Data-driven distributionally robust MPC for systems with multiplicative noise: A semi-infinite semi-definite programming approach
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916421264474112 |
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| author | Das, Souvik Ganguly, Siddhartha Aravind, Ashwin Chatterjee, Debasish |
| author_facet | Das, Souvik Ganguly, Siddhartha Aravind, Ashwin Chatterjee, Debasish |
| contents | This article introduces a novel distributionally robust model predictive control (DRMPC) algorithm for a specific class of controlled dynamical systems where the disturbance multiplies the state and control variables. These classes of systems arise in mathematical finance, where the paradigm of distributionally robust optimization (DRO) fits perfectly, and this serves as the primary motivation for this work. We recast the optimal control problem (OCP) as a semi-definite program with an infinite number of constraints, making the ensuing optimization problem a \emph{semi-infinite semi-definite program} (SI-SDP). To numerically solve the SI-SDP, we advance an approach for solving convex semi-infinite programs (SIPs) to SI-SDPs and, subsequently, solve the DRMPC problem. A numerical example is provided to show the effectiveness of the algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15193 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Data-driven distributionally robust MPC for systems with multiplicative noise: A semi-infinite semi-definite programming approach Das, Souvik Ganguly, Siddhartha Aravind, Ashwin Chatterjee, Debasish Optimization and Control Systems and Control This article introduces a novel distributionally robust model predictive control (DRMPC) algorithm for a specific class of controlled dynamical systems where the disturbance multiplies the state and control variables. These classes of systems arise in mathematical finance, where the paradigm of distributionally robust optimization (DRO) fits perfectly, and this serves as the primary motivation for this work. We recast the optimal control problem (OCP) as a semi-definite program with an infinite number of constraints, making the ensuing optimization problem a \emph{semi-infinite semi-definite program} (SI-SDP). To numerically solve the SI-SDP, we advance an approach for solving convex semi-infinite programs (SIPs) to SI-SDPs and, subsequently, solve the DRMPC problem. A numerical example is provided to show the effectiveness of the algorithm. |
| title | Data-driven distributionally robust MPC for systems with multiplicative noise: A semi-infinite semi-definite programming approach |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2408.15193 |