Viable cascade control and application to a batch polymerization process

A hybrid model based on nonlinear control systems and on control affine systems is investigated. For both cases the defining dynamics (or vector fields) at a given time may undergo abrupt changes. Using the framework of viability theory, a controller is proposed that keeps the states within some user-specified region. This desired region is defined by constant bounds on individual states as well as by bounds on state-dependent functions. A viable cascade controller (VCC) is introduced which combines a typical (existing) controller (C) with a viable controller (VC). We assume that a design for C is given. The design of VC is based on computation of the velocity controlled regulation map which provides a set of control inputs that will both keep the states within the viable region as well as prevent these states from approaching the boundary of the viable region at high velocity. Theoretical background for the design of VCC is presented with a simple example which is used to demonstrate some of the computations. This approach is then applied to a batch polymerization process and simulation results are provided.