Subspace Method for Generalized Controller Synthesis: An Artificial Potential Field Motion Planning Approach

This paper integrates concepts from the frequency domain control methods, state space control and robot motion planning to produce a flexible control synthesis approach that is applicable to a wide class of dynamical systems. The method views a system's frequency response as a trajectory in the complex plane that is evolving under the influence of an artificial force to satisfy a geometric stability-performance criterion. A nonlinear subspace approach is used to translate these forces into an equivalent state space dynamical system that governs the dynamics of the parameters of the compensator used to generate the control signal. The design method places no restrictions on the order of the compensator or geometry of the frequency domain criterion. The approach is developed and a proof of its ability to converge, if a solution exists, to the tuning parameters set that satisfies the desired conditions is provided. The paper provides a set of design examples to demonstrate its applicability to different types of linear, nonlinear, SISO and MIMO systems.