Optimal Control

Code:

PDEEC0075

Acronym:

CO

Keywords
Classification	Keyword
OFICIAL	Electrical and Computer Engineering

Instance: 2023/2024 - 2S

Active?	Yes
Responsible unit:	Department of Electrical and Computer Engineering
Course/CS Responsible:	Doctoral Program in Electrical and Computer Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
PDEEC	1	Syllabus	1	-	6	42	162

Teaching language

Portuguese and english

Objectives

This is an introductory course to optimal control theory for systems driven by vector ordinary differential equations. Students are expected to acquire a solid understanding of basic facts associated to this theory. Analytic tools associated to formulation, analysis and solution of optimal control problems are investigated. For simple optimal control problems this tools will be used to obtain a complete characterization of the optimal solution. Contact with known software packages to solve more complex problems is a further and last goal.

Learning outcomes and competences

To acquire a solid understanding of basic facts associated to optimal control theory.
To be able to characterize the optimal solution of simple optimal control problems, using analytical tools.
To be able to obtain numerical solutions for more complex problems, using known software packages.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Optimization on finite dimension spaces.
Linear Algebra.
Linear differential equations.

Program

I. Introduction
Ia. Formulation of optimal control problems.
Ib. Local and global optima; general conditions on existence and uniqueness.

II. Linear Autonomous Time-Optimal Control Problems
IIa. Properties. Controllability.
IIb. Existence of time optimal control problem.
IIc. Bang-Bang Principle. Pontryagin Maximum Principle.
IId. Examples.

III. More General Optimal Control Problems
IIIa. Existence results.
IIIb. Necessary conditions. Pontryagin Maximum Principle.
IIIc. Sufficient conditions.
IIIc. Linear Quadratic Problem.
IIId. Applications.

IV. Numerical treatment of Optimal Control Problems.
 Working optimal control problems with known software packages

Mandatory literature

Macki Jack; Introduction to optimal control theory. ISBN: 0-387-90624-X

Complementary Bibliography

Athans Michael; Optimal control

Teaching methods and learning activities

Weekly meetings for discussion of subjects.
Every week a list of exercises is proposed. The student has a selected time period to solve and deliver its resolution.

keywords

Physical sciences > Mathematics > Applied mathematics > Engineering mathematics
Technological sciences > Engineering

Evaluation Type

Distributed evaluation without final exam

Assessment Components

Designation	Weight (%)
Participação presencial	30,00
Trabalho escrito	70,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	125,00
Frequência das aulas	42,00
Trabalho escrito	25,00
Total:	192,00

Eligibility for exams

Terms of frequency: 90% of the proposed exercises must be marked with a classification of 10 in 20, at least.

Calculation formula of final grade

Formula Evaluation: 0,70 * written work + 0,30 * meeting oral discussion

Examinations or Special Assignments

Students must work the proposed weekly exercises and deliver its resolution later on. Discussion of these resolutions is also evaluated.