Deterministic global optimization for nonlinear model predictive control of hybrid dynamic systems

Abstract

SUMMARYThis paper applies a deterministic non-convex optimization method for nonlinear model predictive control (NMPC) of systems exhibiting nonlinear hybrid dynamics. The process is represented by a model that incorporates nonlinearity using both continuous state variables and binary variables that define the multiple regimes of operation. The resulting optimization problem is a mixed-integer nonlinear program (MINLP). A deterministic method is employed to provide rigorous bounds on the solution. In some cases, this method can guarantee global optimality of the non-convex MINLP. Novel algorithm modifications are presented to improve convergence rates for the deterministic algorithm. The control algorithm is demonstrated using a simulated system of pressure tanks in which the volumetric flow through the process valves switches between distinct flow regimes. Terminal constraints and regime boundary constraints are imposed to promote stability and improve robustness. Formulation limitations and alternatives are discussed to address instances in which the resulting MINLP cannot be solved rapidly enough for real-time implementation. This work shows that deterministic methods can be applied to NMPC applications while taking stability and uncertainty into account.

Recent progress and challenges in process optimization: Review of recent work at ECUST

“…Unlike linear MPC, nonlinear MPC needs to solve an NLP problem instead of a QP problem online. The optimization problem in NMPC may be solved using heuristic global optimization algorithms, but deterministic algorithms are preferred for the guarantee of converging to a proven global optimal solution (ϵ‐optimal) in every control period. Wang et al adopted a novel deterministic global optimization algorithm, named normalized multi‐parametric disaggregation (NMDT), to solve the optimization problem in NMPC.…”

“…Similar to the integration of steady‐state RTO and MPC, a two‐layered approach based on the automation hierarchy is preferred. The two‐layered integration approach was designed by combining fast updating and re‐optimization strategy . Although the same continuous nonlinear model can be adopted in both layers, different discretization methods will cause extra mismatches, e.g., the collocation method in D‐RTO and backward difference method in NMPC.…”

A moving switching sequence approach for nonlinear model predictive control of switched systems with state‐dependent switches and state jumps

“…In previous studies, optimal control of systems with state‐independent switches and that of systems with state‐dependent switches are often considered in the same framework, and many different optimization approaches have been studied. Mixed‐integer programming (MIP) is a classical method for optimization problem with a kind of switches and numerical methods based on MIP are successfully applied to systems with long sampling period, eg, process systems . Two‐stage methods define two independent optimal control problems (one for the sequence of active subsystems over the horizon, and the other for control input and switching instants) and solve them alternately by conventional numerical methods for optimization.…”

A Hybrid MPC-PID Control System Design for the Continuous Purification and Processing of Active Pharmaceutical Ingredients

“…Ramachandran and Chaudhury [26] have suggested a control scheme for a continuous drum granulation process. An MPC strategy has been proposed for a wet drum granulation process [27][28][29].…”