Optimal control of a hyperbolic system that describes Slutsky demand

A non-linear optimal control problem for a hyperbolic system of first order equations on a line in the case of degeneracy of the initial condition line is considered. This problem describes many natural, economic and social processes, in particular, the optimality of the Slutsky demand, the theory of bio-population, etc. The research is based on the method of characteristics and the use of nonstandard variations of the increment of target functional, which leads to the construction of efficient computational algorithms.

CONTROLE DE CAOS NO MODELO NEURONAL DE HINDMARSH-ROSE COM PARÂMETROS INCERTOS

In bioengineering there is a great motivation in studying the Hindmarsh-Rose (HR) neuron model due to the fact that it represents well the biological neuron, making it possible to simulate several behaviors of a real neuron, including periodic, aperiodic and chaotic behaviors, for example. Based on this model, this article proposes applying a linear optimal control design to the uncertain and chaotic behavior established by changes in the parameters of the system. To do so, the mathematical system of the RH model and its chaotic behavior are presented; afterwards, the fixed parametersare replaced by uncertain ones, and the chaotic dynamics of the system is investigated. At last, the linear optimal control is proposed as a method for controlling the chaotic behavior of the model, and numerical simulations are presented to show the efficiency of this proposal.

A General Framework for Optimal Control of Fractional Nonlinear Delay Systems by Wavelets

An iterative procedure to find the optimal solutions of general fractional nonlinear delay systems with quadraticperformance indices is introduced. The derivatives of state equations are understood in the Caputo sense. By presenting and applying a general framework, we use the Chebyshev wavelet method developed for fractional linear optimal control to convert fractional nonlinear optimal control problems as a sequence of quadratic programming ones. The concepts and computational procedure that are used for fractional linear optimal control are applied on fractional nonlinear optimal control. Different types of nonlinear optimal control problems with fractional or integer order can be solved. To see this, some numerical examples are solved. Another operational property of Chebyshev wavelets is presented.