The composition and validation of heterogeneous control laws

We present a method for creating and validating a nonlinear controller by the composition of heterogeneous local control laws appropriate to diierent operating regions. Like fuzzy logic control, these methods apply even in the presence of incomplete knowledge of the structure of the system, the boundaries of the operating regions, or even the control action to take. Unlike fuzzy logic control, these methods can be analyzed by a combination of classical and qualitative methods. Each operating region of the system has a classical control law, which provides high-resolution control and can be analyzed by classical methods. Operating regions are deened by fuzzy set membership functions. The global control law is the weighted average of the local control laws, where the weights are provided by the operating region membership functions. A heterogeneous control law can be analyzed, even in the presence of incomplete knowledge, by representing it as a qualitative diierential equation and using qualitative simulation to predict the set of possible behaviors of the system. By expressing the desired guarantee as a statement in a modal temporal logic, the validity of the guarantee can be automatically checked against the set of possible behaviors. We demonstrate heterogeneous controllers and our qualitative methods for proving their properties, rst for a simple level controller for a water tank, and second for a highly nonlinear chemical reactor.