Iterative Dissipativity of Partial Difference Equation Dynamics in Open-Loop Iterative Learning Control Mode
Complex physical processes, which could evolve in both spatial and temporal dimensions and be represented by partial difference equations, could also operate in a repetitive mode with iterative learning methods as suitable control laws. For these three-dimensional systems (of the spatial, temporal,...
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2024-10-01
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| author | Tengfei Xiao |
| author_facet | Tengfei Xiao |
| author_sort | Tengfei Xiao |
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| description | Complex physical processes, which could evolve in both spatial and temporal dimensions and be represented by partial difference equations, could also operate in a repetitive mode with iterative learning methods as suitable control laws. For these three-dimensional systems (of the spatial, temporal, and iterative dimensions), the stability in the iterative direction is critical for many applications, which can be analyzed and synthesized under the proposed concept of iterative dissipativity. The definition of iterative dissipativity, which is first introduced in this paper, encapsulates the dominant information in both the spatial and temporal dimensions, while also placing a particular emphasis on the iteration improvement. This property allows for the derivation of sufficient conditions for asymptotic stability in the iteration direction, which are represented by linear matrix inequality criteria that can be readily solved. Performance in both the spatial and temporal dimensions can also be satisfied under this iterative dissipativity concept, even in absence of real-time feedback. Moreover, the optimization solutions of the control parameters can be determined. Finally, a thermal process and a numeric example are presented to illustrate the effectiveness of the proposed iteratively dissipative learning control approach. |
| format | Article |
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| issn | 2227-7390 |
| language | English |
| publishDate | 2024-10-01 |
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| series | Mathematics |
| spelling | doaj-art-72cbbfc6690748d1879139c485fb326e2025-08-20T02:16:54ZengMDPI AGMathematics2227-73902024-10-011219312810.3390/math12193128Iterative Dissipativity of Partial Difference Equation Dynamics in Open-Loop Iterative Learning Control ModeTengfei Xiao0School of Intelligent Systems Engineering, Sun Yat-sen University, Shenzhen 518107, ChinaComplex physical processes, which could evolve in both spatial and temporal dimensions and be represented by partial difference equations, could also operate in a repetitive mode with iterative learning methods as suitable control laws. For these three-dimensional systems (of the spatial, temporal, and iterative dimensions), the stability in the iterative direction is critical for many applications, which can be analyzed and synthesized under the proposed concept of iterative dissipativity. The definition of iterative dissipativity, which is first introduced in this paper, encapsulates the dominant information in both the spatial and temporal dimensions, while also placing a particular emphasis on the iteration improvement. This property allows for the derivation of sufficient conditions for asymptotic stability in the iteration direction, which are represented by linear matrix inequality criteria that can be readily solved. Performance in both the spatial and temporal dimensions can also be satisfied under this iterative dissipativity concept, even in absence of real-time feedback. Moreover, the optimization solutions of the control parameters can be determined. Finally, a thermal process and a numeric example are presented to illustrate the effectiveness of the proposed iteratively dissipative learning control approach.https://www.mdpi.com/2227-7390/12/19/3128iterative dissipativityiterative learning controlthree-dimensional systemspartial difference equationslinear matrix inequality |
| spellingShingle | Tengfei Xiao Iterative Dissipativity of Partial Difference Equation Dynamics in Open-Loop Iterative Learning Control Mode Mathematics iterative dissipativity iterative learning control three-dimensional systems partial difference equations linear matrix inequality |
| title | Iterative Dissipativity of Partial Difference Equation Dynamics in Open-Loop Iterative Learning Control Mode |
| title_full | Iterative Dissipativity of Partial Difference Equation Dynamics in Open-Loop Iterative Learning Control Mode |
| title_fullStr | Iterative Dissipativity of Partial Difference Equation Dynamics in Open-Loop Iterative Learning Control Mode |
| title_full_unstemmed | Iterative Dissipativity of Partial Difference Equation Dynamics in Open-Loop Iterative Learning Control Mode |
| title_short | Iterative Dissipativity of Partial Difference Equation Dynamics in Open-Loop Iterative Learning Control Mode |
| title_sort | iterative dissipativity of partial difference equation dynamics in open loop iterative learning control mode |
| topic | iterative dissipativity iterative learning control three-dimensional systems partial difference equations linear matrix inequality |
| url | https://www.mdpi.com/2227-7390/12/19/3128 |
| work_keys_str_mv | AT tengfeixiao iterativedissipativityofpartialdifferenceequationdynamicsinopenloopiterativelearningcontrolmode |