We have applied a famous engineering method, called model reference control, to control hyperchaos. We have proposed a general description of the hyperchaotic system and its reference system. By using the Lyapunov stability theorem, we have obtained the expression of the controller. Four examples for the both certain case and the uncertain case show that our method is very effective for control...

A family of replicator-like dynamics, called the escort replicator equation, is constructed using information-geometric concepts and generalized information entropies and diverenges from statistical thermodynamics. Lyapunov functions and escort generalizations of basic concepts and constructions in evolutionary game theory are given, such as an escorted Fisher’s Fundamental theorem and generali...

In this paper we survey the topic of bifurcation theory of functional differential equations. We begin with a brief discussion of the position of bifurcation and functional differential equations in dynamical systems. We follow with a survey of the state of the art on the bifurcation theory of functional differential equations, including results on Hopf bifurcation, center manifold theory, norm...

The generalized methodology for the electronic networks optimization was elaborated by means of the optimal control theory approach. In this case the problem of the electronic system design is formulated as a classical problem of functional minimization of the optimal control theory. The minimal time system design algorithm was defined as a controllable dynamic process with an optimal control v...

The active control of the unstable synchronization manifold in a shift-invariant ring of N mutually coupled chaotic oscillators is investigated. After deriving the bifurcation structures and chaotic states in the single oscillator, we find the regime of coupling parameters leading to stable and unstable synchronization phenomena in the ring, using the Master stability function approach with the...

A summarized study of the current state-of-the-art of the controlled intelligent systems based on the synergy of the potential of fuzzy logic in Takagy-Sugeno fuzzy systems with the structural flexibility and sustainability of switched nonlinear dynamic systems. In particular, following some of the fundamental theorems on quadratic stability of general nonlinear dynamic systems, due to Zhao and...

In 1892, the general problem of stability by the first approximation was considered by Lyapunov. He proved that if the system of the first approximation is regular and all its Lyapunov exponents (or characteristic exponents) are negative, then the solution of the original system is asymptotically Lyapunov stable. In 1930, it was stated by O. Perron that the requirement of regularity of the firs...

Some theoretical investigations of large angle attitude manoeuvres have been based on the app l i ca ti on of Lyapunov' s stability theory. With this method r1ortensen derived stable control laws for performing attitude manoeuvres with either thrusters or reaction wheels. Previous results were idealized in that they i qnored the non l i neari ti es inherent in the opera ti on of both types of a...

The generalized methodology for the electronic networks optimization system was elaborated by means of the optimal control theory approach. The problem of the electronic system design is formulated in this case as a classical problem of functional minimization of the optimal control theory. The minimal time system design algorithm was defined as a controllable dynamic process with an optimal co...

One of the main obstacles to the implementation of adaptive controllers for safety critical applications is the absence of analytically justified Verification and Validation (V&V) techniques for such systems. This paper seeks to provide the beginnings of a theoretically motivated V&V technique for adaptive controllers in the context of controlling uncertain flight vehicle dynamics. A set of too...