arXiv subjects

Michael H. Baumann

Publications and source records attributed to Michael H. Baumann.

4 recordsLinked to original sources

arXiv2026

Towards turnpike-based performance analysis of risk-averse stochastic predictive control

In this paper, we present performance estimates for stochastic economic MPC schemes with risk-averse cost formulations. For MPC algorithms with costs given by expectations, it was recently shown that the guaranteed near-optimal performance of abstract MPC in random variables coincides with its implementable variant using pathwise feedback. In general, this property does not extend to costs formulated in terms of risk measures. However, through a turnpike-based analysis, this paper demonstrates that for a particular class of risk measures, this result can still be leveraged to formulate an implementable risk-averse MPC scheme, resulting in near-optimal averaged performance.

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arXiv2026

Closed-loop analysis of linear stochastic MPC with risk-averse constraints

Chance constraints are widely used in stochastic model predictive control (MPC) to enforce probabilistic state and input constraints in the presence of unbounded disturbances. However, they only restrict violation probabilities and do not account for the magnitude of rare but severe constraint violations. In this paper, we extend the indirect feedback approach for linear stochastic MPC from chance constraints to risk-averse constraints like the conditional value-at-risk. For the resulting risk-averse MPC scheme, we establish recursive feasibility and closed-loop constraint satisfaction. Furthermore, based on a stochastic dissipativity notion and suitable conditions on the terminal ingredients we show that (near)-optimality of the averaged closed-loop performance can be ensured.

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arXiv2024

Near-optimal performance of stochastic economic MPC

This paper presents first results for near optimality in expectation of the closed-loop solutions for stochastic economic MPC. The approach relies on a recently developed turnpike property for stochastic optimal control problems at an optimal stationary process, combined with techniques for analyzing time-varying economic MPC schemes. We obtain near optimality in finite time as well as overtaking and average near optimality on infinite time horizons.

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arXiv2024

On the relationship between stochastic turnpike and dissipativity notions

In this paper, we introduce and study different dissipativity notions and different turnpike properties for discrete-time stochastic nonlinear optimal control problems. The proposed stochastic dissipativity notions extend the classic notion of Jan C. Willems to $L^r$ random variables and to probability measures. Our stochastic turnpike properties range from a formulation for random variables via turnpike phenomena in probability and in probability measures to the turnpike property for the moments. Moreover, we investigate how different metrics (such as Wasserstein or Lévy-Prokhorov) can be leveraged in the analysis. Our results are built upon stationarity concepts in distribution and in random variables and on the formulation of the stochastic optimal control problem as a finite-horizon Markov decision process. We investigate how the proposed dissipativity notions connect to the various stochastic turnpike properties and we work out the link between different forms of dissipativity.

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