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Introduction to the special issue on optimal process control

Process engineers routinely use optimization in designing and operating complex systems as a means to improve their performance. Optimization has thus become a major enabling area over the years, where it has evolved from a methodology of academic interest into a technology that has and continues to make a significant impact on industry. To date, most rigorous optimization implementations have been for the design and operation of lumped systems using steady-state simulation and optimization technologies. However, a majority of natural as well as industrial systems either are inherently transient, have important transients between steady-state phases, and/or are spatially distributed. Interest in dynamic optimization and optimal control of process systems has grown significantly over the last few decades and much progress has been achieved in solution strategies. Despite its great potential, however, seldom has this technology made an impact on the process industry sector yet. Its implementation does not come without a cost. It requires a thorough understanding of the underlying phenomena, which is hardly compatible with the limited effort and time that can usually be spent for modeling. Moreover, a high level of expertise is still needed for the solution of optimal control problems (OCPs), which is itself a consequence of the lack of sufficiently fast and reliable numerical solution techniques. In this special issue of Optimal Control Applications and Methods, we have provided a selection of articles that address some of these issues and apply advanced techniques for the optimal operation, control and estimation of complex process systems. Bonilla et al. [1] propose a new method for solving nonconvex OCPs. Their method relies on a homotopy-based approach, whereby the original nonconvex OCP is gradually transformed into a simpler convex OCP by varying an homotopy parameter. A special structure is assumed for the nonconvex OCP, namely the dynamic system is control-affine and the cost function penalizes deviations from a given reference trajectory, which makes the method well suited for model predictive control (MPC) applications. They demonstrate their methodology on two case studies, a simple parameter estimation problem and the optimal control of an isothermal chemical reactor with Van de Vusse reactions and input multiplicities. They find that the likelihood of finding a global solution to the original nonconvex OCP is greatly improved compared to standard local optimization techniques. The paper by Aliyev and Gatzke [2] presents a nonlinear MPC formulation with prioritized constraint handling. This formulation is particularly relevant for control problems that have relatively limited degrees of freedom compared to the number of control objectives of interest. It ensures that the constrained optimization problem remains feasible at each MPC execution. They develop an implementation of prioritized MPC that is computationally efficient. A closed-loop test on multivariate refinery facility simulation with significant nonlinearity and input multiplicity is investigated. Because first principles’ models are difficult to obtain for such processes, second-order