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 the automatic synthesis of nonlinear control systems. The Phase Space Navigator generates global control laws by synthesizing flow shapes of dynamical systems and planning and navigating system trajectories in the phase spaces. It finds optimal global 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. 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. We have demonstrated the strategy with a program that automatically synthesizes global control paths for stabilizing a steel column buckling under compression. The Phase Space Navigator is particularly suitable for synthesizing high-performance control systems that do not lend themselves to traditional design and analysis techniques. It can also assist control engineers in exploring much larger design spaces than otherwise possible.