Recursively Feasible Stochastic Model Predictive Control for Time-Varying Linear Systems Subject to Unbounded Disturbances
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910650879442944 |
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| author | Knaup, Jacob W. Tsiotras, Panagiotis |
| author_facet | Knaup, Jacob W. Tsiotras, Panagiotis |
| contents | Model predictive control solves a constrained optimization problem online in order to compute an implicit closed-loop control policy. Recursive feasibility -- guaranteeing that the optimal control problem will have a solution at every time step -- is an important property to guarantee the success of any model predictive control approach. However, recursive feasibility is difficult to establish in a stochastic setting and, in particular, in the presence of disturbances having unbounded support (e.g., Gaussian noise). The problem is further exacerbated for time-varying systems, in which case recursive feasibility must be established also in a robust sense, over all possible future time-varying parameter values, as well as in a stochastic sense, over all potential disturbance realizations. This work presents a method for ensuring the recursive feasibility of a convex, affine-feedback stochastic model predictive control problem formulation for systems with time-varying system matrices and unbounded disturbances using ideas from covariance steering stochastic model predictive control. It is additionally shown that the proposed approach ensures the closed-loop operation of the system will satisfy the desired chance constraints in practice, and that the stochastic model predictive control problem may be formulated as a convex program so that it may be efficiently solved in real-time. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_11107 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Recursively Feasible Stochastic Model Predictive Control for Time-Varying Linear Systems Subject to Unbounded Disturbances Knaup, Jacob W. Tsiotras, Panagiotis Optimization and Control Systems and Control Model predictive control solves a constrained optimization problem online in order to compute an implicit closed-loop control policy. Recursive feasibility -- guaranteeing that the optimal control problem will have a solution at every time step -- is an important property to guarantee the success of any model predictive control approach. However, recursive feasibility is difficult to establish in a stochastic setting and, in particular, in the presence of disturbances having unbounded support (e.g., Gaussian noise). The problem is further exacerbated for time-varying systems, in which case recursive feasibility must be established also in a robust sense, over all possible future time-varying parameter values, as well as in a stochastic sense, over all potential disturbance realizations. This work presents a method for ensuring the recursive feasibility of a convex, affine-feedback stochastic model predictive control problem formulation for systems with time-varying system matrices and unbounded disturbances using ideas from covariance steering stochastic model predictive control. It is additionally shown that the proposed approach ensures the closed-loop operation of the system will satisfy the desired chance constraints in practice, and that the stochastic model predictive control problem may be formulated as a convex program so that it may be efficiently solved in real-time. |
| title | Recursively Feasible Stochastic Model Predictive Control for Time-Varying Linear Systems Subject to Unbounded Disturbances |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2410.11107 |