(702d) On Identification of Well-Conditioned Nonlinear Systems: Application to Economic Model Predictive Control of Nonlinear Processes

Despite the increasing availability of reasonably accurate first-principles models for broad classes of chemical processes, there are still a large number of processes that involve physico-chemical phenomena that remain poorly characterized, and thus, they cannot be accurately modeled by first-principles models. The implication of this is that recent developments in model predictive control, and specifically in the profit-optimizing strategy of economic model predictive control (EMPC) (e.g., [1]-[3]), may not be readily applied to important chemical processes.  One method for overcoming this issue is through the use of linear empirical models (e.g., [4]), which are widely used in industry and have been addressed in the context of EMPC in [5].  However, to more greatly optimize the economic objective function used in EMPC, it is desirable to take process nonlinearities into account in the process model.  Nonlinear process models typically have no analytic solution, however, so they can only be solved within an EMPC optimization problem by using numerical integration.  Nonlinear empirical models that are identified by the polynomial nonlinear state-space (PNLSS) ([6]) process identification methodology are not guaranteed to produce an empirical model that is well-conditioned such that it can be used for model predictive control.

This work focuses on economic model predictive control (EMPC) of nonlinear processes using well-conditioned polynomial nonlinear state-space models, which has not been addressed in the literature previously. Specifically, we initially address the development of a nonlinear system identification technique for a broad class of nonlinear processes which leads to the construction of polynomial nonlinear state-space dynamic models which are well-conditioned over a broad region of process operation in the sense that they can be correctly integrated in real-time using explicit numerical integration methods via time steps that are significantly larger than the ones required by nonlinear state-space models identified via existing techniques. Working within the framework of polynomial nonlinear state-space models, additional constraints are imposed in the identification procedure to ensure well-conditioning of the identified nonlinear dynamic models. This development is key because it enables the design of Lyapunov-based EMPC (LEMPC) ([2]) systems for nonlinear processes using the well-conditioned nonlinear models that can readily be implemented in real-time owing to the reduced computational burden required to compute the control actions within the process sampling time. Sufficient conditions are derived for closed-loop stability under the LEMPC scheme based on the well-conditioned nonlinear models when these models provide a sufficient degree of accuracy in the region where time-varying economically optimal operation is considered. Finally, both the system identification and LEMPC design techniques are applied to a classical chemical process example and significant advantages in terms of computation time reduction in LEMPC calculations are demonstrated.

[1] Angeli D, Amrit R, Rawlings JB. On average performance and stability of economic model predictive control. IEEE Transactions on Automatic Control. 2012;57:1615-1626.
[2] Heidarinejad M, Liu J, Christofides PD. Economic model predictive control of nonlinear process systems using Lyapunov techniques. AIChE Journal. 2012;58:855-870.
[3] Ellis M, Durand H, Christofides PD. A tutorial review of economic model predictive control methods. Journal of Process Control. 2014;24:1156-1178.
[4] Favoreel W, De Moor B, Van Overschee P. Subspace state space system identification for industrial processes. Journal of Process Control. 2000;10,149-155.
[5] Alanqar A, Ellis M, Christofides PD. Economic model predictive control of nonlinear process systems using empirical models. AIChE Journal. 2015;61:816-830.
[6] Paduart J, Lauwers L, Swevers J, Smolders K, Schoukens J, Pintelon R. Identification of nonlinear systems using polynomial nonlinear state space models. Automatica. 2010;46:647-656.