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Data-driven distributionally robust MPC for constrained stochastic systems
Systems and Control · Submitted 4 Mar 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The resulting control scheme acts as a robust controller when little data is available and converges to the certainty equivalent controller when a large sample count implies high confidence in the estimated second moment.
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The abstract, sentence by sentence
In this paper we introduce a novel approach to distributionally robust optimal control that supports online learning of the ambiguity set, while guaranteeing recursive feasibility. We introduce conic representable risk, which is useful to derive tractable reformulations of distributionally robust optimization problems. Specifically, to illustrate the techniques introduced, we utilize risk measures constructed based on data-driven ambiguity sets, constraining the second moment of the random disturbance. In the optimal control setting, such moment-based risk measures lead to tractable optimal controllers when combined with affine disturbance feedback. Assumptions on the constraints are given that guarantee recursive feasibility. The resulting control scheme acts as a robust controller when little data is available and converges to the certainty equivalent controller when a large sample count implies high confidence in the estimated second moment. This is illustrated in a numerical experiment.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this paper we introduce a novel approach to distributionally robust optimal control that supports online learning of the ambiguity set, while guaranteeing recursive feasibility. | contribution 1.00 | 0.94 | 0.42 | asserted 1.00 |
| s1 | We introduce conic representable risk, which is useful to derive tractable reformulations of distributionally robust optimization problems. | contribution 0.97 | 0.91 | 0.07 | asserted 0.99 |
| s2 | Specifically, to illustrate the techniques introduced, we utilize risk measures constructed based on data-driven ambiguity sets, constraining the second moment of the random disturbance. | method 0.92 | 0.80 | 0.06 | asserted 0.95 |
| s3 | In the optimal control setting, such moment-based risk measures lead to tractable optimal controllers when combined with affine disturbance feedback. | result 0.46 | 0.62 | 0.10 | asserted 0.95 |
| s4 | Assumptions on the constraints are given that guarantee recursive feasibility. | method 0.62 | 0.70 | 0.07 | asserted 0.98 |
| s5 | The resulting control scheme acts as a robust controller when little data is available and converges to the certainty equivalent controller when a large sample count implies high confidence in the estimated second moment. | interpretation 0.62 | 0.82 | 0.43 | asserted 1.00 |
| s6 | This is illustrated in a numerical experiment. | result 0.45 | 0.90 | 0.04 | asserted 0.98 |
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The paper
Original abstract
In this paper we introduce a novel approach to distributionally robust optimal control that supports online learning of the ambiguity set, while guaranteeing recursive feasibility. We introduce conic representable risk, which is useful to derive tractable reformulations of distributionally robust optimization problems. Specifically, to illustrate the techniques introduced, we utilize risk measures constructed based on data-driven ambiguity sets, constraining the second moment of the random disturbance. In the optimal control setting, such moment-based risk measures lead to tractable optimal controllers when combined with affine disturbance feedback. Assumptions on the constraints are given that guarantee recursive feasibility. The resulting control scheme acts as a robust controller when little data is available and converges to the certainty equivalent controller when a large sample count implies high confidence in the estimated second moment. This is illustrated in a numerical experiment.
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How the literature uses it
4 arXiv papers cite this in 6 sentences
Papers citing it · 2 sentences without a confident label
Uses its method or tool 1 paper
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The ambiguity set [ref] belongs to the general set of conic-representable risk measures, which allows us to tractably reformulate the OCP [ref] as a standard nonlinear program, using duality-based techniques described in [ref] .
Safe, Learning-Based MPC for Highway Driving under Lane-Change Uncertainty: A Distributionally Robust Approach · Distributionally robust MPC over scenario trees · 0.81
Cites it as background 2 papers
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This approach has been applied in several different settings, under varying assumptions on the underlying system and data-generating distributions [ref] .
Safe, Learning-Based MPC for Highway Driving under Lane-Change Uncertainty: A Distributionally Robust Approach · Risk and ambiguity · 0.87
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Recently, a data-driven distributionally robust MPC with a moment-based ambiguity set for quadratic objective function under multi-stage risk measures was proposed in [ref] .
Data-driven distributionally robust MPC using the Wasserstein metric · INTRODUCTION · 0.89
What it cites · 5 sentences without a confident label
Uses the method or tool of 1 paper
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To enforce independence of the disturbances $w_t$ we introduce product ambiguity [ref] .
Mathematical Foundations of Distributionally Robust Multistage Optimization · Product ambiguity · 0.93
Compares with 1 paper
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Similar results were achieved in [ref] for a tube-based approach with Wasserstein ambiguity, the radius of which is not data-driven; in [ref] for relaxed, robust constraints; in [ref] for moment-based ambiguity which is not data-driven and does not guarantee recursive feasibility; and [ref] for discrete distributions.
Stochastic MPC with Distributionally Robust Chance Constraints · Introduction · 1.00
Cites as background 2 papers
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The most common are moment-based, $ϕ$-divergence and Wasserstein ambiguity sets [ref] .
Distributionally Robust Optimization: A Review · Introduction · 0.94
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The consequences of this are discussed in [ref] .], multistage risk measures [ref] , $_^t _t →$.
Mathematical Foundations of Distributionally Robust Multistage Optimization · Multi-stage problems · 0.83
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