Control of nonlinear systems with symmetries using chaos

We present a method that exploits chaos for the control of systems composed of subsystems with identical nonlinear dynamics and a shared, common control input. Due to symmetry, these systems are uncontrollable in a deterministic sense. However, the systems may be controllable in a stochastic sense when they are driven by process noise. We present a control strategy that exploits the sensitivity of chaotic motion to process noise. The chaotic subsystem trajectories evolve independently on the strange attractor, which enlarges the reachable set of the system. Specifically, we consider the control of a juggling machine bouncing multiple balls on a single, actuated paddle. The goal is to control the balls to a combination of stable periodic orbits. First, a paddle motion is applied that induces chaotic ball trajectories. Then, when the ball states reach the basins of attraction of the desired periodic orbits, the paddle motion is switched to the motion that stabilizes the orbits. Both simulation and preliminary experimental results are presented.