Controller Synthesis using Qualitative Models and Constraints

Many engineering systems require the synthesis of global behaviors in nonlinear dynamical systems. Multiple model approaches to control design make it possible to synthesize robust and optimal versions of such global behaviors. We propose a methodology called Qualitative Heterogeneous Control that enables this type of control design. This methodology is based on a separation of concerns between qualitative correctness and quantitative optimization. Qualitative sufficient conditions are derived, that define a space of quantitative control strategies. These sufficient conditions are used in conjunction with a numerical optimization procedure to synthesize nonlinear optimal controllers that are robust in practical implementations. We demonstrate this process of controller synthesis for the global control of an inverted pendulum system.