(188n) Computation of Terminal Constraints for Large-Scale NMPC

Model predictive control (MPC) is an optimization based form of control that that uses mathematical programs solved in real time to determine control actions, and it is particularly suited to multiple-input-multiple-output systems with inequality constraints. Nonlinear model predictive control (NMPC) has the added benefit of utilizing a fully nonlinear dynamic model in order to provide greater accuracy at wider state ranges. These properties make NMPC very useful in chemical engineering, since chemical processes with many variables, operational constraints, and significant nonlinearities are common.

Terminal constraints are key to enforcing stability properties for NMPC, and in this work we develop a method to determine terminal regions and costs for NMPC that guarantee asymptotic stability. The terminal cost is determined using a fictitious infinite-horizon linear controller that is stable in a terminal region computed by bounding nonlinear system effects in an approach known as quasi-infinite horizon NMPC. This approach extends previous work for continuous time NMPC [1,2] to discrete time, thereby eliminating the need for sufficiently small discretization steps. This allows larger and more computationally intensive dynamic models to be considered. More importantly, we show a new method for calculating the terminal region that can more effectively handle nonlinear effects and apply to large-scale systems. In addition to determining the terminal region and cost, we also show that a lower bound on the horizon length can be determined from the terminal region and system dynamics.

The results of the stability analysis, along with computational performance of this approach will be demonstrated on a two-state nonlinear system [1] and a quadruple-tank process [3] that have been considered in previous continuous time analyses, and furthermore we show results for a large-scale system of two distillation columns in series [4].

[1] H. Chen and F. Allgöwer. A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability. Automatica, 34:1205–1218, 1998.

[2] C. Rajhans, S. Patwardhan, and H. Pillai. Two Alternate Approaches for Characterization of the Terminal Region for Continuous Time Quasi-Infinite Horizon NMPC. Proceedings of the 12^th IEEE International Conference on Control and Automation, 98-103, 2016. 

[3] T.Raff, S. Huber, Z. Nagy, and Frank Allgöwer. Nonlinear model predictive control of a four tank system: An experimental stability study. Proceedings of the 2006 IEEE Internation Conference on Control Applications, 237-242, 2006.

[4] R.B. Leer. Self-optimizing control structures for active constraint regions of a sequence of distillation columns. Master's thesis, Norweign University of Science and Technology, 2012.