Finite Time Stabilizing Control Law Research Articles

Finite-Time Stabilization for Continuous Triangular Systems via Vector Lyapunov Function Approach

This article provides finite-time stabilizing control laws for the continuous triangular systems, in which the nominal dynamics is the chain of power integrators with the power of a positive odd rational number. For a class of continuous lower-triangular systems, the linear controllers are designed. By invoking a vector Lyapunov function theory, there is no need to use the usual back-stepping technique and a quite number of inequality computations are avoided. For a class of continuous upper-triangular systems, the nested-saturation controllers are constructed. In this case, the use of a vector Lyapunov function theory also helps to reduce computational burden, and allows us to summarize a same group of parameter conditions guaranteeing both the reduction of saturated terms and the finite-time stability of the reduced system.

On finite-time stability and stabilization of nonlinear hybrid dynamical systems

<abstract> Finite time stability involving dynamical systems whose trajectories converge to a Lyapunov stable equilibrium state in finite time have been studied for both continuous-time and discrete-time systems. For continuous-time systems, finite time stability is defined for equilibria of continuous but non-Lipschitzian nonlinear dynamics, whereas discrete-time systems can exhibit finite time stability even when the system dynamics are linear, and hence, Lipschitz continuous. Alternatively, for impulsive dynamical systems it may be possible to reset the system states to an equilibrium state achieving finite time stability without requiring a non-Lipschitz condition for the continuous-time part of the hybrid system dynamics. In this paper, we develop sufficient Lyapunov conditions for finite time stability of impulsive dynamical systems using both a scalar differential Lyapunov inequality on the continuous-time dynamics as well as a scalar difference Lyapunov inequality on the discrete-time resetting dynamics. Furthermore, using our proposed finite time stability results, we design universal hybrid finite time stabilizing control laws for impulsive dynamical systems. Finally, we present several numerical examples for finite time stabilization of network impulsive dynamical systems. </abstract>

Nonsingular terminal sliding-mode control of a tractor–trailer system

This is the first paper considering finite-time stabilization approach to design a control law for a tractor–trailer system. This robot is a nonholonomic system which cannot be stabilized with continuous control laws. The main contributions of this paper are, first, the transformation of the equations of the system to the bilinear chained form, which simplifies the design of finite-time stabilizing control laws, and then, designing a nonsingular finite-time controller based on the terminal sliding-mode technique. This technique needs some recursive sliding surfaces, which should be mathematically derived, for each application. Efficiency of the designed control law in finite-time stabilization of the tractor–trailer system is shown through computer simulations.

Nonsmooth finite-time control of uncertain second-order nonlinear systems

Nonsmooth finite-time stabilizing control laws have been developed for the double integrator system. The objective of this paper is to further explore the finite-time tracking control problem of a general form of uncertain second-order affine nonlinear system with the new forms of terminal sliding mode (TSM). Discontinuous and continuous finite-time controllers are also developed respectively without the singularity problem. Complete robustness can be acquired with the former, and enhanced robustness compared with the conventional boundary layer method can be expressed as explicit bounded function with the latter. Simulation results on the stabilizing and tracking problems are presented to demonstrate the effectiveness of the control algorithms.

Non-smooth finite-time stabilization for a class of nonlinear systems

In this paper, global finite-time stabilization problem for a large class of nonlinear control systems is considered. An iterative design approach is given based on Lyapunov function. The finite time stabilizing control laws are constructed in the form of continuous but non-smooth time-invariant feedback.