Learning-Based Distributionally Robust Model Predictive Control of Markovian Switching Systems with Guaranteed Stability and Recursive Feasibility

Schuurmans, Mathijs; Patrinos, Panagiotis

doi:10.1109/cdc42340.2020.9303988

Cited by 16 publications

(19 citation statements)

References 25 publications

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“…A promising approach, which systematically balances controller performance and robustness with respect to misestimations of the probability distributions, is called distributionally robust control. Due to its attractive theoretical properties, it has become popular for an increasing number of control tasks [4]- [7].…”

Section: A Background and Motivationmentioning

confidence: 99%

“…When designing controllers for this class of systems, it is often assumed that the discrete mode is directly measurable [2], [7]- [9]. However, in practice, the discrete mode typically needs to be inferred from measurements of the continuous M. Schuurmans and P. Patrinos are with the Department of Electrical Engineering (ESAT-STADIUS), KU Leuven, Kasteelpark Arenberg 10, 3001 Leuven, Belgium.…”

Section: A Background and Motivationmentioning

confidence: 99%

“…with ỹ(θ) := y − G(θ)u. In a naive implementation, constructing the set Θ(y t , u t ) would require O(d Nt+1 ) verifications of (7). However, as the next result shows, only the extensions of mode sequences that are in Θ(y t−1 , u t−1 ) need to be considered.…”

Section: A Consistent Mode Sequencesmentioning

confidence: 99%

“…Let β t ∈ [0, 1), t ∈ IN denote a given (summable) sequence of desired confidence levels. Following the approach of [7], we define the ambiguity set as (11) where pt,i = 1 |Dt,i| θ∈Dt,i δ(θ) is the empirical distribution over the set D t,i , and the radius…”

Section: A Data-driven Ambiguity Setsmentioning

confidence: 99%

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Data-driven distributionally robust control of partially observable jump linear systems

Schuurmans¹,

Patrinos²

2021

Preprint

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We study safe, data-driven control of (Markov) jump linear systems with unknown transition probabilities, where both the discrete mode and the continuous state are to be inferred from output measurements. To this end, we develop a receding horizon estimator which uniquely identifies a sub-sequence of past mode transitions and the corresponding continuous state, allowing for arbitrary switching behavior. Unlike traditional approaches to mode estimation, we do not require an offline exhaustive search over mode sequences to determine the size of the observation window, but rather select it online. If the system is weakly mode observable, the window size will be upper bounded, leading to a finite-memory observer. We integrate the estimation procedure with a simple distributionally robust controller, which hedges against misestimations of the transition probabilities due to finite sample sizes. As additional mode transitions are observed, the used ambiguity sets are updated, resulting in continual improvements of the control performance. The practical applicability of the approach is illustrated on small numerical examples.

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Section: A Background and Motivationmentioning

confidence: 99%

Section: A Background and Motivationmentioning

confidence: 99%

Section: A Consistent Mode Sequencesmentioning

confidence: 99%

Section: A Data-driven Ambiguity Setsmentioning

confidence: 99%

See 2 more Smart Citations

Data-driven distributionally robust control of partially observable jump linear systems

Schuurmans¹,

Patrinos²

2021

Preprint

Self Cite

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“…More recently, there has been an interest to also apply such risk measures in robotics and control applications [25]. Riskaware control and estimation frameworks have recently appeared in [26][27][28][29][30][31][32][33] using various forms of risk. We remark that these frameworks are orthogonal to our work as they present design tools while we provide a generic framework for quantifying the risk of complex system specifications expressed in STL.…”

Section: Introductionmentioning

confidence: 99%

STL Robustness Risk over Discrete-Time Stochastic Processes

Lindemann¹,

Matni²,

Pappas³

2021

Preprint

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We present a framework to interpret signal temporal logic (STL) formulas over discrete-time stochastic processes in terms of the induced risk. Each realization of a stochastic process either satisfies or violates an STL formula. In fact, we can assign a robustness value to each realization that indicates how robustly this realization satisfies an STL formula. We then define the risk of a stochastic process not satisfying an STL formula robustly, referred to as the "STL robustness risk ". In our definition, we permit general classes of risk measures such as, but not limited to, the value-at-risk. While in general hard to compute, we propose an approximation of the STL robustness risk. This approximation has the desirable property of being an upper bound of the STL robustness risk when the chosen risk measure is monotone, a property satisfied by most risk measures. Motivated by the interest in data-driven approaches, we present a samplingbased method for calculating an upper bound of the approximate STL robustness risk for the value-at-risk that holds with high probability. While we consider the case of the value-at-risk, we highlight that such sampling-based methods are viable for other risk measures.

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Emerging methodologies in stability and optimization problems of learning‐based nonlinear model predictive control: A survey

Meng

Shen

Karimi

2022

Circuit Theory & Apps

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Since last 40 years, the theory and technology of model predictive control (MPC) have been developed rapidly. However, nonlinear MPC still faces difficulties such as high online computational complexity and inability to accurately model the system. In order to improve or solve the problems mentioned above of MPC, recent researches have deepened the learning‐based control. The learned method can model unknown or highly uncertain nonlinearities. And the emergence of efficient algorithms has greatly improved the feasibility of computing. Stability is at the heart of control design. Learning‐based nonlinear model predictive control (LB‐NMPC) has achieved systematic research results in the past 10 years. But the stability of LB‐NMPC is still an open question that has not been fully addressed in the literature. This review mainly summarizes the latest research progress of LB‐NMPC. More specifically, the uncertainty and online optimization problems of the considered systems are investigated mainly focusing on the use of learning techniques. At the same time, the research hotspots such as the control stability and constraint satisfaction of LB‐NMPC are briefly discussed. Finally, the application of LB‐NMPC technology in integrated circuits, path tracking control, and other fields is reviewed, which provides a reference for the research and application of LB‐NMPC.

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Learning-Based Distributionally Robust Model Predictive Control of Markovian Switching Systems with Guaranteed Stability and Recursive Feasibility

Cited by 16 publications

References 25 publications

Data-driven distributionally robust control of partially observable jump linear systems

Data-driven distributionally robust control of partially observable jump linear systems

STL Robustness Risk over Discrete-Time Stochastic Processes

Emerging methodologies in stability and optimization problems of learning‐based nonlinear model predictive control: A survey

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