Nonlinear systems analysis (2nd ed.)
Nonlinear systems analysis (2nd ed.)
Swarm intelligence
Journal of Global Optimization
Automatica (Journal of IFAC)
Brief paper: Estimating the domain of attraction for non-polynomial systems via LMI optimizations
Automatica (Journal of IFAC)
Paper: Maximal lyapunov functions and domains of attraction for autonomous nonlinear systems
Automatica (Journal of IFAC)
Enlarging the domain of attraction of MPC controllers
Automatica (Journal of IFAC)
Estimation of domains of attraction: A global optimization approach
Mathematical and Computer Modelling: An International Journal
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In this paper an optimization-based methodology for the design of the operating equilibrium of a nonlinear dynamic system based on a measure of the extension of its domain of attraction is proposed. The approach consists in maximizing the radius of a ball in the state space contained in the region of negative definiteness of the time derivative of a quadratic Lyapunov function, using a two level optimization strategy. A deterministic global optimization problem is solved at the inner level to ensure proper estimation of the domain of attraction for each feasible realization of the design variables which are optimized at the outer level. In order to cope with the non-differentiable nature of the inner problem, a stochastic algorithm is applied to manipulate the design variables at the outer level. The methodology is applied to several examples to illustrate different aspects of the approach.