Optimal control of nonlinear Markov jump systems by control parametrisation technique
This paper considers an optimal control problem of nonlinear Markov jump systems with continuous state inequality constraints. Due to the presence of continuous-time Markov chain, no existing computation method is available to solve such an optimal control problem. In this paper, a derandomisation t...
| Main Authors: | , , , , , |
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| Format: | Journal Article |
| Language: | English |
| Published: |
WILEY
2022
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| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/89485 |
| _version_ | 1848765230011645952 |
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| author | Jin, L. Yin, YanYan Loxton, Ryan Lin, Qun Liu, F. Teo, Kok Lay |
| author_facet | Jin, L. Yin, YanYan Loxton, Ryan Lin, Qun Liu, F. Teo, Kok Lay |
| author_sort | Jin, L. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | This paper considers an optimal control problem of nonlinear Markov jump systems with continuous state inequality constraints. Due to the presence of continuous-time Markov chain, no existing computation method is available to solve such an optimal control problem. In this paper, a derandomisation technique is introduced to transform the nonlinear Markov jump system into a deterministic system, which simultaneously gives rise to an equivalent deterministic dynamic optimisation problem. The control parametrisation technique is then used to partition the time horizon into a sequence of subintervals such that the control function is approximated by a piecewise constant function consistent with the partition. The heights of the piecewise constant function on the corresponding subintervals are taken as decision variables to be optimised. In this way, the approximate dynamic optimisation problem is an optimal parameter selection problem, which can be viewed as a finite dimensional optimisation problem. To solve it using a gradient-based optimisation method, the gradient formulas of the cost function and the constraint functions are derived. Finally, a real-world practical problem involving a bioreactor tank model is solved using the method proposed. |
| first_indexed | 2025-11-14T11:31:56Z |
| format | Journal Article |
| id | curtin-20.500.11937-89485 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T11:31:56Z |
| publishDate | 2022 |
| publisher | WILEY |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-894852023-07-26T05:49:05Z Optimal control of nonlinear Markov jump systems by control parametrisation technique Jin, L. Yin, YanYan Loxton, Ryan Lin, Qun Liu, F. Teo, Kok Lay Science & Technology Technology Automation & Control Systems Engineering, Electrical & Electronic Instruments & Instrumentation Engineering TIME-DELAY SYSTEMS INEXACT RESTORATION EULER DISCRETIZATION DYNAMIC OPTIMIZATION LINEAR-SYSTEMS STATE STABILITY APPROXIMATION STABILIZATION This paper considers an optimal control problem of nonlinear Markov jump systems with continuous state inequality constraints. Due to the presence of continuous-time Markov chain, no existing computation method is available to solve such an optimal control problem. In this paper, a derandomisation technique is introduced to transform the nonlinear Markov jump system into a deterministic system, which simultaneously gives rise to an equivalent deterministic dynamic optimisation problem. The control parametrisation technique is then used to partition the time horizon into a sequence of subintervals such that the control function is approximated by a piecewise constant function consistent with the partition. The heights of the piecewise constant function on the corresponding subintervals are taken as decision variables to be optimised. In this way, the approximate dynamic optimisation problem is an optimal parameter selection problem, which can be viewed as a finite dimensional optimisation problem. To solve it using a gradient-based optimisation method, the gradient formulas of the cost function and the constraint functions are derived. Finally, a real-world practical problem involving a bioreactor tank model is solved using the method proposed. 2022 Journal Article http://hdl.handle.net/20.500.11937/89485 10.1049/cth2.12249 English http://creativecommons.org/licenses/by-nc-nd/4.0/ WILEY fulltext |
| spellingShingle | Science & Technology Technology Automation & Control Systems Engineering, Electrical & Electronic Instruments & Instrumentation Engineering TIME-DELAY SYSTEMS INEXACT RESTORATION EULER DISCRETIZATION DYNAMIC OPTIMIZATION LINEAR-SYSTEMS STATE STABILITY APPROXIMATION STABILIZATION Jin, L. Yin, YanYan Loxton, Ryan Lin, Qun Liu, F. Teo, Kok Lay Optimal control of nonlinear Markov jump systems by control parametrisation technique |
| title | Optimal control of nonlinear Markov jump systems by control parametrisation technique |
| title_full | Optimal control of nonlinear Markov jump systems by control parametrisation technique |
| title_fullStr | Optimal control of nonlinear Markov jump systems by control parametrisation technique |
| title_full_unstemmed | Optimal control of nonlinear Markov jump systems by control parametrisation technique |
| title_short | Optimal control of nonlinear Markov jump systems by control parametrisation technique |
| title_sort | optimal control of nonlinear markov jump systems by control parametrisation technique |
| topic | Science & Technology Technology Automation & Control Systems Engineering, Electrical & Electronic Instruments & Instrumentation Engineering TIME-DELAY SYSTEMS INEXACT RESTORATION EULER DISCRETIZATION DYNAMIC OPTIMIZATION LINEAR-SYSTEMS STATE STABILITY APPROXIMATION STABILIZATION |
| url | http://hdl.handle.net/20.500.11937/89485 |