Slovakia

This paper highlights the benefits of a feedback linearization local controller and the associated terminal bound constraints (box-type inequalities) in an NMPC (Nonlinear Model Predictive Control) design for a multicopter system. We replace the standard invariant construction for the terminal region of the NMPC design with two sets: i) a $\delta$-invariant set (with $\delta$ the sampling time) which constrains the trajectories to re-enter it periodically, at pre-defined moments of time; ii) a constraint admissible safe set in which the trajectories lie in the remaining time instants. We show that this alternative construction verifies the recursive feasibility and asymptotic stability. Moreover, the additional degrees of freedom and simpler construction show advantages over similar NMPC designs with standard ellipsoidal terminal region.

Nonlinear Model Predictive Control Conference 2021

Stabilizing a multicopter using an NMPC design with a relaxed terminal region

delta invariant set

terminal constraint set

multicopter

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

**Read paper on the following link:**

https://drive.google.com/file/d/10Ja3BWljpdOVUSBzNBzD-RJgnxp0Z-fD/view?usp=sharing

**Abstract:**



State and Parameter Estimation for Model-Based Retinal Laser Treatment

This paper presents an approach to design nonlinear control policies for the class of systems with nonlinear steady-state characteristics while assuming constant dynamic behavior. We present an approach where the nonlinear steady-state characteristics are approximated with a nonlinear function. Such a model then serves as the design model for the nonlinear model predictive control strategy. The validity of such a control approach is experimentally implemented on a laboratory scale device.

Nonlinear MPC Policy for Systems with Data Driven Identification

Model predictive control (MPC) is a powerful trajectory

Reinforcement Learning of the Prediction Horizon in Model Predictive Control

In the Economic Nonlinear Model Predictive (ENMPC) context, closed-loop stability relates to the existence of a storage function satisfying a dissipation inequality. Finding the storage function is in general-- for nonlinear dynamics and cost-- challenging, and has attracted attentions recently. Q-Learning is a well-known Reinforcement Learning (RL) techniques that attempts to capture action-value functions based on the state-input transitions and stage cost of the system. In this paper, we present the use of the Q-Learning approach to obtain the storage function and verify the dissipativity for discrete-time systems subject to state-input constraints. We show that undiscounted Q-learning is able to capture the storage function for dissipative problems when the parameterization is rich enough. The efficiency of the proposed method will be illustrated in the different case studies.

Verification of Dissipativity and Evaluation of Storage Function in Economic Nonlinear MPC Using Q-Learning

Many processes operate repetitively, for example, batch processes in biotechnology or chemical engineering. We propose a method for risk-aware run-to-run optimization and model predictive control of repetitive processes with uncertain models. The goal is to increase the performance as the number of runs increases by improving the model despite limited measurements while considering model uncertainty and avoiding uncertain areas. The method uses a gray-box model, i.e. a model formed by a first principle and a machine learning component, in this case, an artificial neural network. The model uncertainty might be large, particularly in the first runs, where only a few measurements are available. We propose to quantify this uncertainty using Bayesian inference. This is in turn reflected by a risk measure entering an open-loop optimal control problem and a shrinking-horizon Model Predictive Controller as a constraint to limit control and exploitation in high-risk areas. We show that using this risk measure we are able to efficiently reach high process performance. The proposed method is tested in simulations on two biotechnological fed-batch processes.

Towards Risk-Aware Machine Learning Supported Model Predictive Control and Open-Loop Optimization for Repetitive Processes

Often, systems need to adapt their behavior to other systems in their surroundings while obeying constraints to achieve good performance or due to safety reasons. We consider repetitive applications, where the reference for the controller stems from noisy sensor data. Including preview information of the reference, e.g. extrapolating from previous cycles or similar instances, can significantly improve the overall tracking performance and ensure constraint satisfaction.

Constrained reference learning for continuous-time model predictive tracking control of autonomous systems

Mecanum-wheeled robots have been thoroughly used to automate tasks in many different applications. However, they are usually controlled by neglecting their dynamics and relying only on their kinematic model. In this paper, we model the behaviour of such robots by taking into account both their equations of motion and the electrodynamic response of their actuators, including dry and viscous friction at their shafts. This allows us to design a model predictive controller aimed to minimise the energy consumed by the robot. The controller also satisfies a number of non-linear inequalities modelling motor voltage limits and obstacle avoidance constraints. The result is an agile controller that can quickly adapt to changes in the environment, while generating fast and energy-efficient manoeuvres towards the goal.

Model Predictive Control for a Mecanum-Wheeled Robot Navigating among Obstacles

Trajectory planning with the consideration of obstacles is a classical task in

Mixed-Integer optimization-based planning for autonomous racing with obstacles and rewards

We propose the design of a nonlinear model predictive controller (NMPC) for the

Control of Fixed-Wing UAV Attitude and Speed Based on Embedded Nonlinear Model Predictive Control

We consider an input-constrained differential-drive robot with actuator dynamics.

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Stabilizing a multicopter using an NMPC design with a relaxed terminal region

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State and Parameter Estimation for Model-Based Retinal Laser Treatment

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