Journal article
Convergence of stochastic nonlinear systems and implications for Stochastic Model Predictive Control
- Abstract:
- The stability of stochastic Model Predictive Control (MPC) subject to additive disturbances is often demonstrated in the literature by constructing Lyapunov-like inequalities that ensure closed-loop performance bounds and boundedness of the state, but tight ultimate bounds for the state and non-conservative performance bounds are typically not determined. In this work we use an input-to-state stability property to find conditions that imply convergence with probability 1 of a disturbed nonlinear system to a minimal robust positively invariant set. We discuss implications for the convergence of the state and control laws of stochastic MPC formulations, and we prove convergence results for several existing stochastic MPC formulations for linear and nonlinear systems.
- Publication status:
- Published
- Peer review status:
- Reviewed (other)
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- Files:
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(Preview, Accepted manuscript, 241.0KB, Terms of use)
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- Publisher copy:
- 10.1109/TAC.2020.3011845
Authors
- Publisher:
- Institute of Electrical and Electronics Engineers
- Journal:
- IEEE Transactions on Automatic Control More from this journal
- Volume:
- 66
- Issue:
- 6
- Pages:
- 2832 - 2839
- Publication date:
- 2020-07-24
- Acceptance date:
- 2020-07-10
- DOI:
- EISSN:
-
1558-2523
- ISSN:
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0018-9286
Terms of use
- Copyright holder:
- IEEE.
- Copyright date:
- 2020
- Rights statement:
- © 2020 IEEE.
- Notes:
- This is the accepted manuscript version of the article. The final version is available from IEEE at: https://doi.org/10.1109/TAC.2020.3011845
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