Slovakia

In this paper, we propose an efficient zero-order algorithm that can be used to compute an approximate solution to robust optimal control problems (OCP) and robustified nonconvex programs in general. In particular, we focus on robustified OCPs that make use of ellipsoidal uncertainty sets and show that, with the proposed zero-order method, we can efficiently obtain suboptimal, but robustly feasible solutions. The main idea lies in leveraging an inexact sequential quadratic programming (SQP) algorithm in which an advantageous sparsity structure is enforced. The obtained sparsity allows one to eliminate the variables associated

Nonlinear Model Predictive Control Conference 2021

Zero-Order Robust Nonlinear Model Predictive Control with Ellipsoidal Uncertainty Sets

numerical methods

robust nmpc

The IFAC Conference on Nonlinear Model Predictive Control (NMPC 2021) aims to bring together researchers interested in and work in the MPC field from both academia and industry. This allows us to reflect and establish the current state-of-the-art and focus on the future development of the MPC field towards relevant directions.

Model predictive control (MPC) is indisputably one of the advanced control techniques that have significantly affected control engineering practice with thousands of controllers implemented in various fields, spanning from the process industry to automotive and robotics. This is due to its unique ability to handle constraints, take preview information about disturbances and setpoint changes into account, and optimize performance. Furthermore, MPC allows the consideration of various types of dynamics, from linear to nonlinear, discrete to continuous, as well as an online adaptation of models and parameters. The research community on MPC is very active, with hundreds of papers published every year. Over the past decades, many theoretical, as well as implementation results, have been achieved.

### **All content presented at NMPC2021, including videos, papers and slides will be available only to registered (regular/student) participants. The content can be accessed until August 31st, 2021.**



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The IFAC Conference on Nonlinear Model Predictive Control (NMPC 2021) aims to bring together researchers interested in and work in the MPC field from both academia and industry. This allows us to reflect and establish the current state-of-the-art and focus on the future development of the MPC field towards relevant directions.

technical paper

In this paper we present a distributed second-order augmented Lagrangian method

A Distributed Second-Order Augmented Lagrangian Method for Distributed Model Predictive Control

This paper investigates how various caching strategies can reduce the computational effort of the active set method (ASM) applied to solve constrained model predictive control problems with quadratic objective function and linear constraints. Specifically, we show that during closed-loop operation, the active set method often re-visits the same combination of active constraints while searching for optimal control inputs by factoring Karush-Kuhn-Tucker (KKT) systems. By storing the factors of the corresponding KKT system in a cache, these repetitive

Streamlining Active Set Method in MPC Using Cache Memory

Objective of the vehicle thermal management system is to achieve precise coolant temperature control that ensures operation of the combustion engine in the region with the maximum thermal efficiency. In this study it is achieved by a combined effect of coolant temperature control algorithm that is operating an advanced electronic valve with one input and three outputs that balances distribution of the coolant flow

Advanced Coolant Temperature Control Study with Integrated Thermal Management System Valve

We address the problem of operating up- and down-time restricted components with activation thresholds using linear predictive control instead of hybrid predictive control. Accounting for operational requirements of this kind usually requires optimal control problems with discrete variables, which are computationally demanding. As a workaround, run-time requirements are often ignored in the control design and enforced independently from the optimal input value. We present conditions and an algorithm that ensures minimum run-time requirements in linear MPC. The control performance for a heating application is compared to linear MPC with rule-based post-processing and hybrid MPC. The results show that our approach ensures the up-and down-time requirements at a high control performance and is significantly faster than hybrid MPC.

MPC for Heating Systems with Minimum up- and Down-Time Requirements

This presentation gives an introduction to an application of MPC to an industrial process. The aim is to control the temperature of a substrate that is transported through a heating zone with changing speed. The heat is applied using hot air. The talk gives an overview on the modeling approach, the MPC setup and some experimental results.

Modeling and Temperature Control of a Moving Substrate

In recent years, theoretical results for model predictive control (MPC) have been expanded to address discrete actuators (decisions) and high-level planning and scheduling problems. The application of MPC-style methods to scheduling problems has been driven, in part, by the robustness afforded by feedback. The ability of MPC, and feedback methods in general, to reject small persistent disturbances is well-recognized. In many planning and scheduling applications, however, we must also consider an additional class of discrete and infrequent disturbances, such as breakdowns and unplanned maintenance. In this paper, we establish that nominal MPC is robust, in a stochastic context, to this class of discrete and infrequent disturbances. We illustrate these results with a nonlinear blending example.

Robustness of Model Predictive Control to (Large) Discrete Disturbances

Recently, a regional MPC approach has been proposed that exploits the piecewise affine structure of the optimal solution (without computing the entire explicit solution before). Here, regional refers to the idea of using the affine feedback law that is optimal in a vicinity of the current state of operation, and therefore provides the optimal input signal without requiring to solve a QP. In the present paper, we apply the idea of regional MPC to min-max MPC problems. We show that the new robust approach can significantly reduce the number of QPs to be solved within min-max MPC resulting in a reduced overall computational effort. Moreover, we compare the performance of the new approach to an existing robust regional MPC approach using a numerical example with varying horizon. Finally, we provide a rule for choosing a suitable robust regional MPC approach based on the horizon.

Reducing the computational effort of min-max model predictive control with regional feedback laws

A new polynomial systems method is defined for the restricted structure nonlinear predictive controllers design. The control algorithm is established for a discrete-time nonlinear system, described in the polynomial matrix linear parameter varying form. The low-order restricted structure controller is parameterized in terms of discrete transfer operators set that the designer chooses multiplied by a set of optimized gains. The controller within the feedback loop can have a general linear parameter varying form or something as simple as a PI structure. The predictive control multi-step cost-index, which is minimized, comprises weighted error, control signal costing, and gain magnitude terms. A simulation of an automotive example is used to evaluate the nonlinear restricted structure controller performance.

Restricted Structure Polynomial Systems Approach to LPV Generalized Predictive Control

In this presentation, we present transient performance guarantees for recently developed, tube-based robust economic model predictive control (MPC) schemes. In particular, we consider both tube-based MPC schemes with and without terminal conditions. We show that the closed-loop performance obtained by applying such MPC schemes is approximately optimal when evaluated on finite time horizons. These performance bounds are similar to those derived previously for nominal economic MPC. The theoretical results are discussed in a numerical example.

Transient Performance of Tube-Based Robust Economic Model Predictive Control

Stochastic Model Predictive Control (MPC) has established itself as a simple method to approximate stochastically disturbed optimal control problems, yet it comes with significant computational effort. In particular, taking into account all information of stochastic disturbances—if at all possible—can be expensive. However, due to the continuous re- optimization, MPC schemes also have a certain inherent robustness. Hence, we ask the question, which part of the perturbation is absorbed by the MPC-inherent robustness, and which needs to be explicitly taken into account in the optimization.

Zero-Order Robust Nonlinear Model Predictive Control with Ellipsoidal Uncertainty Sets

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