Direct adaptive control for nonlinear matrix second-order systems with time-varying and sign-indefinite damping and stiffness operators

2004 ◽  
Author(s):  
W.M. Haddad ◽  
M.C. Stasko ◽  
T. Hayakawa
Keyword(s):  
Adaptive Control ◽  
Second Order ◽  
Time Varying ◽  
Direct Adaptive Control ◽  
Nonlinear Matrix ◽  
Second Order Systems

Adaptive Control for Nonlinear Matrix Second-Order Systems With Sign-Varying Damping and Stiffness Operators

2001 ◽  
Author(s):  
VijaySekhar Chellaboina ◽  
Wassim M. Haddad ◽  
Tomohisa Hayakawa
Keyword(s):  
Adaptive Control ◽  
Closed Loop ◽  
Adaptive Controller ◽  
Second Order ◽  
Direct Adaptive Control ◽  
State Dependent ◽  
Control Framework ◽  
Nonlinear Matrix ◽  
System States ◽  
Second Order Systems

Abstract A direct adaptive control framework for a class of nonlinear matrix second-order dynamical systems with state-dependent uncertainty is developed. The proposed framework guarantees global asymptotic stability of the closed-loop system states associated with the plant dynamics without requiring any knowledge of the system nonlinearities other than the assumption that they are continuous and lower bounded. Generalizations to the case where the system nonlinearities are unbounded are also considered. In the special case of matrix second-order systems with polynomial nonlinearities with unknown coefficients and unknown order, we provide a universal adaptive controller that guarantees closed-loop stability of the plant states.

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.

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