### A Leighton-Borůvka formula for Morse conjugate points

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

In this paper, the finite-time stabilization problem of chained form systems with parametric uncertainties is investigated. A novel switching control strategy is proposed for adaptive finite-time control design with the help of Lyapunov-based method and time-rescaling technique. With the proposed control law, the uncertain closed-loop system under consideration is finite-time stable within a given settling time. An illustrative example is also given to show the effectiveness of the proposed controller....

This paper is concerned with the finite-time synchronization problem for a class of cross-strict feedback underactuated hyperchaotic systems. Using finite-time control and backstepping control approaches, a new robust adaptive synchronization scheme is proposed to make the synchronization errors of the systems with parameter uncertainties zero in a finite time. Appropriate adaptive laws are derived to deal with the unknown parameters of the systems. The proposed method can be applied to a variety...

This paper deals with integrability issues of the Euler-Lagrange equations associated to a variational problem, where the energy function depends on acceleration and drag. Although the motivation came from applications to path planning of underwater robot manipulators, the approach is rather theoretical and the main difficulties result from the fact that the power needed to push an object through a fluid increases as the cube of its speed.

The use of a multi-input control design procedure for uncertain nonlinear systems expressible in multi-input parametric-pure feedback form to determine the control law for a class of mechanical systems is described in this paper. The proposed procedure, based on the well-known backstepping design technique, relies on the possibility of extending to multi-input uncertain systems a second order sliding mode control approach recently developed, thus reducing the computational load, as well as increasing...

By introducing a feedback control to a proposed Sprott E system, an extremely complex chaotic attractor with only one stable equilibrium is derived. The system evolves into periodic and chaotic behaviors by detailed numerical as well as theoretical analysis. Analysis results show that chaos also can be generated via a period-doubling bifurcation when the system has one and only one stable equilibrium. Based on Lyapunov stability theory, the adaptive control law and the parameter update law are derived...