Strong solvability of interval max-plus systems and applications to optimal control

Zhang, Hongwei; Tao, Yuegang; Zhang, Zilong

doi:10.1016/j.sysconle.2016.07.005

Cited by 12 publications

(6 citation statements)

References 17 publications

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“…Proof. It has been proven in theorem 5 in the work of Zhang et al 26 that the algorithm for checking the strong solvability of interval system (4) has a time complexity of O(n 2 ). By (5), n subtraction ( − ) operations and n − 1 minimum (min) operations are required to compute the principal solution u * (H, ) for each ∈  .…”

Section: Theorem 3 Algorithm 1 Has a Time Complexity Of O(n 2 )mentioning

confidence: 99%

“…*An interval system is uniquely strongly solvable means that the interval strong solution is unique. † The algorithm for checking the strong solvability of a max-plus interval system can be found in section 4 in the work of Zhang et al 26…”

Section: Theorem 3 Algorithm 1 Has a Time Complexity Of O(n 2 )mentioning

confidence: 99%

“…The transfer of the system may fluctuate due to the uncertain or variable parameters caused by noises, time delays, or system malfunctions, and such fluctuations can be framed by an interval describing the transfer's upper and lower behaviors. To take parameter perturbations into account, a class of uncertain max-plus linear systems whose parameters are not exactly known but belong to intervals is drawing increasing attention from researchers, and several analysis and control problems have been studied, including predictive control, 19,20 optimal control, 21-23 solvability, [24][25][26][27][28][29] robustness, 8,30,31 disturbance decoupling, 32 and reachability. 33 One problem inherent in control systems is how to design inputs so that the outputs can meet the predetermined requirements.…”

Section: Introductionmentioning

confidence: 99%

“…To limit the input to a minimum range, the exact interval input of uncertain max‐plus linear systems is introduced. The exact interval inputs are closely relevant to the interval strong solutions of max‐plus interval systems, which were proposed in the work of Zhang et al and developed further in the work of Wang and Tao . The optimal input design for uncertain max‐plus linear systems can be formulated as an optimal control problem that finds the maximum element of the set of exact interval inputs with respect to the order of max‐plus interval vectors.…”

Section: Introductionmentioning

confidence: 99%

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Optimal input design for uncertain max‐plus linear systems

Wang

Tao

Yan

2018

Intl J Robust & Nonlinear

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Summary This paper investigates the optimal input design for uncertain max‐plus linear systems whose parameters are only known to belong to certain intervals. The exact interval input is introduced to minimize the regulating range of the input that ensures that the system can output at any specified value in the desired interval regardless of how the parameters vary in certain ranges. The optimal input design for uncertain max‐plus linear systems is formulated as an optimal control problem that finds the maximum element of the set of exact interval inputs with respect to the order of max‐plus interval vectors. This paper also considers the optimal approximate interval input of an uncertain max‐plus linear system that has no exact interval input. A polynomial algorithm is developed to find the optimal interval input and optimal approximate interval input of an uncertain max‐plus linear system. A data transmission system with parameter perturbations is employed as an example to demonstrate how the proposed results work in practical applications.

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Section: Theorem 3 Algorithm 1 Has a Time Complexity Of O(n 2 )mentioning

confidence: 99%

Section: Theorem 3 Algorithm 1 Has a Time Complexity Of O(n 2 )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal input design for uncertain max‐plus linear systems

Wang

Tao

Yan

2018

Intl J Robust & Nonlinear

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“…Model predictive control (MPC) is one of the popular methods used in the industry because MPC is exactly in practical control processes and is widely accepted in industrial processes. To produce the performance as desired, the MPL system and systems in general, given a control [9]. One of them can be used; predictive model control techniques is a form of control that uses a system process model to predict future system behavior over a specified period.…”

Section: Introductionmentioning

confidence: 99%

Modeling Predictive Tracking Control for Max-Plus Linear Systems in Manufacturing

Aulia

Widowati

Tjahjana

et al. 2020

JFMA

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Discrete event systems, also known as DES, are class of system that can be applied to systems having an event that occurred instantaneously and may change the state. It can also be said that a discrete event system occurs under certain conditions for a certain period because of the network that describes the process flow or sequence of events. Discrete event systems belong to class of nonlinear systems in classical algebra. Based on this situation, it is necessary to do some treatments, one of which is linearization process. In the other hand, a Max-Plus Linear system is known as a system that produces linear models. This system is a development of a discrete event system that contains synchronization when it is modeled in Max-Plus Algebra. This paper discusses the production system model in manufacturing industries where the model pays the attention into the process flow or sequence of events at each time step. In particular, Model Predictive Control (MPC) is a popular control design method used in many fields including manufacturing systems. MPC for Max-Plus-Linear Systems is used here as the approach that can be used to model the optimal input and output sequences of discrete event systems. The main advantage of MPC is its ability to provide certain constraints on the input and output control signals. While deciding the optimal control value, a cost criterion is minimized by determining the optimal time in the production system that modeled as a Max-Plus Linear (MPL) system. A numerical experiment is performed in the end of this paper for tracking control purposes of a production system. The results were good that is the controlled system showed a good performance.

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Relatively maximal perturbation bounds for global robustness of max‐plus linear systems

Yin

Tao

Wang

2021

Intl J Robust & Nonlinear

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The perturbation bounds for the global robustness of max‐plus linear systems are constructed, which guarantee that parameter perturbations within such bounds do not affect the original states and outputs. The eigenelement of a max‐plus matrix is introduced to characterize the variable elements and to determine the maximal number of variable elements. The relatively maximal perturbation bound is proposed to describe the maximal variation range of system parameters. A polynomial algorithm is developed to find a relatively maximal perturbation bounds. The globally robust approach presented is applied in scheduling of container quay cranes to delimit the maximal traveling time delay.

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Strong solvability of interval max-plus systems and applications to optimal control

Cited by 12 publications

References 17 publications

Optimal input design for uncertain max‐plus linear systems

Optimal input design for uncertain max‐plus linear systems

Modeling Predictive Tracking Control for Max-Plus Linear Systems in Manufacturing

Relatively maximal perturbation bounds for global robustness of max‐plus linear systems

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