A linear framework on the distributed model predictive control of positive systems

Zhang, Junfeng; Zhang, Langwen; Raïssi, Tarek

doi:10.1016/j.sysconle.2020.104665

Cited by 12 publications

(16 citation statements)

References 45 publications

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“…. , L, then the constraints in 7are handled under the control law (5) with (19) and (20). Proof (a) Interval uncertainty.…”

Section: Handling Constraintsmentioning

confidence: 99%

“…Step 4 : Implement the control law u(k) = F (ℵ)x(k|k 0 ) for k > ℵ. Theorem 3 Suppose that Algorithm 2 is feasible at the initial sample time instant k 0 , then it is also feasible for all k s > k 0 , where k s represents the sth event-triggering time instant. Moreover, the event-triggered MPC control law (16) with the gain of domain of attraction (17) ( (19) with the gain of domain of attraction (20)) can guarantee the robustly stability of the interval system (1) (the polytopic system (1)). Proof Algorithm 2 is feasible at the initial sample time instant k 0 , that is, the conditions (15), (14), and (50) are valid.…”

Section: Algorithmmentioning

confidence: 99%

“…In [16], an ℓ 1 -gain model predictive control (MPC) was proposed for positive systems with disturbances. Linear framework based MPC and distributed MPC were introduced for constrained positive systems in [17,18] and [19], respectively. Linear copositive Lyapunov functions associated with linear programming were commonly used in [16,17,18,19].…”

Section: Introductionmentioning

confidence: 99%

“…Linear framework based MPC and distributed MPC were introduced for constrained positive systems in [17,18] and [19], respectively. Linear copositive Lyapunov functions associated with linear programming were commonly used in [16,17,18,19]. MPC is an advanced control approach and can explicitly deal with uncertainties and constraints of systems [20,21,22].…”

Section: Introductionmentioning

confidence: 99%

“…MPC is also a kind of optimal control strategy, in which the control input is chosen by computing an optimization at each time instant. These literature [16,17,18,19] have partly solved the optimal control problem of positive systems. It should be noted that the MPC also contains untractable issues since the MPC algorithm is continuously implemented at each time instant.…”

Section: Introductionmentioning

confidence: 99%

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Event-triggered model predictive control of positive systems with random actuator saturation

Zhang

Lin

2021

Preprint

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This paper investigates the event-triggered model predictive control of positive systems with actuator saturation. Interval and polytopic uncertainties are imposed on the systems, respectively. First, a new model with actuator saturation obeying Bernoulli distribution is established, which is more general and powerful for describing the saturation phenomenon than the saturation in a certain way. Then, a linear event-triggering condition is constructed based on the state and error signal. An interval estimate approach is presented to reach the positivity and stability of the systems. The saturation part in the controller is technically transformed into a non-saturation part. Thus, a linear programming approach is proposed to compute the event-triggered controller gain and the corresponding domain of attraction gain. A predictive algorithm is introduced for the computation of the event-triggered controller parameters. Finally, an example is provided to illustrate the validity of the design.

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“…. , L, then the constraints in 7are handled under the control law (5) with (19) and (20). Proof (a) Interval uncertainty.…”

Section: Handling Constraintsmentioning

confidence: 99%

Section: Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Event-triggered model predictive control of positive systems with random actuator saturation

Zhang

Lin

2021

Preprint

Self Cite

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A mesh‐based partitioning algorithm for decreasing conservatism in solving bilinear matrix inequality problems

Javanmardi

Dehghani

Mohammadi

et al. 2023

Optim Control Appl Methods

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SummaryIn this paper, a mesh‐based partitioning algorithm (MBPA) to solve bilinear matrix inequality (BMI) problems is proposed, where the main idea is to divide the solution space of a non‐convex BMI problem into smaller parts in the form of Simplexes through meshing the space. In each simplex, only the concave part of BMI constraints is approximated by piecewise affine matrix (PAM), which eventually leads to a convex sub‐problem. After that, the feasible solution can be easily obtained in each simplex through the linear matrix inequality (LMI) optimization. Although the proposed MBPA exploits PAM approximation, it relaxes several restrictive conditions used in other methods, so, it can be used as an effective approach for solving BMI problems. Various numerical examples on systems from COMPleib library to design static output feedback controller are provided to validate the proposed MBPA. Simulation results reveal the satisfactory performance of MBPA in several examined problems and provide acceptable performance compared to other existing BMI solution algorithms. Comparing the percentage of superiority of MBPA with some existing prominent BMI algorithms in several control problems including spectral abscissa optimization problems, and optimization problems for the closed‐loop systems of COMPleib show that the proposed algorithm is more successful than the previous ones.

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A distributed model predictive control with neighborhood state feedback invariant set for reconfigurable networked systems

Zheng

Hou

2022

Intl J Robust & Nonlinear

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For a class of networked systems, this article proposed a distributed model predictive control (DMPC) design where the actual control law is composed of the solution of an independent optimization problem and a neighborhood states feedback part. By the proposed method, each subsystem‐based MPC is designed in a distributed way and the neighborhood feedback provides more potential for the designed DMPC to be applied to a wider class of systems. First, an LMI optimization problem is designed for determining the parameters of the neighborhood feedback matrix and corresponding invariant sets where the information of neighboring subsystems is explicitly involved. The designed feedback control law deals with the affection of the interacted subsystems and limits the deviation between the nominal model and the real system within the robust invariant set. Then, the independent suboptimal problem is developed using a predictive model without considering interconnections among subsystems, where the state is restricted by a tightened constraint which is related to the designed robust invariant set. The feasibility and stability of the closed‐loop system are analyzed. The proposed DMPC enables the direct removal or plugging‐in of subsystems. Simulation results demonstrated the effectiveness of the method.

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A linear framework on the distributed model predictive control of positive systems

Cited by 12 publications

References 45 publications

Event-triggered model predictive control of positive systems with random actuator saturation

Event-triggered model predictive control of positive systems with random actuator saturation

A mesh‐based partitioning algorithm for decreasing conservatism in solving bilinear matrix inequality problems

A distributed model predictive control with neighborhood state feedback invariant set for reconfigurable networked systems

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