Parameter-dependent Lyapunov function based model predictive control for positive systems and its application in urban water management

Zhang, Junfeng; Jia, Xianglei; Zhang, Ridong; Fu, Shizhou

doi:10.23919/chicc.2017.8028077

Cited by 4 publications

(3 citation statements)

References 31 publications

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“…Positive systems are an important class of systems whose states and outputs are always non-negative for any non-negative initial states and inputs. They have been covered in [1][2][3] and are widely used in applications such as water systems [4], ecology [5], industrial engineering [6], and so on. Linear switched positive systems (SPSs) are a class of hybrid systems consisting of a finite number of positive subsystems and a switching rule.…”

Section: Introductionmentioning

confidence: 99%

Double-Observer-Based Bumpless Transfer Control of Switched Positive Systems

Yang,

Huang,

Zhang

2024

Mathematics

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This paper investigates the bumpless transfer control of linear switched positive systems based on state and disturbance observers. First, state and disturbance observers are designed for linear switched positive systems to estimate the state and the disturbance. By combining the designed state observer, the disturbance observer, and the output, a new controller is constructed for the systems. All gain matrices are described in the form of linear programming. By using co-positive Lyapunov functions, the positivity and stability of the closed-loop system can be ensured. In order to achieve the bumpless transfer property, some additional sufficient conditions are imposed on the control conditions. The novelties of this paper lie in that (i) a novel framework is presented for positive disturbance observer, (ii) double observers are constructed for linear switched positive systems, and (iii) a bumpless transfer controller is proposed in terms of linear programming. Finally, two examples are given to illustrate the effectiveness of the proposed results.

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Section: Introductionmentioning

confidence: 99%

Double-Observer-Based Bumpless Transfer Control of Switched Positive Systems

Yang,

Huang,

Zhang

2024

Mathematics

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“…A system consisting of non-negative variables is called positive system [1][2][3]. Over past several decades, positive systems have been paid much attention owing to their modeling advantages in water systems [4], communication networks [5], chemical engineering [6], and so on. These applications also motivate the theoretical research of positive systems.…”

Section: Introductionmentioning

confidence: 99%

Linear programming‐based proportional‐integral‐derivative control of positive systems

Zhou

Zhang

Jia

et al. 2023

IET Control Theory & Appl

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This paper investigates the proportional‐integral‐derivative (PID) control of positive systems in the discrete‐time case. First, a tuning parameter is introduced to construct the proportional‐integral‐derivative control framework of positive systems. The proportional‐integral‐derivative control problem is thus transformed into the control synthesis of positive systems with time‐delay. By virtue of a matrix decomposition approach, the gain matrices of proportional‐integral‐derivative controller are designed. Using co‐positive Lyapunov functions and linear programming, the positivity and stability of positive systems are achieved under the designed proportional‐integral‐derivative controller. Then, the proportional‐integral‐derivative control of positive systems with reference signal is solved. The main contribution of this paper lies in that linear programming associated to the matrix decomposition approach is first presented to handle the proportional‐integral‐derivative control of positive systems. Finally, two illustrative examples are provided to verify the effectiveness of the proposed design.

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“…Positive systems are largely encountered in many real process (biology, statistics, thermodynamics, ecology, networking, etc.). Accordingly, many researchers are continuously interested in these systems (Luenberger, 1976;Shorten et al, 2006;Zhang and Yang, 2013;Kaczorek, 2014;2016;Shuqian et al, 2014;Junfeng et al, 2017). Starting from a nonnegative initial state, the key mathematical property of positive systems is the state evolution in the positive orthant for all nonnegative inputs.…”

Section: Introductionmentioning

confidence: 99%

Robust Controlled Positive Delayed Systems with Interval Parameter Uncertainties: A Delay Uniform Decomposition Approach

Elloumi

Mehdi

Chaabane

2018

International Journal of Applied Mathematics and Computer Science

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This paper is concerned with robust stabilization of continuous linear positive time-delay systems with parametric uncertainties. The delay considered in this work is a bounded time-varying function. Previously, we have demonstrated that the equidistant delay-decomposition technique is less conservative when it is applied to linear positive time-delay systems. Thus, we use simply a delay bi-decomposition in an appropriate Lyapunov-Krasovskii functional. By using classical and partitioned control gains, the state-feedback controllers developed in our work are formulated in terms of linear matrix inequalities. The efficiency of the proposed robust control laws is illustrated with via an example.

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Parameter-dependent Lyapunov function based model predictive control for positive systems and its application in urban water management

Cited by 4 publications

References 31 publications

Double-Observer-Based Bumpless Transfer Control of Switched Positive Systems

Double-Observer-Based Bumpless Transfer Control of Switched Positive Systems

Linear programming‐based proportional‐integral‐derivative control of positive systems

Robust Controlled Positive Delayed Systems with Interval Parameter Uncertainties: A Delay Uniform Decomposition Approach

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