ACADEMICS
Course Details
ELE755 - Linear Optimal Control
2024-2025 Spring term information
The course is not open this term
ELE755 - Linear Optimal Control
| Program | Theoretıcal hours | Practical hours | Local credit | ECTS credit |
| PhD | 3 | 0 | 3 | 10 |
| Obligation | : | Elective |
| Prerequisite courses | : | - |
| Concurrent courses | : | - |
| Delivery modes | : | Face-to-face |
| Learning and teaching strategies | : | Lecture. Discussion. Question and Answer. |
| Course objective | : | This course aims to equip the students with the necessary skills to design, analyze and apply through simulations the following robust control approaches: Linear quadratic Gaussian (LGQ) and H∞ optimal control. |
| Learning outcomes | : | Definition of a quadratic cost function for a given control problem and perform optimization using calculus of variations. Design of an optimal controller for a system with uncertainties and disturbances. Regulator design and reference following. State estimation using Kalman Filter. Simulations of LQR, Kalman Filter, LQG and H∞ optimal control schemes. |
| Course content | : | Linear quadratic regulator (LQR). H2 optimal control. Linear minimum mean squares estimation. Linear quadratic Gaussian control. H∞ optimal control and estimation. |
| References | : | H. Kwakernaak, R. Sivan, Linear Optimal Control Systems, John Wiley and Sons, 1972.;B. D. O. Anderson, J. B. Moore, Optimal Control, Linear Quadratic Methods, Prentice-Hall, 1989.;D. E. Kirk, Optimal Control Theory, An Introduction, Dover, 1998.;J. B. Burl, Linear Optimal Control, H2 and H∞ methods, Addison-Wesley, 1999.;D. S. Naidu, Optimal Control Systems, CRC Press, 2003.;A. Sinha, Linear Systems â€" Optimal and Robust Control, CRC Press, 2007.;F. L. Lewis, D. L. Vrabie, V. L. Syrmos, Optimal Control, John Wiley and Sons, 2012.;L. Fortuna, M. Frasca, A. Buscarino, Optimal and Robust Control â€" Advanced Topics with Matlab, CRC Press, 2021. |
| Weeks | Topics |
|---|---|
| 1 | A brief review of basic concepts: State-space model, transfer function, poles and zeros, modes, stability, similarity transformations, controllability and observability, norms, calculus of variations, Lagrange multipliers method. |
| 2 | Linear quadratic regulator (LQR): Cost function, Hamiltonian system, matrix Riccati equation, control law |
| 3 | Steady-state LQR: Algebraic Riccati equation, closed-loop system |
| 4 | Stochastic regulator, H2 optimal control |
| 5 | Linear minimum mean squares estimation, principle of orthogonality |
| 6 | Kalman Filter: Predictor form, observer form, estimation error, Hamiltonian system |
| 7 | Kalman Filter: Steady-state Kalman Filter, H2 optimal estimation, duality, Kalman Filter poles |
| 8 | Midterm Exam |
| 9 | Linear quadratic Gaussian control (LQG): Derivation of the control law, transient response, reference following and disturbance rejection analyses |
| 10 | Linear quadratic Gaussian control (LQG): Steady-state, closed-loop poles, Lyapunov equation, reference following, disturbance rejection |
| 11 | H∞ optimal control: Full information control, control law, cost function, performance bound |
| 12 | H∞ optimal control: Hamiltonian system, control law, steady-state H∞ optimal control |
| 13 | H∞ optimal estimation: Problem definition, adjoint system |
| 14 | H∞ optimal estimation: Finite-time estimation, steady-state estimation, stability condition |
| 15 | Final exam |
| 16 | Final exam |
| Course activities | Number | Percentage |
|---|---|---|
| Attendance | 0 | 0 |
| Laboratory | 0 | 0 |
| Application | 0 | 0 |
| Field activities | 0 | 0 |
| Specific practical training | 0 | 0 |
| Assignments | 6 | 40 |
| Presentation | 0 | 0 |
| Project | 0 | 0 |
| Seminar | 0 | 0 |
| Quiz | 0 | 0 |
| Midterms | 1 | 20 |
| Final exam | 1 | 40 |
| Total | 100 | |
| Percentage of semester activities contributing grade success | 60 | |
| Percentage of final exam contributing grade success | 40 | |
| Total | 100 | |
| Course activities | Number | Duration (hours) | Total workload |
|---|---|---|---|
| Course Duration | 13 | 3 | 39 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Specific practical training | 0 | 0 | 0 |
| Field activities | 0 | 0 | 0 |
| Study Hours Out of Class (Preliminary work, reinforcement, etc.) | 14 | 5 | 70 |
| Presentation / Seminar Preparation | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework assignment | 0 | 0 | 0 |
| Quiz | 6 | 20 | 120 |
| Midterms (Study duration) | 1 | 25 | 25 |
| Final Exam (Study duration) | 1 | 35 | 35 |
| Total workload | 35 | 88 | 289 |
| Key learning outcomes | Contribution level | |||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1. | Has highest level of knowledge in certain areas of Electrical and Electronics Engineering. | |||||
| 2. | Has knowledge, skills and and competence to develop novel approaches in science and technology. | |||||
| 3. | Follows the scientific literature, and the developments in his/her field, critically analyze, synthesize, interpret and apply them effectively in his/her research. | |||||
| 4. | Can independently carry out all stages of a novel research project. | |||||
| 5. | Designs, plans and manages novel research projects; can lead multidisiplinary projects. | |||||
| 6. | Contributes to the science and technology literature. | |||||
| 7. | Can present his/her ideas and works in written and oral forms effectively; in Turkish or English. | |||||
| 8. | Is aware of his/her social responsibilities, evaluates scientific and technological developments with impartiality and ethical responsibility and disseminates them. | |||||
1: Lowest, 2: Low, 3: Average, 4: High, 5: Highest