Slovakia

Model predictive control requires the real-time solution of an optimal control problem, which can be challenging on computationally limited systems. Approximating the solution such as by neural networks or series expansions, or deriving an explicit solution, can overcome this challenge. Using neural networks for approximation, a question arises as to how to guarantee closed-loop safety and stability. We use robust control theoretic tools to provide stability guarantees using a neural network trained to approximate a model predictive controller. Notably, the model predictive controller, which might offer desirable closed-loop performance, is not required to provide provable stability properties. To provide stability guarantees for the neural network approximated controller, the closed-loop system is reformulated as a diagonal nonlinear differential form, exploiting that the neural network activation functions are sector bounded and that their slopes are globally bounded. Based on this representation, we establish sufficient closed-loop stability conditions in form of linear matrix inequalities for the nominal and the disturbed system using the neural network approximated model predictive controller.

Nonlinear Model Predictive Control Conference 2021

Robust Control Theory Based Stability Certificates for Neural Network Approximated Nonlinear Model Predictive Control

stability analysis

neural network approximated controller

nonlinear 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.

technical paper

This paper proposes a Model Predictive Control (MPC) design method for the intake manifold pressure of an internal combustion engine. This controller uses a nominal nonlinear model of the physical system to optimize a cost function. The noise sensibility of MPC is reduced and the robustness of the state estimation is achieved by using an Extended Kalman Filter (EKF). The proposed approach is evaluated using the Matlab Simulink model of the intake manifold of a spark ignition combustion engine in which parametric uncertainties and saturation are added. Different settings for EKF and MPC are tested for comparison purposes.

First Results on Turnpike Bounds for Stabilizing Horizons in NMPC

Cells within the same battery pack age unequally fast due to the non-uniform manufacturing process, and inhomogeneous operating conditions, and environment. This paper proposes a nonlinear Model Predictive Control approach for optimal pack balancing while taking pack and cell limitations into account. The control is designed for a sophisticated battery pack, which is a pack augmented by semiconductor switches to vary the number of cells connected in series. This pack is usually composed of more cells than a conventional battery pack. Each serial cell in the pack can be activated or deactivated while keeping the serial connection. Simulation results based on a realistic mission profile illustrate the effectiveness of the proposed approach by optimizing the overall performance and degradation of the battery architecture.

Nonlinear Model Predictive Control for a Simulated Reconfigurable Battery Pack

This paper presents a real-time capable nonlinear model predictive control (NMPC) strategy to effectively control the driving performance of an electric vehicle (EV) while optimizing thermal utilization. The prediction model is based on an experimentally validated two-node lumped parameter thermal network (LPTN) and one-dimensional driving dynamics. An efficient solver for the trajectory tracking problem is exported using acados and deployed on a dSPACE SCALEXIO embedded system. The lap time of a high-load driving cycle compared to a state-of-the-art derating strategy improved by 2.56% with an energy consumption reduction of 2.43% while respecting the temperature constraints of the electric drive.

Embedded Real-Time Nonlinear Model Predictive Control for the Thermal Torque Derating of an Electric Vehicle

**Read paper on the following link:**

https://drive.google.com/file/d/1WNxyobfYRHi6Mnx3X9En_M5cgzIbDRAO/view?usp=sharing

**Abstract:**



Motion Cueing Control Design Based on a Nonlinear MPC Algorithm

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

While the potential of learning-based control paradigms is being demonstrated in numerous applications, the supporting theory addressing questions related to their safety, reliability, performance or also their computational properties is still in its infancy.

Model predictive control offers a promising framework to approach this problem. It directly facilitates online learning to improve the description of any problem component, i.e. the model, cost or constraints, with the goal of enhancing closed-loop performance. Despite the opportunities, however, the MPC approach is often challenged by complex and long-term tasks. In this talk, I will discuss different flavours of learning-based MPC as well as tools for their analysis, and also address how MPC principles can be used to enrich the theoretical properties of other learning-based control techniques. Throughout the talk, the ideas will be highlighted using demonstrations of autonomous vehicles and robotics.

The Role of Learning in MPC and Vice Versa

In this talk, various formulations and tools are revisited and mixed in order to accommodate for different challenges arising in nowadays Nonlinear Model Predictive Control (NMPC) and Moving-Horizon Estimation (MHE). The past and undergoing considered tracks involve various ingredients such as probabilistic certification, Machine-Learning, GPU-parallel computation as well as non conventional formulations of NMPC and MHE.

While each of the visited tracks might become obsolete sooner than expected or desired, the overall message is hopefully sustainable in the medium term: our community need to be, more than ever, opened to new opportunities and tools while building upon a carefully selected set of our solid foundations.

Tango steps in a moving-window cabaret!

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.

Output-Lifted Learning Model Predictive Control

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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Robust Control Theory Based Stability Certificates for Neural Network Approximated Nonlinear Model Predictive Control

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