Structure-Exploiting Distributionally Robust Control of Non-Homogeneous Markov Jump Linear Systems
- 19 December 2024
- journal article
- research article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Control Systems Letters
- Vol. 8, 3069-3074
Abstract
The contribution of this paper is the mean-square stabilization of discrete-time Markov jump linear systems with mixed known, unknown, and time-varying transition probabilities. To handle uncertainties in the transition probabilities, we develop a control strategy utilizing mode-dependent static state feedback controllers and introduce data-based ambiguity sets that, extending existing literature, account for known, unknown and time-varying probabilities. These ambiguity sets are constructed using estimated transition matrices and probabilistic bounds derived from the Dvoretzky-Kiefer-Wolfowitz inequality. We validate the effectiveness of our method with numerical simulations on a control system subject to deadline overruns, demonstrating the improvements of incorporating partial knowledge of the transition probabilities.Keywords
Funding Information
- German Federal Ministry for Economic Affairs & Climate Action (13IPC021)
This publication has 17 references indexed in Scilit:
- Uncertain uncertainty in data-driven stochastic optimization: towards structured ambiguity sets2022
- Recursively Feasible Data-Driven Distributionally Robust Model Predictive Control With Additive DisturbancesIEEE Control Systems Letters, 2022
- Safe Learning-Based Control of Stochastic Jump Linear Systems: a Distributionally Robust Approach2019
- On stability of time-inhomogeneous Markov jump linear systems2016
- Stochastic model predictive control for constrained discrete-time Markovian switching systemsAutomatica, 2014
- On robust stabilization of Markovian jump systems with uncertain switching probabilitiesAutomatica, 2005
- YALMIP : a toolbox for modeling and optimization in MATLAB2005
- Discrete-Time Markov Jump Linear Systems2005
- Control with random communication delays via a discrete-time jump system approach2000
- Duality for the Sum of Convex Functions in General Banach Spaces1986