Finite Control Set Model Predictive Control with Limit Cycle Stability Guarantees
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913424862085120 |
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| author | Xu, Duo Lazar, Mircea |
| author_facet | Xu, Duo Lazar, Mircea |
| contents | This paper considers the design of finite control set model predictive control (FCS-MPC) for discrete-time switched affine systems. Existing FCS-MPC methods typically pursue practical stability guarantees, which ensure convergence to a bounded invariant set that contains a desired steady state. As such, current FCS-MPC methods result in unpredictable steady-state behavior due to arbitrary switching among the available finite control inputs. Motivated by this, we present a FCS-MPC design that aims to stabilize a steady-state limit cycle compatible with a desired output reference via a suitable cost function. We provide conditions in terms of periodic terminal costs and finite control set control laws that guarantee asymptotic stability of the developed limit cycle FCS-MPC algorithm. Moreover, we develop conditions for recursive feasibility of limit cycle FCS-MPC in terms of periodic terminal sets and we provide systematic methods for computing ellipsoidal and polytopic periodically invariant sets that contain a desired steady-state limit cycle. Compared to existing periodic terminal ingredients for tracking MPC with a continuous control set, we design and compute terminal ingredients using a finite control set. The developed methodology is validated on switched systems and power electronics benchmark examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07615 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite Control Set Model Predictive Control with Limit Cycle Stability Guarantees Xu, Duo Lazar, Mircea Optimization and Control Systems and Control This paper considers the design of finite control set model predictive control (FCS-MPC) for discrete-time switched affine systems. Existing FCS-MPC methods typically pursue practical stability guarantees, which ensure convergence to a bounded invariant set that contains a desired steady state. As such, current FCS-MPC methods result in unpredictable steady-state behavior due to arbitrary switching among the available finite control inputs. Motivated by this, we present a FCS-MPC design that aims to stabilize a steady-state limit cycle compatible with a desired output reference via a suitable cost function. We provide conditions in terms of periodic terminal costs and finite control set control laws that guarantee asymptotic stability of the developed limit cycle FCS-MPC algorithm. Moreover, we develop conditions for recursive feasibility of limit cycle FCS-MPC in terms of periodic terminal sets and we provide systematic methods for computing ellipsoidal and polytopic periodically invariant sets that contain a desired steady-state limit cycle. Compared to existing periodic terminal ingredients for tracking MPC with a continuous control set, we design and compute terminal ingredients using a finite control set. The developed methodology is validated on switched systems and power electronics benchmark examples. |
| title | Finite Control Set Model Predictive Control with Limit Cycle Stability Guarantees |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2407.07615 |