Robust optimal control using conditional risk mappings in infinite horizon

Uğurlu, Kerem

doi:10.1016/j.cam.2018.05.030

Cited by 13 publications

(9 citation statements)

References 39 publications

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“…This allows us to simplify expression (17) as Since x t ∈ X , t ∈ IN, and X is a compact set containing the origin, there exists an r ≥ 0 such that x 2 ≤ r. Therefore,…”

Section: Appendixmentioning

confidence: 99%

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

Schuurmans

Patrinos

2020

2020 59th IEEE Conference on Decision and Control (CDC)

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We present a data-driven model predictive control scheme for chance-constrained Markovian switching systems with unknown switching probabilities. Using samples of the underlying Markov chain, ambiguity sets of transition probabilities are estimated which include the true conditional probability distributions with high probability. These sets are updated online and used to formulate a time-varying, risk-averse optimal control problem. We prove recursive feasibility of the resulting MPC scheme and show that the original chance constraints remain satisfied at every time step. Furthermore, we show that under sufficient decrease of the confidence levels, the resulting MPC scheme renders the closed-loop system mean-square stable with respect to the true-but-unknown distributions, while remaining less conservative than a fully robust approach.

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“…This allows us to simplify expression (17) as Since x t ∈ X , t ∈ IN, and X is a compact set containing the origin, there exists an r ≥ 0 such that x 2 ≤ r. Therefore,…”

Section: Appendixmentioning

confidence: 99%

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

Schuurmans

Patrinos

2020

2020 59th IEEE Conference on Decision and Control (CDC)

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“…• For s, t ∈ T with s ≤ t, let ρ s,t be the finite-horizon aggregated (or nested) risk mapping generated by ρ ( [5,14,15,20,21]; see also [2]): that is, ρ t,t (W t ) = ρ t (W t ) and…”

Section: Finite-horizon Risk-aware Optimal Switching Under General Fi...mentioning

confidence: 99%

Discrete-time risk-aware optimal switching with non-adapted costs

2022

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“…The recent works [5], [14], [37], and [41] also consider infinite horizon robust stochastic optimal control problems and follow a similar paradigm but use different underlying frameworks. More precisely, [14] and [41] assume a finite action and state space.…”

Section: Introductionmentioning

confidence: 99%

Markov Decision Processes under Model Uncertainty

Neufeld¹,

Sester²,

Sikic³

2022

Preprint

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We introduce a general framework for Markov decision problems under model uncertainty in a discrete-time infinite horizon setting. By providing a dynamic programming principle we obtain a local-to-global paradigm, namely solving a local, i.e., a one time-step robust optimization problem leads to an optimizer of the global (i.e. infinite time-steps) robust stochastic optimal control problem, as well as to a corresponding worst-case measure.Moreover, we apply this framework to portfolio optimization involving data of the S&P 500. We present two different types of ambiguity sets; one is fully data-driven given by a Wasserstein-ball around the empirical measure, the second one is described by a parametric set of multivariate normal distributions, where the corresponding uncertainty sets of the parameters are estimated from the data. It turns out that in scenarios where the market is volatile or bearish, the optimal portfolio strategies from the corresponding robust optimization problem outperforms the ones without model uncertainty, showcasing the importance of taking model uncertainty into account.

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Robust optimal control using conditional risk mappings in infinite horizon

Cited by 13 publications

References 39 publications

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

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

Discrete-time risk-aware optimal switching with non-adapted costs

Markov Decision Processes under Model Uncertainty

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