Tube-based Robust Model Predictive Control for a Distributed Parameter System Modeled as a Polytopic LPV (extended version)
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
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2020
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| _version_ | 1866929686648455168 |
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| author | Ismail, Joe Liu, Steven |
| author_facet | Ismail, Joe Liu, Steven |
| contents | Distributed parameter systems (DPS) are formulated as partial differential equations (PDE). Especially, under time-varying boundary conditions, PDE introduce force coupling. In the case of the flexible stacker crane (STC), nonlinear coupling is introduced. Accordingly, online trajectory planning and tracking can be addressed using a nonlinear model predictive control (NMPC). However, due to the high computational demands of a NMPC, this paper discusses a possibility of embedding nonlinearities inside a linear parameter varying (LPV) system and thus make a use of a numerically low-demanding linear MPC. The resulting mismatches are treated as parametric and additive uncertainties in the context of robust tube-based MPC (TMPC). For the proposed approach, most of the computations are carried out offline. Only a simple convex quadratic program (QP) is conducted online. Additionally a soft-constrained extension was briefly proposed. Simulation results are used to illustrate the good performance, closed-loop stability and recursive feasibility of the proposed approach despite uncertainties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_05962 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Tube-based Robust Model Predictive Control for a Distributed Parameter System Modeled as a Polytopic LPV (extended version) Ismail, Joe Liu, Steven Optimization and Control Systems and Control Distributed parameter systems (DPS) are formulated as partial differential equations (PDE). Especially, under time-varying boundary conditions, PDE introduce force coupling. In the case of the flexible stacker crane (STC), nonlinear coupling is introduced. Accordingly, online trajectory planning and tracking can be addressed using a nonlinear model predictive control (NMPC). However, due to the high computational demands of a NMPC, this paper discusses a possibility of embedding nonlinearities inside a linear parameter varying (LPV) system and thus make a use of a numerically low-demanding linear MPC. The resulting mismatches are treated as parametric and additive uncertainties in the context of robust tube-based MPC (TMPC). For the proposed approach, most of the computations are carried out offline. Only a simple convex quadratic program (QP) is conducted online. Additionally a soft-constrained extension was briefly proposed. Simulation results are used to illustrate the good performance, closed-loop stability and recursive feasibility of the proposed approach despite uncertainties. |
| title | Tube-based Robust Model Predictive Control for a Distributed Parameter System Modeled as a Polytopic LPV (extended version) |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2003.05962 |