D.J. Braun, Adaptive steady-state stabilization for nonlinear dynamical systems, Physical Review E, vol. 78, no. 1, p. 016213, 2008. Reply to Comment on Adaptive steady-state stabilization for nonlinear dynamical systems, Physical Review E, vol. 81, no. 1, p. 038202, 2010.
This paper proposes an adaptive control strategy for stabilizing unstable steady states in nonlinear dynamical systems. Using LaSalle’s invariance principle, the method requires no analytical model of the system or explicit knowledge of the target steady state. Instead, it generates control inputs directly from observed system states. The approach is validated on benchmark nonlinear systems including the Lorenz, van der Pol, and pendulum equations.
Why it matters: Many nonlinear systems are difficult to control because their models are unknown or unstable. This work demonstrates a model-free strategy for steady-state stabilization, providing a foundation for adaptive control methods that can be applied broadly in physics and engineering.