Constructive Nonlinear Dynamics in Optimisation and Process Systems

Model based optimization is common practice in process systems and control engineering. Nonlinear programming, for example, can be applied to find economically optimal steady states, if a system model (such as a set of nonlinear ODE) is available. However, optimization naturally drives dynamical systems to their limits. This may result in modes of operation that are optimal economically, but unstable, or that are optimal but have other undesirable dynamical properties. An approach is presented that integrates stability boundaries and related boundaries into nonlinear programming. These boundaries cannot be treated as simple constraints in nonlinear programs, because they are hidden in the model and therefore no explicit characterization exists for them. Essentially, the critical boundaries of interest are manifolds of bifurcation points, and the distance of any candidate optimal point to these manifolds can locally be described with normal vectors. The approach has successfully been applied to the steady state and periodic mode optimization of nonlinear ODE, discrete time systems and delay differential equations with uncertain parameters. It is illustrated with examples from energy systems, chemical and biochemical engineering.