Constraint-Tightening and Stability in Stochastic Model Predictive Control
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In this paper, the authors propose a constraint tightening approach to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control (SMPC), and prove asymptotic stability in probability of the minimal robust positively invariant set obtained by the unconstrained LQ-optimal controller.Abstract:
Constraint tightening to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control is addressed. Stability and feasibility requirements are considered separately, highlighting the difference between existence of a solution and feasibility of a suitable, a priori known candidate solution. Subsequently, a Stochastic Model Predictive Control algorithm which unifies previous results is derived, leaving the designer the option to balance an increased feasible region against guaranteed bounds on the asymptotic average performance and convergence time. Besides typical performance bounds, under mild assumptions, we prove asymptotic stability in probability of the minimal robust positively invariant set obtained by the unconstrained LQ-optimal controller. A numerical example, demonstrating the efficacy of the proposed approach in comparison with classical, recursively feasible Stochastic MPC and Robust MPC, is provided.read more
Citations
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All you need to know about model predictive control for buildings
Ján Drgoňa,Ján Drgoňa,Javier Arroyo,Iago Cupeiro Figueroa,David Blum,Krzysztof Arendt,Donghun Kim,Donghun Kim,Enric Perarnau Ollé,Juraj Oravec,Michael Wetter,Draguna Vrabie,Lieve Helsen +12 more
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A review of optimization techniques in spacecraft flight trajectory design
TL;DR: The state-of-the-art development in numerical multi-objective trajectory optimization algorithms and stochastic trajectory planning techniques for spacecraft flight operations is reviewed.
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Recursively feasible stochastic model predictive control using indirect feedback
TL;DR: An initialization of each MPC iteration is introduced which allows that chance constraint satisfaction for the closed-loop system can readily be shown, and an average asymptotic performance bound is provided.
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An efficient method for stochastic optimal control with joint chance constraints for nonlinear systems
Joel A. Paulson,Ali Mesbah +1 more
TL;DR: The proposed solution method is significantly superior to a standard random sampling method for stochastic optimal control in terms of computational requirements and the moment-based surrogate for the JCC is shown to be substantially less conservative than the widely used distributionally robust Cantelli-Chebyshev inequality for chance constraint approximation.
References
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