Optimal Control and Bifurcation Issues for Lorenz-Rössler Model

Abstract

Optimal control is one of the most popular decision-making tools recently in many researches and in many areas. The Lorenz-Rossler model is one of the interesting models because of the idea of consolidation of the two models: Lorenz and ossler. This paper discusses the Lorenz-Rossler model from the bifurcation phenomena and the optimal control problem (OCP). The bifurcation property at the system equilibrium is studied and it is found that saddle-node and Hopf bifurcations can be holed under some conditions on the parameters. Also, the problem of the optimal control of Lorenz-Rossler model is discussed and it uses the Pontryagin’s Maximum Principle (PMP) to derive the optimal control inputs that achieve the optimal trajectory. Numerical examples and solutions for bifurcation cases and the optimal controlled system are carried out and shown graphically to show the effectiveness of the used procedure.