Region of attraction estimation using invariant sets and rational Lyapunov functions

In the dual-mode model predictive control (MPC) framework, the size of the stabilizable set, which is also the region of attraction, depends on the terminal constraint set. This paper aims to formulate a larger terminal set for enlarging the region of attraction in a nonlinear MPC. Given several control laws and their corresponding terminal invariant sets, a convex combination of the given sets is used to construct a time-varying terminal set. The resulting region of attraction is the union of the regions of attraction from each invariant set. Simulation results show that the proposed MPC has a larger stabilizable initial set than the one obtained when a fixed terminal set is used.

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Estimating the region of attraction of uncertain systems with invariant sets

IFAC-PapersOnLine ◽

10.1016/j.ifacol.2018.11.113 ◽

2018 ◽

Vol 51 (25) ◽

pp. 246-251

Author(s):

A. Iannelli ◽

A. Marcos ◽

M. Lowenberg

Keyword(s):

Uncertain Systems ◽

Invariant Sets ◽

Region Of Attraction

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Exact Asymptotic Stability Analysis and Region-of-Attraction Estimation for Nonlinear Systems

Abstract and Applied Analysis ◽

10.1155/2013/146137 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Min Wu ◽

Zhengfeng Yang ◽

Wang Lin

Keyword(s):

Stability Analysis ◽

Nonlinear Systems ◽

Asymptotic Stability ◽

Lyapunov Function ◽

Lyapunov Functions ◽

Nonlinear Dynamical Systems ◽

Region Of Attraction ◽

Nonlinear Dynamical ◽

Recovery Techniques ◽

Regions Of Attraction

We address the problem of asymptotic stability and region-of-attraction analysis of nonlinear dynamical systems. A hybrid symbolic-numeric method is presented to compute exact Lyapunov functions and exact estimates of regions of attraction of nonlinear systems efficiently. A numerical Lyapunov function and an estimate of region of attraction can be obtained by solving an (bilinear) SOS programming via BMI solver, then the modified Newton refinement and rational vector recovery techniques are applied to obtain exact Lyapunov functions and verified estimates of regions of attraction with rational coefficients. Experiments on some benchmarks are given to illustrate the efficiency of our algorithm.

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Algorithms for the estimation of the region of attraction with positively invariant sets

2018 7th International Conference on Systems and Control (ICSC) ◽

10.1109/icosc.2018.8587774 ◽

2018 ◽

Author(s):

Andrea Iannelli ◽

Andres Marcos ◽

Mark Lowenberg

Keyword(s):

Invariant Sets ◽

Region Of Attraction ◽

Positively Invariant Sets

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Stability for a Class of State Constrained Impulsive Nonlinear Systems: Barrier Lyapunov Functions Method

10.21203/rs.3.rs-796093/v1 ◽

2021 ◽

Author(s):

Liangliang Li ◽

Zhengwen Tu ◽

Guanghui Zhou

Keyword(s):

Nonlinear Systems ◽

Hybrid Systems ◽

Lyapunov Functions ◽

Sufficient Conditions ◽

Invariant Sets ◽

Inductive Method ◽

Linear Matrix ◽

Ellipsoid Method ◽

Lyapunov Functions Method ◽

Barrier Lyapunov Functions

Abstract This paper studies the problem for a class of state constrained impulsive nonlinear systems. Firstly, we establish two sufficient conditions for the stability of invariant sets of state constrained hybrid systems. Secondly, we construct the symmetric and asymmetric barrier Lyapunov functions, respectively. A feedback method is presented to solve the stabilization problem of constrained hybrid systems. Introduce the auxiliary matrix, combining with inductive method and linear matrix inequality theory, some sufficient conditions are obtained to ensure stability for state constrained hybrid dynamical networks by the attractive ellipsoid method approach. Finally, one example with simulations is given to validate the effectiveness of the proposed criteria.

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