we establish a relationship between general constrained pseudoconvex optimization problems and globally projected dynamical systems. a corresponding novel neural network model, which is globally convergent and stable in the sense of lyapunov, is proposed. both theoretical and numerical approaches are considered. numerical simulations for three constrained nonlinear optimization problems a...

we establish a relationship between general constrained pseudoconvex optimization problems and globally projected dynamical systems. a corresponding novel neural network model, which is globally convergent and stable in the sense of lyapunov, is proposed. both theoretical and numerical approaches are considered. numerical simulations for three constrained nonlinear optimization problems are giv...

Some connections between constructive real algebraic geometry and constrained optimization are exploited. We show how the problem of determining the projection of a real-algebraic variety on a certain axis is equivalent to a problem in nonlinear programming. As an application, Grr obner bases are used to deal with an optimization problem arising in the theory of local Lyapunov functions. The pr...

We establish a relationship between general constrained pseudoconvex optimization problems and globally projected dynamical systems. A corresponding novel neural network model, which is globally convergent and stable in the sense of Lyapunov, is proposed. Both theoretical and numerical approaches are considered. Numerical simulations for three constrained nonlinear optimization problems a...

Lyapunov drift and Lyapunov optimization are powerful techniques for optimizing time averages in stochastic queueing networks subject to stability. However, there are various definitions of queue stability in the literature, and the most convenient Lyapunov drift conditions often provide stability and performance bounds only in terms of a time average expectation, rather than a pure time averag...

In this paper, optimization of the backstepping controller parameters in a grid-connected single-phase inverter is studied using Imperialist competitive algorithm (ICA), Genetic Algorithm (GA) and Particle swarm optimization (PSO) algorithm. The controller is developed for the system based on state-space averaged model. By selection of a suitable Lyapunov function, stability of the proposed con...

In this paper, we present an automatable decompositional method for the computation of Lyapunov functions for hybrid systems with complex discrete state spaces. We use graph-based reasoning to decompose hybrid automata into subgraphs, for which we then solve semidefinite optimization problems to obtain local Lyapunov functions. These local computations are made in a way that ensures that the fa...

In this paper, we are going to estimate the domain of attraction of tumor-free equilibrium points in a perturbed cancer tumor model describing the tumor-immune system competition dynamics. The proposed method is based on an optimization problem solution for a chosen Lyapunov function that can be casted in terms of Linear Matrix Inequalities constraint and Taylor expansion of nonlinear terms. We...

In this paper a procedure for construction of complete type Lyapunov–Krasovskii functionals for a scalar neutral type time delay equation is considered. The construction of the functionals depends on the so-called Lyapunov functions which satisfy a delay equation with additional boundary conditions. It is shown that these functionals admit lower and upper quadratic bounds. Exponential estimates...