Slovakia

We present a Learning MPC framework for a class of nonlinear systems that employs data-driven construction of continuous, convex terminal sets and terminal costs in the space of specific output sequences.

Nonlinear Model Predictive Control Conference 2021

Output-Lifted Learning Model Predictive Control

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.

keynote

Nonlinear model predictive control (NMPC) has established as a standard tool in many different industrial applications ranging from process control solutions in metal production, pumped-storage power plants, high-performance electric and hydraulic drives to power electronics systems, with sampling times from minutes to a few microseconds. Clearly, the steady increase in computational power and the advances in the theoretical concepts have paved the way for the general acceptance and versatility of NMPC and this is expected to continue also in the future. Most of the more theoretically oriented works in the literature deal with the important topics of how to formulate and solve the underlying optimization problem and how to prove stability and convergence properties. In many of our industrial applications, we found out that the design of an appropriate mathematical model is an essential requirement for the success of an NMPC strategy. In this talk, we will focus on the interplay between mathematical modelling and NMPC. Based on different industrial examples, we will demonstrate how a tailored modelling approach can help to reduce the computational costs and improve the overall performance of NMPC applications.

Nonlinear Model Predictive Control: How Important Is the Model?

Nonlinear Model Predictive Control (NMPC) based on stochastic differential equation (SDE) models offers a systematic method for implementation of NMPC. We demonstrate how the filtering and prediction with SDE models can be used for experimental design (input design), parameter estimation and system identification as well as monitoring and fault detection. Also, we address the importance of disturbance modelling for SDE systems and provide a potential based approach inspired by barrier functions. Efficient numerical procedures for the optimal control problem (OCP) based on the SDE-based identified filtering and prediction model are described. High performance scientific computing is used for uncertainty quantification of the closed-loop system. We illustrate the methods using a number of examples from reactive systems as they arise in chemical engineering, biotechnology, biomedicine, and energy systems. The range and broadness of these systems demonstrates the power of a uniform system approach based on merging systems and control, high-performance scientific computing, and chemical engineering science.

Nonlinear Model Predictive Control based on Stochastic Differential Equation Models

Stochastic nonlinear model predictive control (SNMPC) allows to directly take model uncertainty into account, e.g., by including probabilistic chance constraints. This paper proposes linear-regression Kalman filtering to perform high-accuracy propagation of mean and covariance information for the nonlinear system dynamics in a tractable approximation of the stochastic optimal control problem. In addition, a tailored adjoint-based sequential quadratic programming (SQP) algorithm is presented to considerably reduce the computational cost and allow a real-time implementation of the resulting SNMPC. The prediction accuracy and control performance of the proposed approach are illustrated on a vehicle control application subject to external disturbances, while highlighting a worst-case computation time of 10 ms for SNMPC which is close to that of deterministic NMPC for this particular case study.

Uncertainty Propagation by Linear Regression Kalman Filters for Stochastic NMPC

Offset-free action of model predictive control (MPC) for nonlinear systems with the number of measured outputs greater than controlled outputs is a nontrivial problem. Motivated by investigating the possible application of MPC for the control system of magnetic levitation (Maglev) vehicles -- tracking only the gap while measuring the gap, acceleration, and current -- for higher speeds than hitherto travelled, different possible offset-free nonlinear MPC strategies are reviewed and discussed.

Moreover, a novel approach based on a two-stage observer is introduced, requiring less effort to design an offset-free MPC. The different strategies are applied and analyzed in detail for a realistic model of the control system of the latest Transrapid vehicle, called TR09. Unlike usual offset-free MPC studies, the controller performance is also studied in a typical dynamic scenario, revealing the conflict and trade-off between the requirements for speed of command response and the robustness of closed-loop stability.

Offset-free Nonlinear Model Predictive Control by the Example of Maglev Vehicles

During the last 20 years there has been increased interest in estimating the INTENT of the Human motion (as part of human action) during the man-machine interaction. The main motivation has been to prepare the robot to act safely and being as helpful as possible during their interaction with the Human.

While the Control community has had predictive control formulation (the literature on this topic is quite rich, see references 16-18) unfortunately this formulation is based on the assumption that one has the knowledge of the dynamics of the system. This of course is not the case for human. As we all know humans are many times unpredictable. However during the last 20 years thanks to brain imaging techniques, such as MRI.FMRI,EEG and more ,the neuroscientists, the psychologists, cognitive scientists have identified unconscious signals in the cortex that are precursors to humans in their motion planning. We have reviewed a selected list of those articles and in our full talk will give the essence of these papers 1-15. One fundamental observation we can already make is that while during 20th century the prevalent modus operandi both for behavioral psychologists and roboticists was the stimulus-response, perception-action cycle, the 21st century hypothesis is combination of feedforward and feedback, action –perception, hence the anticipatory behavior in addition reactive behavior.

Anticipating and Predictive Behavior

We discuss state-of-the-art in mixed-integer nonlinear optimization (MINLP) solver software and the current state of research in the field. We hope to spark a conversation about the connections to NMPC.

Numerical approaches to mixed-integer nonlinear optimization

In this talk, we propose a suboptimal moving horizon estimator for nonlinear systems. For the stability analysis we transfer the “feasibility-implies-stability/robustness” paradigm from model predictive control to the context of moving horizon estimation in the following sense: Using a suitably defined, feasible candidate solution based on the trajectory of an auxiliary observer, robust stability of the proposed suboptimal estimator is inherited independently of the horizon length and even if no optimization is performed.

Robust Stability of Suboptimal Moving Horizon Estimation Using an Observer-Based Candidate Solution

In this presentation, I cover the basic concepts used in our paper which enables real-time MPC for large scale system. To this end, the contraint selection/removal procedure is detailed and the requirements for recursive feasbility and constraint satisfaction are explained. Last, a simulation study is presented to visualize the ca-MPC scheme.

Constraint-Adaptive MPC for Large-Scale Systems: Satisfying State Constraints without Imposing Them

This talk presents recently developed methods for non-standard NMPC problems which cannot directly be formulated and solved in the form of smooth nonlinear programs (NLP).

NMPC with state dependent discontinuities, and homotopy based active set solution methods tailored to mathematical programs with complementarity constraints (MPCC). NMPC with state dependent jumps, and their reformulation to case 1) via “time freezing”. NMPC with discrete actuators, and a Gauss-Newton inspired heuristic. Throughout the talk, the focus will be on the exploitation of convex structure in these strongly non-convex problems The algorithms and methods will be illustrated by tutorial and some real-world examples.

The talk presents joint work with Armin Nurkanovic, Sebastian Albrecht, Jonas Hall, Florian Messerer, Sebastian Sager, Clemens Zeile, and Adrian Bürger.

Related Papers:
• [Time-Freezing for State Dependent Jumps](https://syscop.de/files/users/Moritz.diehl/Nurkanovic2021Freezing.pdf)

• [LCQP Algorithm for Quadratic Programs with Complementarity Contstraints](https://syscop.de/files/users/Moritz.diehl/Hall2022LCQP.pdf)

• [Survey of Sequential Convex Programming (SCP) and GGN](https://syscop.de/files/users/Moritz.diehl/Messerer2022-SCP-GGN.pdf)

• [Software pycombina for CIA MILP arising in MIOCP](https://cdn.syscop.de/publications/Buerger2020a.pdf)

Numerical methods for NMPC for systems with state dependent jumps and discrete actuators

With Nonlinear Model Predictive Control being well understood from a theoretical perspective, there has been tremendous progress in the last decade towards transferring the approach to real implementations on resource constrained, embedded systems. In this talk, I will highlight some successful applications in the area of Autonomous Driving, Space, and Robotics. Unlike many other control methodologies, the ultimate proliferation of NMPC into a wide range of applications critically relies on the availability of standardized software. To this end, I will present some challenges in developing reliable NMPC software and the impact on industry adoption.

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