Numbering Code	G-INF05 63517 LJ10 G-INF05 63517 LJ77	Year/Term	2022 ・ Second semester
Number of Credits	2	Course Type	Lecture
Target Year		Target Student
Language	Japanese	Day/Period	Mon.4
Instructor name	OHTSUKA TOSHIYUKI (Graduate School of Informatics Professor) SAKURAMA KAZUNORI (Graduate School of Informatics Associate Professor)
Outline and Purpose of the Course	In this course, as a methodology for modeling, analyzing, designing, and controlling a dynamical system integrating various elements (such as humans, machines, society, and environment), optimal control problems for nonlinear systems and the theory of multi-agent systems will be discussed. The first half of the course begins with the foundation of optimization and describes the general framework of the optimal control problem: the task of finding the most desirable operation and movement for a given dynamical system. We will also study how to obtain numerical solutions when the optimal solution cannot be analytically sought. These are relatively classic methods that were developed in the mid-twentieth century, but they still have broad applications. Furthermore, recent developments in computers and numerical solutions have created an unprecedented control framework in which feedback control is performed by numerically solving complex optimal control problems in real time. In this lecture, we will learn the basic concept of real-time optimization in control and its application examples. If time permits, we will also introduce the optimal control of discrete-time systems in comparison with continuous-time systems. Later in the lecture, we will study the theory of multi-agent systems, which express global functions based on the local interactions of multiple agents. In particular, from the viewpoint of control engineering, we will discuss the design theory of distributed control systems, which revolves around bringing the entire system to a desirable state by controlling based on local information. Furthermore, the methodology for implementing such a distributed control system in swarm robots is also introduced. Optimal control and multi-agent system theories and algorithms have a very wide range of applications. In addition to control theory, there is also the aspect of utilizing advances in various fields such as numerical calculations and computers. Knowledge of the connection between optimal control and multi-agent systems and other fields will broaden your horizons regardless of your specialty.
Course Goals	Understand that optimal control can be applied to various problems, set appropriate models, evaluation functions, and constraint conditions according to the control purpose, and be able to derive optimal conditions. Furthermore, you will be able to understand numerical solution methods for optimal control problems and actually calculate these numerical solution. In addition, you will learn that various phenomena and engineering problems can be expressed as multi-agent systems, and you will study how to mathematically describe, analyze, and design those models and control principles.
Schedule and Contents	1. Optimization problem (1 lecture) Evaluation function, constraint condition 2. Function minimization (mathematical planning problem) (2 lectures) Basic concepts, KKT conditions 4. Formulation of optimal control problem and optimal condition (2 lectures) Variations, stationary conditions, dynamic programming, minimum principle 5. Numerical solutions for optimal control problems (2 lectures) Gradient method, Newton's method 6. Feedback control via numerical optimization (1 lecture) Model prediction control problem, numerical solution, application example 7. Multi-agent systems (1 lecture) Multi-agent system is distributed control, graph 8. Problem configurations (2 lectures) Coordination problem, coordinate system, motion / measurement model, network 9. Pair coordination (2 lectures) Examples of pair coordination, gradient flow method, distance-based formation, graph rigidity 10. Generalized coordination (2 lectures) Examples of generalized coordination, optimal distributed control design, creek
Evaluation Methods and Policy	You will be evaluated on the degree to which you demonstrate mastery of the learning goals in reports.
Course Requirements	This course will assume that you have knowledge of fundamental mathematical concepts (derivatives of multivariate functions, linear algebra). We recommend that you have an undergraduate-level understanding of control theory, optimization, and related concepts.
Study outside of Class (preparation and review)	It is advisable to grasp the outline of the lecture content by looking at the textbook before attending lecture. After the lecture, you should go over your notes and confirm unclear points using the textbook and by asking questions after the lecture. The reports will ask course members to individually tackle problem setting and numerical calculations.
Textbooks	Textbooks/References	Toshiyuki Ohtsuka, "非線形最適制御入門." (Corona), ISBN:4339033189 K. Sakurama and T. Sugie, "Generalized Coordination of Multi-robot Systems" (Foundations and Trends in Systems and Control: Vol. 9: No. 1,: 978-1-68083-902-9 (Book), ISBN: 978-1-68083-903-6 (E-book) http://dx.doi.org/10.1561/2600000025
References, etc.	A. E. Bryson, Jr., and Y.-C. Ho "Applied Optimal Control" (Taylor & Francis) ISBN: 0891162283: Rich in topics and examples. R. F. Stengel "Optimal Control and Optimization" (Dover) ISBN: 0486682005: Covers a wide range of topics. D. E. Kirk "Optimal Control Theory: An Introduction" (Dover) ISBN: 0486434842: Written plainly with a focus on optimal control. Hideaki Kano, "システムの最適理論と最適化" (Corona Publishing Co., Ltd.) ISBN: 4339041238: Provides details regarding numerical solutions. Yoshiyuki Sakawa, "最適化と最適制御" (Morikita Publishing) ISBN: 4627005393: Detailed theory. Toshiyuki Otsuka et al. "実時間最適化による制御の実応用" (Corona Publishing Co., Ltd.) ISBN: 4339032107: Introduces numerical solutions of model predictive control, automatic code generation, and application examples. Azuma & Nagahara et al. "マルチエージェントシステムの制御" (Corona Publishing Co., Ltd.) ISBN: 4339033227 M. Mesbahi and M. Egerstedt "Graph Theoretic Methods in Multiagent Networks" (Princeton University Press) ISBN: 0691140618: Covers a wide range of topics, from basics to wide-ranging applications.