Enlargement of contractive sets of discrete-time systems: The generators approach

Bitsoris, George; Vassilaki, Marina

doi:10.1109/med.2017.7984114

Cited by 4 publications

(2 citation statements)

References 17 publications

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“…Remark The sets used in the algorithm ( γ ‐invariant set Ω and its corresponding input set Φ(Ω)) are obtained offline with a computational complexity depending on the form of the dynamic function involved in the model . Regarding online calculations, the cost function measures distances between sets and points.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Set invariance theory is a very useful tool for analyzing dynamical systems subject to constraints, allowing the extension of stability concepts from equilibrium points to equilibrium state‐space regions (ie, invariant sets). In the work of Rawlings and Mayne, for instance, a Lyapunov function for asymptotic stability of general invariant sets was defined, although no controller formulations are presented to explicitly account for it.…”

Section: Introductionmentioning

confidence: 99%

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Finite‐time convergence results in robust model predictive control

Anderson

González

Ferramosca

et al. 2018

Optim Control Appl Methods

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Robust asymptotic stability (asymptotic attractivity and -stability) of equilibrium regions under robust model predictive control (MPC) strategies was extensively studied in the last decades making use of Lyapunov theory in most cases. However, in spite of its potential application benefits, the problem of finite-time convergence under fixed prediction horizon has not received, with some few exceptions, much attention in the literature. Considering the importance in several applications of having finite-time convergence results in the context of fixed horizon MPC controllers and the lack of studies on this matter, this work presents a new set-based robust MPC (RMPC) for which, in addition to traditional stability guarantees, finite-time convergence to a target set is proved, and moreover, an upper bound on the time necessary to reach that set is provided. It is remarkable that the results apply to general nonlinear systems and only require some weak assumptions on the model, cost function, and target set.

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%