Rolf Findeisen

Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations

Abstract Optimization problems in chemical engineering often involve complex systems of nonlinear DAE as the model equations. The direct multiple shooting method has been known for a while as a fast off-line method for optimization problems in ODE and later in DAE. Some factors crucial for its fast performance are briefly reviewed. The direct multiple shooting approach has been successfully adapted to the specific requirements of real-time optimization. Special strategies have been developed to effectively minimize the on-line computational effort, in which the progress of the optimization iterations is nested with the progress of the process. They use precalculated information as far as possible (e.g. Hessians, gradients and QP presolves for iterated reference trajectories) to minimize response time in case of perturbations. In typical real-time problems they have proven much faster than fast off-line strategies. Compared with an optimal feedback control computable upper bounds for the loss of optimality can be established that are small in practice. Numerical results for the Nonlinear Model Predictive Control (NMPC) of a high-purity distillation column subject to parameter disturbances are presented.

State and Output Feedback Nonlinear Model Predictive Control: An Overview

The purpose of this paper is twofold. In the first part, we give a review on the current state of nonlinear model predictive control (NMPC). After a brief presentation of the basic principle of predictive control we outline some of the theoretical, computational, and implementational aspects of this control strategy. Most of the theoretical developments in the area of NMPC are based on the assumption that the full state is available for measurement, an assumption that does not hold in the typical practical case. Thus, in the second part of this paper the focus on the output feedback problem in NMPC. After a brief overview on existing output feedback NMPC approaches we derive conditions that guarantee stability of the closed-loop if an NMPC state feedback controller is used together with a full state observer for the recovery of the system state.

Nonlinear Model Predictive Control: From Theory to Application

While linear model predictive control is popular since the 70s of the past century, only since the 90s there is a steadily increasing interest from control theoreticians as well as control practitioners in nonlinear model predictive control (NMPC). The practical interest is mainly driven by the fact that todays processes need to be operated under tight performance specifications. At the same time more and more constraints, stemming for example from environmental and safety considerations, need to be satisfied. Often, these demands can only be met when process nonlinearities and constraints are explicitly taken into account in the controller design. Nonlinear predictive control, the extension of the well established linear predictive control to the nonlinear world, is one possible candidate to meet these demands. This paper reviews the basic principle of NMPC, and outlines some of the theoretical, computational, and implementational aspects of this control strategy.

Assessment and Future Directions of Nonlinear Model Predictive Control

Foundations and History of NMPC.- Theoretical Aspects of NMPC.- Numerical Aspects of NMPC.- Robustness, Robust Design, and Uncertainty.- State Estimation and Output Feedback.- Industrial Perspective on NMPC.- NMPC and Process Control.- NMPC for Fast Systems.- Novel Applications of NMPC.- Distributed NMPC, Obstacle Avoidance, and Path Planning.

Electrochemical Model Based Observer Design for a Lithium-Ion Battery

Batteries are the key technology for enabling further mobile electrification and energy storage. Accurate prediction of the state of the battery is needed not only for safety reasons, but also for better utilization of the battery. In this work we present a state estimation strategy for a detailed electrochemical model of a lithium-ion battery. The benefit of using a detailed model is the additional information obtained about the battery, such as accurate estimates of the internal temperature, the state of charge within the individual electrodes, overpotential, concentration and current distribution across the electrodes, which can be utilized for safety and optimal operation. Based on physical insight, we propose an output error injection observer based on a reduced set of partial differential-algebraic equations. This reduced model has a less complex structure, while it still captures the main dynamics. The observer is extensively studied in simulations and validated in experiments for actual electric-vehicle drive cycles. Experimental results show the observer to be robust with respect to unmodeled dynamics as well as to noisy and biased voltage and current measurements. The available state estimates can be used for monitoring purposes or incorporated into a model based controller to improve the performance of the battery while guaranteeing safe operation.

Brief paper: Robust output feedback model predictive control of constrained linear systems: Time varying case

The problem of output feedback model predictive control of discrete time systems in the presence of additive but bounded state and output disturbances is considered. The overall controller consists of two components, a stable state estimator and a tube based, robustly stabilizing model predictive controller. Earlier results are extended by allowing the estimator to be time varying. The proposed robust output feedback controller requires the online solution of a standard quadratic program. The closed loop system renders a specified invariant set robustly exponentially stable.

Computational Delay in Nonlinear Model Predictive Control

Abstract By now a series of NMPC schemes exist that lead to guaranteed stability of the closed-loop. However, in these schemes the computation time to find a solution of the open-loop optimal control problem is often neglected. In practice the necessary computation time is often not negligible, and leads, since not explicitly considered, to a delay between the state information and the input signal implemented on the system. This delay can lead to a drastic performance decrease or even to instability of the closed-loop. In this paper we outline a simple approach how the computational delay can be considered in nonlinear model predictive control schemes and provide conditions under which the stability of the c1osed loop can be guaranteed. This allows to employ nonlinear model predictive control even in the case that the necessary numerical solution time is significant. The presented approach is exemplified considering the control of a continuous reactor.

Integrating cellular metabolism into a multiscale whole-body model.

Cellular metabolism continuously processes an enormous range of external compounds into endogenous metabolites and is as such a key element in human physiology. The multifaceted physiological role of the metabolic network fulfilling the catalytic conversions can only be fully understood from a whole-body perspective where the causal interplay of the metabolic states of individual cells, the surrounding tissue and the whole organism are simultaneously considered. We here present an approach relying on dynamic flux balance analysis that allows the integration of metabolic networks at the cellular scale into standardized physiologically-based pharmacokinetic models at the whole-body level. To evaluate our approach we integrated a genome-scale network reconstruction of a human hepatocyte into the liver tissue of a physiologically-based pharmacokinetic model of a human adult. The resulting multiscale model was used to investigate hyperuricemia therapy, ammonia detoxification and paracetamol-induced toxication at a systems level. The specific models simultaneously integrate multiple layers of biological organization and offer mechanistic insights into pathology and medication. The approach presented may in future support a mechanistic understanding in diagnostics and drug development.

Stochastic nonlinear model predictive control with probabilistic constraints

Stochastic uncertainties are ubiquitous in complex dynamical systems and can lead to undesired variability of system outputs and, therefore, a notable degradation of closed-loop performance. This paper investigates model predictive control of nonlinear dynamical systems subject to probabilistic parametric uncertainties. A nonlinear model predictive control framework is presented for control of the probability distribution of system states while ensuring the satisfaction of constraints with some desired probability levels. To obtain a computationally tractable formulation for real control applications, polynomial chaos expansions are utilized to propagate the probabilistic parametric uncertainties through the system model. The paper considers individual probabilistic constraints, which are converted explicitly into convex second-order cone constraints for a general class of probability distributions. An algorithm is presented for receding horizon implementation of the finite-horizon stochastic optimal control problem. The capability of the stochastic model predictive control approach in terms of shaping the probability distribution of system states and fulfilling state constraints in a stochastic setting is demonstrated for optimal control of polymorphic transformation in batch crystallization.

Parameterized Tube Model Predictive Control

This paper develops a parameterized tube model predictive control (MPC) synthesis method. The most relevant novel feature of our proposal is the online use of a single tractable linear program that optimizes parameterized, Minkowski decomposable, state and control tubes and an associated, fully separable, nonlinear, control policy. The induced control policy enjoys a higher degree of nonlinearity than existing tube MPC and robust MPC using disturbance affine control policy. Our proposal offers greater generality than the state of the art robust MPC methods. It is conjectured, and also established in three cases, that our proposal is equivalent, feasibility-wise, to dynamic programming (DP). It is also shown that, under natural assumptions, our method is computationally efficient while it possesses rather strong system theoretic properties.