIVE control systems - Abstract
This paper addresses the problem of dissipative proportional–integral–derivative (PID) control for the delayed positive Roesser system with interval uncertainties under the try-once-discard (TOD) protocol. To alleviate the undesired data congestion phenomenon in the shared communication network, the TOD protocol is introduced to regulate which sensor node could release its measurement at each transmission instant. An output-feedback-based PID controller is designed for the two-dimensional (2-D) system with TOD protocol. Based on the co-positive Lyapunov–Krasovskii function method, sufficient criteria in the linear programming form are attained to ensure the positivity, 2-D (ζ , η) - γ -dissipativity and robust asymptotic stability of the closed-loop system. Finally, an illustrative example is given to show effectiveness of the PID control scheme designed. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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8. Robust dissipative filtering for impulsive switched positive systems described by the Fornasini-Marchesini second model.
- Author
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Wang, Jinling, Liang, Jinling, Zhang, Cheng-Tang, and Fan, Dongmei
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POSITIVE systems , *KALMAN filtering , *LINEAR programming - Abstract
In this paper, the robust dissipative filtering issue is discussed for a class of impulsive switched positive systems described by the Fornasini-Marchesini second model. To be more specific, both lower- and upper-bounding filters are dexterously designed, and sufficient conditions guaranteeing the resulting filtering error systems to be positive and 2-D (ζ , η)- α -dissipative are given in the form of linear programming. Moreover, the explicit expressions are also provided for the related filter parameters with desired system performance. Finally, the effectiveness of the proposed results is illustrated by a numerical example. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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9. Stochastic finite-time stabilization for discrete-time positive Markov jump time-delay systems.
- Author
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Liu, Li-Juan, Zhang, Xuesong, Zhao, Xudong, and Yang, Bin
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MARKOVIAN jump linear systems , *STATE feedback (Feedback control systems) , *ELECTRICAL conductivity transitions , *LINEAR programming - Abstract
In this paper, the problems of stochastic finite-time stability and stabilization of discrete-time positive Markov jump systems are investigated. To deal with time-varying delays and switching transition probability (STP), stochastic finite-time stability conditions are established under mode-dependent average dwell time (MDADT) switching signal by developing a stochastic copositive Lyapunov-Krasovskii functional approach. Then a dual-mode dependent output feedback controller is designed, thus stochastic finite-time stabilization is achieved based on linear programming technique. Finally, two examples are given to show the effectiveness of our results. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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10. Finite-time stabilization of continuous-time switched positive delayed systems.
- Author
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Xu, Ning, Chen, Yun, Xue, Anke, and Zong, Guangdeng
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POSITIVE systems , *LINEAR programming , *PSYCHOLOGICAL feedback , *TIME delay estimation - Abstract
This paper deals with the problems of finite-time stability and stabilization for continuous-time switched positive linear time-delay systems under mode-dependent average dwell time switching signals. First, finite-time stability conditions are established by constructing an multiple piecewise copositive Lyapunov–Krasovskii functional. Then, finite-time stabilization is achieved by designing a state-feedback controller in the form of linear programming. This numerical construction approach proposed for controller cancels the restriction of the multiple piecewise copositive Lyapunov–Krasovskii functional on controllers, which can decrease the conservatism. Finally, two numerical examples are given to show the advantages of our methods. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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11. Homogenized first-moment analysis of two-time-scale positive Markov jump linear systems.
- Author
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Todorov, M.G., dos Santos, F.O., and Graciani Rodrigues, C.C.
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MOBILE communication systems , *MARKOV processes , *SINGULAR perturbations , *JUMP processes , *LINEAR programming , *MARKOVIAN jump linear systems , *SYSTEM dynamics - Abstract
We address in this paper the mean stability and L ∞ performance of continuous-time Positive Markov Jump Linear Systems (PMJLS). The distinguishing aspect of our approach vis-à-vis the existing literature is that the underlying Markov jump process is a two-time-scale Markov chain, and we consider the singular perturbation setup which arises when a small parameter (which determines the time-scale separation) goes to zero. The interest in this limiting scenario stems from large-scale situations, where complexity reduction is a central issue. To achieve this, we carry out a convergence analysis involving the semigroup that describes the first moment dynamics of the system state. This analysis allows us to subsequently characterize homogenized notions of stability and L ∞ performance, and we show how these can be connected with linear programming methods. A numerical example, regarding a version of the Foschini-Miljanic algorithm for power allocation in a mobile communication system, illustrates the proposed results. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
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12. Finite-time boundedness and control of positive coupled differential-difference equations with bounded time-varying delay.
- Author
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Zhao, Ping and Liu, Guomin
- Subjects
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LINEAR programming , *CLOSED loop systems , *COORDINATE transformations , *LINEAR matrix inequalities , *DIFFERENTIAL-difference equations , *OPTIMISM , *PSYCHOLOGICAL feedback - Abstract
This paper is concerned with the problems of finite-time boundedness and finite-time control for positive coupled differential-difference equations (CDDEs) with bounded time-varying delay. The finite-time stability of such systems is analyzed by constructing an estimate of the solutions over a finite time interval. And, sufficient conditions based on linear programming (LP) are provided for finite-time stability of positive CDDEs with bounded time-varying delay. Then, by coordinate transformation, the obtained results are extended to the finite-time bounedness of positive CDDEs with bounded time-varying delay. By the obtained result of finite-time boundedness, static output-feedback controllers and static state-feedback controllers are designed and a sufficient condition is derived to ensure the positivity and finite-time boundedness of closed-loop system. Three illustrative examples are given to show the validity of our results. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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13. Non-fragile control of positive Markovian jump systems.
- Author
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Yang, Haoyue, Zhang, Junfeng, Jia, Xianglei, and Li, Shicheng
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DISCRETE-time systems , *LINEAR programming , *JUMPING - Abstract
Abstract This paper investigates the non-fragile control for positive Markovian jump systems both in continuous-time and discrete-time cases with actuator uncertainty. It is assumed that the coefficient matrices of the non-fragile controller is unknown and bounded. The state-feedback controller gain consists of nominal controller gain and gain perturbation. First, a set of state-feedback controllers for the considered system are designed by using a stochastic co-positive Lyapunov function integrated with linear programming approach. Under the designed controllers, the resulting closed-loop systems are positive and stochastically stable. Then, the proposed controller design approach is extended to discrete-time systems. Through comparisons, it is shown that existing results are special cases of the presented ones in the paper. Finally, two examples are given to illustrate the effectiveness of the proposed design. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
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14. Distributed model predictive control of positive Markov jump systems.
- Author
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Zhang, Junfeng, Deng, Xuanjin, Zhang, Langwen, and Liu, Laiyou
- Subjects
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ALGORITHMS , *LINEAR programming , *PREDICTION models , *MATRIX decomposition , *LYAPUNOV functions , *STOCHASTIC programming - Abstract
This paper proposes a new distributed model predictive control (DMPC) for positive Markov jump systems subject to uncertainties and constraints. The uncertainties refer to interval and polytopic types, and the constraints are described in the form of 1-norm inequalities. A linear DMPC framework containing a linear performance index, linear robust stability conditions, a stochastic linear co-positive Lyapunov function, a cone invariant set, and a linear programming based DMPC algorithm is introduced. A global positive Markov jump system is decomposed into several subsystems. These subsystems can exchange information with each other and each subsystem has its own controller. Using a matrix decomposition technique, the DMPC controller gain matrix is divided into nonnegative and non-positive components and thus the corresponding stochastic stability conditions are transformed into linear programming. By virtue of a stochastic linear co-positive Lyapunov function, the positivity and stochastic stability of the systems are achieved under the DMPC controller. A lower computation burden DMPC algorithm is presented for solving the min-max optimization problem of performance index. The proposed DMPC design approach is extended for general systems. Finally, an example is given to verify the effectiveness of the DMPC design. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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15. L1-gain analysis and control of impulsive positive systems with interval uncertainty and time delay.
- Author
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Hu, Meng-Jie, Wang, Yan-Wu, Xiao, Jiang-Wen, and Yang, Wu
- Subjects
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POSITIVE systems , *EXPONENTIAL stability , *TIME delay systems , *LINEAR programming , *LYAPUNOV functions - Abstract
This paper investigates L 1 -gain analysis and control of impulsive positive systems (IPSs) with interval uncertainty and time delay. For different types of impulsive effect, by means of the Razumikhin techniques and Lyapunov function theory, conditions are developed for guaranteeing the robust exponential stability with L 1 -gain performance. Then the positive stabilization with L 1 -gain performance is also addressed for IPSs with interval uncertainty and time delay through the state feedback control. In addition, the way to explore the minimum L 1 -gain is discussed. All the obtained conditions can be easily inspected by the linear programming (LP) method when some parameters are preset. Finally, simulations are provided to demonstrate the validity of the theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
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16. An optimization approach to static output-feedback control of LTI positive systems with delayed measurements.
- Author
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Hien, Le Van and Hong, Mai Thi
- Subjects
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POSITIVE systems , *EXPONENTIAL stability , *MATRIX inequalities , *CLOSED loop systems , *LINEAR programming , *FEEDBACK control systems - Abstract
In this paper, we investigate the static output-feedback stabilization problem for LTI positive systems with a time-varying delay in the state and output vectors. By exploiting the induced monotonicity, necessary and sufficient conditions ensuring exponential stability of the closed-loop system are first quoted. Based on the derived stability conditions, necessary and sufficient stabilization conditions are formulated in terms of matrix inequalities. This general setting is then transformed into suitable vertex optimization problems by which necessary and sufficient conditions for the existence of a desired static output-feedback controller are obtained. The proposed synthesis conditions are presented in the form of linear programming conditions, which can be effectively solved by various convex algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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17. l1 filtering for continuous-discrete T-S fuzzy positive Roesser model.
- Author
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Wang, Jinling, Liang, Jinling, and Huang, Tingwen
- Subjects
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LYAPUNOV functions , *LINEAR programming , *ENGINEERING , *SIGNAL processing , *ROBUST statistics - Abstract
Abstract This paper addresses the positive filter design problem for a class of continuous-discrete Roesser model in Takagi-Sugeno fuzzy form. Both the observer-based and the general form of filters are designed with l 1 performance constraint. By utilizing the co-positive Lyapunov function approach, sufficient criteria are derived in the form of linear programming, which not only guarantee the existence of the positive lower-bounding/upper-bounding filters but also assure the resulting filtering error system to be asymptotically stable and having a prescribed l 1 -gain performance index. In addition, the explicit design schemes for the corresponding filter parameters are also presented. Finally, two numerical examples are provided to illustrate effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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18. Interventional bipartite consensus on coopetition networks with unknown dynamics.
- Author
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Hu, Jiangping and Wu, Yanzhi
- Subjects
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BIPARTITE graphs , *CONSENSUS (Social sciences) , *COOPETITION , *LINEAR programming , *SUBGROUP analysis (Experimental design) - Abstract
In this paper, an interventional bipartite consensus problem is considered for a high-order multi-agent system with unknown disturbance dynamics. The interactions among the agents are cooperative and competitive simultaneously and thus the interaction network (just called coopetition network in sequel for simplicity) is conveniently modeled by a signed graph. When the coopetition network is structurally balanced, all the agents are split into two competitive subgroups. An exogenous system (called leader for simplicity) is introduced to intervene the two competitive subgroups such that they can reach a bipartite consensus. The unknown disturbance dynamics are assumed to have linear parametric models. With the help of the notation of a disagreement state variable, decentralized adaptive laws are proposed to estimate the unknown disturbances and a dynamic output-feedback consensus control is designed for each agent in a fully distributed fashion, respectively. The controller design guarantees that the state matrix of the closed-loop system can be an arbitrary predefined Hurwitz matrix. Under the assumption that the coopetition network is structurally balanced and the leader is a root of the spanning tree in an augmented graph, the bipartite consensus and the parameter estimation are analyzed by invoking a common Lyapunov function method when the coopetition network is time-varying according to a piecewise constant switching signal. Finally, simulation results are given to demonstrate the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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19. Positivity and stability of positive singular Markovian jump time-delay systems with partially unknown transition rates.
- Author
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Zhang, Di, Zhang, Qingling, and Du, Baozhu
- Subjects
- *
MARKOVIAN jump linear systems , *LYAPUNOV functions , *LINEAR programming , *DYNAMICAL systems , *POPULATION dynamics - Abstract
This paper is concerned with positivity and stochastic stability of a class of positive singular Markovian jump time-delay systems with partially unknown transition rates. First, a necessary and sufficient condition is established to check the positivity of singular Markovian jump time-delay systems. By constructing an appropriate linear co-positive Lyapunov–Krasovskii function, a sufficient condition of stochastic stability for positive singular Markovian jump time-delay systems is established, which can be solved in terms of linear programming. Based on the results obtained, we give a necessary and sufficient condition of stability for normal positive Markovian jump systems and build some relationships with some existing results. Finally, three numerical examples are used to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
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20. Stabilization of positive Markov jump systems.
- Author
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Guo, Yafeng
- Subjects
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MARKOVIAN jump linear systems , *STABILITY theory , *STOCHASTIC analysis , *DISCRETE-time systems , *LINEAR programming , *CONTINUOUS-time filters - Abstract
This paper is concerned with investigating the problems of stability and stabilization for positive Markov jump systems. A notion of mean stability is introduced, which is shown to be equivalent to the common notions of stochastic stability in the literature. Necessary and sufficient conditions of mean stability and stabilization are established for both continuous-time and discrete-time positive Markov jump systems. All the conditions are solvable in terms of standard linear programming. Numerical examples are given to illustrate the effectiveness and the merits of the proposed methods. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
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21. Robust model predictive control with ℓ1-gain performance for positive systems.
- Author
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Zhang, Junfeng, Cai, Xiushan, Zhang, Wei, and Han, Zhengzhi
- Subjects
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POSITIVE systems , *LYAPUNOV functions , *ROBUST control , *PERFORMANCE evaluation , *PREDICTION theory , *LINEAR programming - Abstract
This paper is concerned with robust model predictive control for positive systems. The technique of model predictive control is extended to the context of positive systems. By using the linear copositive Lyapunov function approach, a robust model predictive controller for positive systems is first constructed. Being unlike the classic robust control with ℓ 2 -gain performance, the robustness of the underlying systems is guaranteed by means of ℓ 1 -gain performance. In order to increase the feasibility of the present conditions, a multi-step control strategy is then utilized. Accordingly, a cone invariant set is addressed to satisfy the recursive feasibility of the present design. All present conditions can be described by linear programming. Meanwhile, the main computation of these conditions is completely off-line, by which the computational burden is reduced. Finally, an illustrative example is given to show the effectiveness of the design. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
22. Stabilization of positive constrained T-S fuzzy systems: Application to a Buck converter.
- Author
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Benzaouia, A., Mesquine, F., Benhayoun, M., Schulte, H., and Georg, S.
- Subjects
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FUZZY systems , *LINEAR programming , *CLOSED loop systems , *PHOTOVOLTAIC power systems , *CASCADE converters , *SIMULATION methods & models - Abstract
This paper deals with the problem of constrained stability and tracking of Takagi-Sugeno (T-S) fuzzy positive systems. Linear programming (LP) is used to insert the constraints in the design phase while imposing positivity in closed-loop. The theoretical results are applied to the buck DC-DC converter which is widely used in the photovoltaic generators. Based on the simulation results success of the method is shown for this application. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
23. Stabilization of positive Takagi–Sugeno fuzzy discrete-time systems with multiple delays and bounded controls.
- Author
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Benzaouia, Abdellah, Oubah, Rkia, and El Hajjaji, Ahmed
- Subjects
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FUZZY control systems , *STABILITY theory , *DISCRETE-time systems , *FEEDBACK control systems , *LYAPUNOV functions , *LINEAR programming - Abstract
Abstract: This paper deals with the problem of stabilization by state feedback control of Takagi–Sugeno (T–S) fuzzy discrete-time systems with multiple fixed delays while imposing positivity in closed-loop. The obtained results are presented under linear programming (LP) form. In particular, the synthesis of state feedback controllers is first solved in terms of Linear programming for the unbounded controls case. This result is then extended to the stabilization problem by nonnegative controls, and stabilization by bounded controls. The stabilization conditions are derived using the single Lyapunov–Krasovskii functional (LKF). An example of a real plant is studied to show the advantages of the design procedure. A comparison between linear programming and LMI approaches is presented. [Copyright &y& Elsevier]
- Published
- 2014
- Full Text
- View/download PDF
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