Constraint-Tightening and Stability in Stochastic Model Predictive Control

Abstract

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.

“Flyable” Guidance and Control Algorithms for Orbital Rendezvous Maneuver

“…Tube-based model predictive control is proposed in [43], in which the results show that it can be implemented onboard for the real-time control of the final phase of a rendezvous and docking (RVD) maneuver. c. Stochastic model predictive control (SMPC) is introduced in [44], starting from the work of the authors in [45], [46]. A sampling-based SMPC approach is proposed in [44] to control the proximity phase of an ARVD.…”

“…From a theoretical viewpoint, the approach in [44] is based on the works [45] and [46], extending the results by considering the simultaneous presence of parametric uncertainties and of the additive noise, modeled in accordance to an experimental setup. It should be remarked that the approach proposed in [44] shares all the attractive features of [45] and [46].…”

“…It should be remarked that the approach proposed in [44] shares all the attractive features of [45] and [46]. First, the sampling is performed offline, thus allowing to reduce the online computational cost of the algorithm.…”

Stochastic model predictive control: Insights and performance comparisons for linear systems

“…Examples of stochastic MPC can be found in related works. [18][19][20][21][22][23] . In-depth discussions of the topic can be found in the works of Mayne 2 and Mesbah.…”

An efficient method for stochastic optimal control with joint chance constraints for nonlinear systems

“…28 For other types of distributions, chance constraints are commonly replaced with the distributionally robust Cantelli-Chebyshev inequality, 26 or stochastic tubes are utilized to rewrite chance constraints in terms of a backoff parameter that can be computed off-line. 29,30 However, these approaches do not readily extend to nonlinear systems, nor can they naturally handle probabilistic parametric uncertainty. Methods for chance constraint approximations in nonlinear settings have taken 2 somewhat different directions.…”