Course title
Adaptive and Optimal Control

ITO Kazuhisa Click to show questionnaire result at 2019
Course content
This course provides basic knowledge and tools for designing adaptive control system and/or optimal control system. These control strategies are effective for stabilization, regulation, or tracking control for real system. For easy comprehension, mathematical and system control preliminaries such as signal norm, linear control theory, system stability and matrix-vector operations so on are reviewed in first several lectures.
In real applications, control system designers need to consider parameter uncertainty of a given system in design step. For such systems, adaptive identification of uncertain parameters is needed, and then adaptive controller, which tunes controller parameters adaptively depending on the error between reference output and the system output to be controlled is introduced as an option. In the first half of course, the adaptive identification and adaptive controller design including their characteristics are discussed with examples.
On the other hand, the optimal control strategy which ensures a balance between control performance and effort based on the designed evaluation function is also powerful design approach. In the second half of this course, the model predictive control which can deal with a wide variety of constraints such as input saturation and state/output limitations at the design step is discussed with examples.
Purpose of class
Topics include 1) basic knowledge of adaptive control and optimal control, 2) concept of adaptive identification and its properties, 3) concept of model reference adaptive control system (MRACS) and its properties, and 3) concept of model predictive control (MPC) and its solution. In this lecture, how to take on different merits depending on requirements and condition to be needed is also considered.
Goals and objectives
  1. -can understand and explain concept of adaptive identification and its properties
    -can understand and explain concept of model reference adaptive control system (MRACS) and its properties
    -can construct numerical simulations of MRACS
  2. -can understand and explain concept of model predictive control (MPC) and its solution
    -can construct numerical simulation of MPC
  3. -can choose better approaches for controller design
Relationship between 'Goals and Objectives' and 'Course Outcomes'

assignment discussion in lecture Total.
1. 30% 15% 45%
2. 30% 15% 45%
3. 5% 5% 10%
Total. 65% 35% -
Class schedule

Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Preliminaries-1
-Cauchy's inequality
axiom of norm, vector norm 60minutes
induced norm 60minutes
proof of Cauchy's inequality 100minutes
2. Preliminaries-2
-matrix inversion lemma
-positive definite function and positive definite matrix
proof of matrix inversion lemma 60minutes
examples of positive definite function, negative definite function, and indefinite function 60minutes
examples of positive definite matrix, Sylvester's criterion 100minutes
3. Stability theorem-1
-uniformly stable
-asymptotic stable
-global/local characteristic
equilibrium point 30minutes
uniformly stable with epsilon-delta 200minutes
examples of stabilities
4. Stability theorem-2
-Lyapunov theorem
-linear system case
-stability condition for LIT system
energy function 30minutes
Lyapunov equation and its characteristics 150minutes
eigenvalue condition 60minutes
5. Adaptive estimation-1
-system description
-projection algorithm
equation error, hypersurface 60minutes
projection algorithm 200minutes
6. Adaptive estimation-2
-least square algorithm
least square algorithm 200minutes
7. Adaptive estimation-3
-property of LS algorithm
positive definite amtrix 100minutes
Cauchy's inequality 100minutes
8. Key Technical Lemma Cauchy sequence 100minutes
boundedness 100minutes
9. One-step-ahead adaptive control for SISO case-1 derivation of One-step-ahead adaptive control with gradient algorithm 200minutes
10. One-step-ahead adaptive control for SISO case-2 property of One-step-ahead adaptive control with gradient algorithm 200minutes
11. One-step-ahead adaptive control for SISO case-3 derivation of One-step-ahead adaptive control with least square algorithm 60minutes
property of One-step-ahead adaptive control with least square algorithm 200minutes
12. Concept of model predictive control and examples
-examples of model predictive control
constraint 100minutes
receding horizon, control horizon, coincident point, step response 100minutes
13. Model predictive control without constraint
-problem formulation
convex set 60minutes
free response for step input 100minutes
quadratic cost function 60minutes
14. Model predictive control with constraint level set method, inner point method, CVX-gen 200minutes
Total. - - 3050minutes
Evaluation method and criteria
reporting assignments (100%): evaluations are based on
-well written and well explained
-original analysis with unique view

Accreditation criteria is to be able to solve and explain problems in assignments.
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Textbooks and reference materials
no specified text book for the lecture

-J.M.Maciejowski, Predictive control: with constraints, Pearson education, 2002
-G.C.Goodwin and K.S.Sin, Adaptive Filtering Prediction and Control, Dover Books on Electrical Engineering, 2009
signal processing, Laplace transform, Fourier transform etc.
Office hours and How to contact professors for questions
  • 13:30-17:00 on Mon.-Wed.
  • students need appointment
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
  • Course that cultivates a basic problem-solving skills
Active-learning course
More than one class is interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
Applicable Based on control engineering studies, the lecturer utilizes his experience designing control systems in the manufacturing department of a construction machinery company. By introducing an intuitive understanding of controller design and performance evaluations, the lecturer is able to create a realistic image.
Education related SDGs:the Sustainable Development Goals
Last modified : Tue Mar 05 04:06:11 JST 2024