(594a) Infinite Horizon NMPC for Systems with a Cyclic Steady State

Fast non-linear solvers have enabled online implementation of advanced optimal control techniques such as nonlinear model predictive control (NMPC). An NMPC controller solves a non-linear dynamic optimization problem to determine the optimal control actions that drive the plant to optimal operation. Traditional NMPC has a finite control horizon length, mainly to limit the size of the optimization problem for faster online computation. On the other hand, the performance of the controller improves with a longer control horizon and therefore ideally, a control horizon of infinite length is desired.

Infinite horizon NMPC has been introduced in the past through a time transformation in the final sampling time, which approximates the dynamics and the stage costs of an infinite horizon length. Würth and Marquardt [1] presented an infinite horizon NMPC formulation for open loop stable systems without a terminal constraint set. This was recently extended to infinite horizon NMPC for a system that has a steady state equality terminal constraint [2]. In this work we extend the infinite horizon NMPC to dynamic systems with a cyclic steady state, commonly found in periodic processes and scheduling operations. This talk also includes a rigorous stability analysis for the infinite horizon NMPC formulation for systems with cyclic steady states.

We describe the implementation of the infinite horizon NMPC approach, presenting case study results obtained using PyomoDAE [3] and IPOPT. Here, we show that the optimization problem represented with an infinite horizon NMPC, has improved performance and better computational efficiency than with finite horizon NMPC. The efficacy of the approach is validated on two case studies - a Continuous Stirred Tank Reactor (CSTR) and a dynamic gas pipeline network with cyclic demands [4].

References

[1] L. Würth and W. Marquardt, "Infinite-Horizon Continuous-Time NMPC via Time Transformation," in IEEE Transactions on Automatic Control, vol. 59, no. 9, pp. 2543-2548, (2014)

[2] S. Dinh, Y. Tong, Z.Y. Wei, O. Gerdes and L. T. Biegler, ``Nonlinear Model Predictive Control with an Infinite Horizon Approximation," submitted for publication (2025)

[3] Nicholson, B., Siirola, J.D., Watson, JP. et al. pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations. Math. Prog. Comp. 10, 187–223 (2018).

[4] L. Ghilardi, S. Naik, E. Martelli, F. Casella, L. T. Biegler, “Economic Nonlinear Model Predictive Control for cyclic gas pipeline operation”, Computers and Chemical Engineering, Volume 196, 2025