Dynamic Modeling and Optimal Control for Complex Systems with Statistical Trajectory

Guo, Lingli; Xu, Zhengguang; Wang, Ye

doi:10.1155/2015/245685

Cited by 7 publications

(18 citation statements)

References 23 publications

(31 reference statements)

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“…Step 1 : At the sampling time k , the trajectory point dx ( k ) in the pattern‐moving “space” is measured by a point in a computable space, eg, a class center, an interval number, or the output‐class posterior probability, ie,

\overset{d x}{true} ((), k) = D ((), d x ((), k)),

where

\overset{d x}{true} ((), k)

is a point of the computable space, D is a measurement mapping. In this paper,

\overset{d x}{true} ((), k)

is an output‐class center in the Euclidean space.…”

Section: Dynamics Description Based On Pattern Movingmentioning

confidence: 99%

“…In this section, the PNSSM is built based on the initial control model (4). Then, the stability definition is given.…”

Section: Stability and Stabilization For A Nonlinear Systemmentioning

confidence: 99%

“…Thus, dynamic properties of the system were depicted in the pattern‐moving “space,” and control methods of the system were given. In recent years, many research results have been published on the proposed method of modeling and control …”

Section: Introductionmentioning

confidence: 99%

“…1,2 For the processes, a method of pattern-moving-based modeling and control was put forward. 3 Subsequently, many papers on the method [4][5][6][7][8][9][10][11][12][13][14] have appeared. However, the stability of a pattern-moving-based control system is rarely defined and analyzed.…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, many research results have been published on the proposed method of modeling and control. [4][5][6][7][8][9][10][11][12][13][14] However, the definition and analysis of stability are rarely studied, and the main reasons are listed as follows: (i) It is not easy to define and analyze stability of the system because of incomputibility of patterns in the pattern-moving "space." (ii) The method of pattern-moving-based modeling consists of three parts, ie, the classification mapping, the measurement mapping, and modeling in computable space.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Stability and stabilization for a class of complex production processes via LMIs

Wang

Guo

2019

Optim Control Appl Methods

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Summary This paper deals with the problem of stability and stabilization for a non‐Newton mechanical system, and the system is described by the so‐called pattern class variable rather than a state or output variable. At the beginning of this paper, the method of pattern‐moving–based dynamics description is introduced, and it describes the dynamic properties of a concerned production process at a larger granularity. Then, a pattern‐moving–based nonlinear state space model is put forward. Moreover, a feature of output‐class partition is defined and extracted, and two constraint conditions are given for the system based on the feature. Through dealing with difference of a Lyapunov function in two cases, new methods of stability and stabilization are proposed by using the LMI and S‐procedure approaches. They guarantee the stability and robust stabilization of the system and present the relationship between the feature of output‐class partition and system stability. A sintering process and numerical examples are used to demonstrate the effectiveness and practicability of the proposed method.

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\overset{d x}{true} ((), k) = D ((), d x ((), k)),

where

\overset{d x}{true} ((), k)

is a point of the computable space, D is a measurement mapping. In this paper,

\overset{d x}{true} ((), k)

is an output‐class center in the Euclidean space.…”

Section: Dynamics Description Based On Pattern Movingmentioning

confidence: 99%

“…In this section, the PNSSM is built based on the initial control model (4). Then, the stability definition is given.…”

Section: Stability and Stabilization For A Nonlinear Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Stability and stabilization for a class of complex production processes via LMIs

Wang

Guo

2019

Optim Control Appl Methods

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A pattern‐based controller for a class of production processes with input delay

Wang

Pan

2022

Asian Journal of Control

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For the problem of stabilizing a non‐Newton mechanical system with input delay, a pattern‐based state‐feedback controller is proposed. At the beginning of the paper, pattern‐based dynamic description is introduced, and a discrete‐time state‐space model with input delay (DSMID) is obtained from the description method. Then based on the DSMID, an augmentation state‐space model without input delay is built by using the lifting technique. A stabilization method is put forward, and the relationship between stability and the feature of output‐class partition is given. At last, two simulations are carried out to demonstrate the effectiveness of the proposed method.

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System asymptotic stability analysis of a kind of complex production processes based on multi-dimensional moving pattern

2022

SN Appl. Sci.

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This paper presents a new method to study the system stability of a kind of complex production processes. The system dynamics is described by multi-dimensional pattern class variables instead of state variables or output variables. The system asymptotic stability is defined by system matrix and output class partition. Firstly, “pattern moving space” is constructed by a new maximum entropy clustering method. Multi-dimensional pattern class variables measured by pattern class centers are defined in this new space. Then the nonlinear state space model of the relevant control system is derived and established through two-step prediction model. On the basis of the original stability in Euclidean space, the multi-dimensional pattern moving state space is defined and Lyapunov stability is given in this space. Finally, experimental results show the effectiveness of the proposed conditions.

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Dynamic Modeling and Optimal Control for Complex Systems with Statistical Trajectory

Cited by 7 publications

References 23 publications

Stability and stabilization for a class of complex production processes via LMIs

Stability and stabilization for a class of complex production processes via LMIs

A pattern‐based controller for a class of production processes with input delay

System asymptotic stability analysis of a kind of complex production processes based on multi-dimensional moving pattern

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