Stabilizing saddles.

A synergetic control technique for stabilizing a priori unknown saddle steady states of dynamical systems is described. The method involves an unstable filter technique combined with a derivative feedback. The cut-off frequency of the filter is not limited by the damping of the system, and therefore can be set relatively high.

Enhanced control of saddle steady states of dynamical systems.

An adaptive feedback technique for stabilizing a priori unknown saddle steady states of dynamical systems is described. The method is based on an unstable low-pass filter combined with a stable low-pass filter. The cutoff frequencies of both filters can be set relatively high.

Stabilization of saddle steady states of conservative and weakly damped dissipative dynamical systems.

An adaptive feedback method for tracking and stabilizing unknown and/or slowly varying saddle-type steady states of conservative and weakly damped dissipative dynamical systems is proposed. We demonstrate that a conservative saddle point can be stabilized with neither unstable nor stable filter technique. The proposed controller involves both filters working in parallel.

Switching from stable to unknown unstable steady states of dynamical systems.

We demonstrate that a dynamical system can be switched from a stable steady state to a previously unknown unstable (saddle) steady state using proportional feedback coupling to an auxiliary unstable system. The simplest one-dimensional nonlinear model is treated analytically, the more complicated two-dimensional pendulum is considered numerically, while the damped Duffing-Holmes oscillator is investigated analytically, numerically, and experimentally. Experiments have been performed using a simplified version of the electronic Young-Silva circuit imitating the dynamical behavior of the Duffing-Holmes system.