No abstract

No abstract

No abstract

No abstract

In this paper a methodology for the estimation of domains of attraction of stable equilibriums based on maximal Lyapunov functions is proposed. The basic idea consists in finding the best level set of a Lyapunov function which is fully contained in the region of negative definiteness of its time derivative. An optimization problem is formulated, which includes a tangency requirement between the level sets and constraints on the sign of the numerator and denominator of the Lyapunov function. Such constraints help in avoiding a large number of potential dummy solutions of the nonlinear optimization model. Moreover, since global optimality is also required for proper estimation, a deterministic global optimization solver of the branch and bound type is adopted. The methodology is applied to several examples to illustrate different aspects of the approach.

No abstract

SUMMARYNon-linear regression (NLR) techniques are used widely to fit weed field emergence patterns to soil microclimatic indices using S-type functions. Artificial neural networks (ANNs) present interesting and alternative features for such modelling purposes. In the present work, a univariate hydrothermal-time based Weibull model and a bivariate (hydro-time and thermal-time) ANN were developed to study wild oat emergence under non-moisture restriction conditions using data from different locations worldwide. Results indicated a higher accuracy of the neural network in comparison with the NLR approach due to the improved descriptive capacity of thermal-time and the hydro-time as independent explanatory variables. The bivariate ANN model outperformed the conventional Weibull approach, in terms of RMSE of the test set, by 70·8%. These outcomes suggest the potential applicability of the proposed modelling approach in the design of weed management decision support systems.

a b s t r a c tIn 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.