Phase Space Navigator: Towards Automating Control Synthesis in Phase Spaces for Nonlinear Control Systems

Abstract
We develop a novel autonomous control synthesis strategy called Phase Space Navigator for nonlinear control systems, with which a controller for a nonlinear system can be automatically synthesized in phase spaces. The Phase Space Navigator generates control laws by synthesizing flow shapes of dynamical systems and planning and navigating system trajectories in the phase spaces. More specifically, the control synthesis strategy consists of a global control path planner, a local trajectory generator, and a reference trajectory follower. The global path planner finds optimal paths from an initial state to the goal state in the phase space, consisting of a sequence of path segments connected at intermediate points where the control parameter changes. A brute-force, fine- grain search in high-dimensional phase spaces would be prohibitively expensive. Modeling and parsing phase spaces into trajectory flow pipes provide a way to efficiently reason about the phase space structures and search for global control paths. The local trajectory generator uses the flow information about the phase space trajectories to produce smoothed trajectories. The trajectory follower tracks the planned reference trajectory, reactively corrects deviations, and resynthesizes the reference trajectory if the dynamics of the system changes significantly. We have demonstrated the strategy with a program that automatically synthesizes global control paths for stabilizing a steel column buckling under compression.

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