MICNON 2021 will offer tutorial workshops addressing novel methodologies and nonstandard applications in the modeling, identification, and control of nonlinear systems. The tutorial workshops will be held online at 9:00-13:00 (UTC+1:00) or 13:30-17:30 (UTC+1:00) on September 14, 2021. Participation in a workshop requires registration for MICNON 2021. The registration fee for MICNON 2021 includes access to the workshops. The following is tentative information about workshops. Details will be announced in due course.

Mario Sassano (University of Rome, Tor Vergata), Thulasi Mylvaganam (Imperial College London), Alessandro Astolfi (Imperial College London)

Problems involving dynamic (multi-objective) optimisation are ubiquitous in modern applications and are therefore of paramount interest.
In addition, such problems have a rich mathematical structure, hence have been extensively studying im mathematical systems theory.
Such problems entail the minimization of one or more cost functionals, while satisfying a dynamic constraint.
The latter captures the behaviour of the *environment* that is influenced by the actions of the decision-making agents.
Arising in various guises, such as optimal control, differential games and mean-field games, problems involving dynamic optimisation are notoriously difficult to solve, particularly in the presence of nonlinear cost functionals and/or nonlinear dynamics.
Consequently, significant effort has been dedicated to develop methods to efficiently tackle such problems.
Existing methods are diverse and can roughly be divided into two classes, namely *off-line* methods, aimed at obtaining solutions (or approximations thereof), and *on-line methods*, aimed at *learning* solutions in *real-time.*
In the context of optimal control, the latter include iterative learning control and reinforcement learning.
The objective of this workshop is to present recent results related to both *off-line* and *on-line* methods for solving optimal control problems and differential games.

Anyone who is interested in recent developments concerning constructive design strategies to tackle dynamic optimisation problems, including optimal control and differential games, in the presence of nonlinear dynamic constraints.

- An Introduction to Dynamic Optimisation Problems

(Imperial College London)**Alessandro Astolfi** - Off-Line Solutions of Dynamic Optimisation Problems via Immersion and Algebraic Conditions

(Imperial College London)**Thulasi Mylvaganam** - Multi-Agent Collision Avoidance: A Case Study

(Imperial College London)**Thulasi Mylvaganam** - A Fixed-Point Characterization of Optimal Control Laws

(University of Rome, Tor Vergata)**Mario Sassano** - A Finite-Dimensional Characterisation of Optimal Control Laws

(University of Rome, Tor Vergata)**Mario Sassano** - Model-Based Reinforcement Learning for Nonlinear Systems via Controlled Hamiltonian Dynamics

(University of Rome, Tor Vergata)**Mario Sassano**

Daisuke Tsubakino (Nagoya University)

Contrary to tremendous development of the model-based approaches to controller design, the most widely used feedback controllers in industry are PID controllers.
One of advantages of PID controllers is that parameters in a controller can be tuned without knowledge of a mathematical model of the systems to be controlled.
Nevertheless, there seems to be a consensus among control engineers, independent from their interests, that controllers designed based on the information about models usually perform better than PID controllers.
Even if there is uncertainty in a model, some tools in the robust control theory provide model-based controllers that have robustness against the uncertainty.

On the other hand, due to the recent development of control or measurement devices, industrial systems involve highly-developed and complex components.
In those components, nonlinearity often plays an essential role and it can not be ignored.
Furthermore, as the use of such components increases, improvement of control performance of conventional devices are also required.
Then, paying attention to neglected parts of conventional devices, typically nonlinearity, is a natural and reasonable option to improve the control performance.
However, the more we focus on accuracy of a mathematical model, the more the resulting model becomes complicated.
Hence, it is important to understand essential parts of nonlinearity inherent in systems to be controlled and choose a suitable model in accordance with given purposes.

The objective of this tutorial workshop is to provide audience with an opportunity to learn nonlinear modeling of several practically important systems and associated controller design.
We choose four systems that seem to be appealing to persons in industry. The first topic is hydraulic machinery.
Hydraulic systems are undoubtedly necessary components especially for heavy machinery. The next topic is a battery.
In view of the recent increase in interests in electric vehicles and airplanes, management and control of batteries are necessary technologies.
The third topic deals with biomolecular systems. Synthetic biology is a multidisciplinary research area and developing rapidly.
It is definitely valuable for control engineers to understand how control engineering can contribute to development of synthetic biology.
The last one is fluid flow. Fluid flow is a ubiquitous but complex phenomenon.
Hence, feedback control of fluid flows is a practically important issue.

This workshop is mainly intended for persons in industry who are interested in nonlinear modeling and control. Other potential audiences are persons working on nonlinear control theory and seeking systems to which their theories are applicable.

- Modeling and Identification of Hydraulic Cylinder Dynamics
(Shinshu University)**Satoru Sakai** - Control, State Estimation, and Model Identification of Batteries
(Advanced Technology R&D Center, Mitsubishi Electric Corporation)**Toshihiro Wada** - Theory-Based Design and Control of Biomolecular Systems
(Keio University)**Yutaka Hori** - Approximate Modeling and Controller Design for Fluid Flows
(Nagoya University)**Daisuke Tsubakino**

Yoshihiko Susuki (Osaka Prefecture University), Alexandre Mauroy (University of Namur), Igor Mezic (University of California, Santa Barbara)

The Koopman operator provides a global description of nonlinear dynamical systems in terms of the evolution of “observable-functions” of the state space. Although this description seems to be overlooked in control theory at first sight, it has evocatively been considered for decades: for instance, it is reminiscent of Lyapunov functions characterization in stability analysis and to the use of value functions in optimal control. The most noticeable advantage of the Koopman approach relies on the fact that it turns a nonlinear system into a linear (but infinite-dimensional) system. At the cost of working in high-dimensional spaces providing a good approximation of the observable dynamics, systematic methods from linear control theory can be applied in a straightforward manner to controlled nonlinear systems. Moreover, the Koopman operator framework is amenable to data analysis through the so-called Koopman mode decomposition and is directly connected to efficient numerical algorithms such as dynamic mode decomposition. Therefore, it provides data-driven methods for model-free control of nonlinear systems. This tutorial is motivated by the increasing interest in the Koopman operator framework in the control community and aims at providing a snapshot of the current research effort in this area. This tutorial will provide a broad overview of the Koopman formalism in various topics of interest in nonlinear control theory. Also, it will open up to a wealth of research perspectives, with limitations to be overcome and open problems to be solved. Relevant topics will be picked up from the recent book, “The Koopman Operator in Systems and Control: Concepts, Methodologies, and Applications (Springer Nature, 2020),” edited by the organizers.

Anyone who is interested in emergent methods in nonlinear control theory and in the operator-theoretic approach to nonlinear dynamical systems and machine learning.

- Koopman Operator in Systems and Control: Concepts and Methodologies
(University of Namur)**Alexandre Mauroy** - Koopman Operator in Systems and Control: Applications
(Osaka Prefecture University)**Yoshihiko Susuki** - Koopman Operator, Geometry, and Machine Learning
(University of California, Santa Barbara),**Igor Mezic**