Time-varying sliding modes for second-order systems

1996 ◽  
Vol 143 (5) ◽  
pp. 455-462 ◽  
Author(s):  
A. Bartoszewicz
Keyword(s):  
Second Order ◽  
Time Varying ◽  
Sliding Modes ◽  
Second Order Systems

Adaptive Stabilization of Linear Second-Order Systems with Bounded Time-Varying Coefficients

2004 ◽  
Vol 10 (7) ◽  
pp. 963-978 ◽  
Author(s):  
Alexander V. Roup ◽  
Dennis S. Bernstein
Keyword(s):  
Linear Time ◽  
Adaptive Controller ◽  
Second Order ◽  
Lyapunov Methods ◽  
Time Varying ◽  
Adaptive Stabilization ◽  
Varying Coefficients ◽  
System States ◽  
Time Varying Coefficients ◽  
Second Order Systems

We consider adaptive stabilization for a class of linear time-varying second-order systems. Interpreting the system states as position and velocity, the system is assumed to have unknown, non-paranetric, bounded time-varying damping and stiffness coefficients. The coefficient bounds need not be known to implement the adaptive controller. Lyapunov methods are used to prove global convergence of the system states. For illustration, the controller is used to stabilize several example systems.

scholarly journals Robust flocking for non-identical second-order nonlinear multi-agent systems

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Xiuxian Li ◽  
Housheng Su ◽  
Li Li
Keyword(s):  
Second Order ◽  
Time Varying ◽  
Multi Agent Systems ◽  
External Disturbances ◽  
Control Laws ◽  
Multi Agent ◽  
Model Independent ◽  
Second Order Systems ◽  
Interaction Topology ◽  
Theoretical Results

AbstractThis paper investigates the robust flocking problem for second-order nonlinear systems with a leader and external disturbances. In contrast with most of second-order systems in the literature, the intrinsic dynamics here are nonlinear and non-identical that depend not only on the velocity but also on the position, which is more realistic. Moreover, the interaction topology is undirected and switching. Provided that the leader’s velocity may be constant or time-varying, two distributed flocking control laws have been proposed for two cases to make the differences of the velocities between all followers and the leader approach to zero asymptotically. The proposed distributed flocking control laws are both model-independent which results in the effectiveness of the controllers to cope with the different intrinsic dynamics of the followers and the leader under some assumptions on boundedness of several states. An example is given to illustrate the validity of the theoretical results.

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