This course provides basic knowledge and tools for designing an adaptive controller and an optimal controller. 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 controller, which tunes controller parameters adaptively depending on the error between reference output and the system output to be controlled is an option. In the first half of course, the adaptive controller design and its 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 in design step is discussed with examples.
In real applications, control system designers need to consider parameter uncertainty of a given system in design step. For such systems, adaptive controller, which tunes controller parameters adaptively depending on the error between reference output and the system output to be controlled is an option. In the first half of course, the adaptive controller design and its 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 in design step is discussed with examples.
Topics include 1) basic knowledge of adaptive control and optimal control, 2) 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.
- -understanding and explaining of concept of model reference adaptive control system (MRACS) and its properties
-construct of numerical simulations of MRACS - -understanding and explaining of concept of model predictive control (MPC) and its solution
-construct of numerical simulation of MPC - -understanding and explaining how to select these approaches
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1． | Preliminaries-1 -norm -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 |
constraint | 100minutes |
| receding horizon, control horizon, coincident point, step response | 100minutes | ||
| 13． | Model predictive control without constraint -problem formulation -generalization |
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 |
| assignment | Total. | |
|---|---|---|
| 1. | 45% | 45% |
| 2. | 45% | 45% |
| 3. | 10% | 10% |
| Total. | 100% | - |
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.
-well written and well explained
-original analysis with unique view
Accreditation criteria is to be able to solve and explain problems in assignments.
no specified text book for the lecture
references:
-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
references:
-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
- 13:30-17:00 on Mon.-Wed.
- students need appointment
- Course that cultivates an ability for utilizing knowledge
- Course that cultivates a basic problem-solving skills
| Work experience | Work experience and relevance to the course content if applicatable |
|---|---|
| Applicatable | Lecturer designed controllers in company. In lecture, some comments are made for practical image. |
Last modified : Thu Mar 21 15:45:32 JST 2019