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The unit delves into the principles of optimal control and estimation, addressing both theoretical foundations and the practical challenges associated with implementing these techniques in real-world scenarios. It covers key topics such as dynamic programming, linear quadratic regulators (LQR), linear quadratic Gaussian (LQG) methods, and Kalman filtering, ensuring a robust understanding of the underlying mathematics and algorithms. A significant emphasis is placed on the discrete-time implementation of these methods, exploring how they can be effectively applied in digital systems. Additionally, the unit integrates practical case studies across various engineering applications, providing insights into the limitations, trade-offs, and adaptations required for successful deployment in diverse contexts, such as robotics, aerospace, and industrial automation. Through hands-on exercises and problem-solving, students will gain both theoretical knowledge and practical experience, preparing them for tackling complex control and estimation challenges in modern engineering systems. 

The course unit aims to:
•    Introduce students to the fundamentals of LQR and KF 
•    Introduce students to the fundamentals of LQG control
•    Introduce students to the fundamentals of robustness analysis, robust control law synthesis and robust control design
 

To select Unit EEEN40122, you need to have selected EEEN30231 Control Systems II in your 3rd year AND select EEEN40221 Linear Systems Theory in your 4th Year.

The course unit aims to:

•    Introduce students to the fundamentals of LQR and KF 
 

•    Introduce students to the fundamentals of LQG control
 

•    Introduce students to the fundamentals of robustness analysis, robust control law synthesis and robust control design

Brief Description of the unit

•    Quadratic Lyapunov functions for linear systems
•    LQR (optimal state feedback) control in both Continuous-Time and Discrete-Time
•    Robustness of LQR control in both Continuous-Time and Discrete-Time
•    Kalman filter (optimal observers) in both Continuous-Time and Discrete-Time
•    Linear Quadratic Gaussian (LQG) control (combining LQR state feedback and optimal observer) in both Continuous-Time and Discrete-Time
•    Loop transfer recovery
•    Adding integral action
•    H2 norms and H2 optimal control
•    Connection of LQG control and MPC (Model Predictive Control)
•    Practical considerations in optimal control and estimation
 

On the successful completion of the course, students will be able to:

ILO 1    Demonstrate a comprehensive understanding of optimal control theory   

ILO 2    Explain the process of synthesising optimal controllers.    

ILO 3    Develop strategies for controlling systems in scenarios where accurate mathematical models are unavailable.     

ILO 4    Implement optimal control methods in systems across various technological domains.    

ILO 5    Employ optimal estimation techniques in a range of practical applications.    

ILO 6    Utilise design methodologies for developing controllers in real-world systems.    

ILO 7    Adapt and utilise the learned methods effectively in diverse applications.    
 

Theoretical knowledge is delivered over lectures and demonstrated over tutorial. 

3 hour Unseen Written Examination (80%)

Coursework Assessment (20%)

Written Exam

Feedback is provided after exam board.

Coursework 

Individual feedback is provided 3 weeks after submission  

1 Applied optimal control: optimization, estimation and control. Bryson, Arthur Earl. Routledge, 2018.

2 Optimal Control. Lewis, Frank L. John Wiley & Sons 2012
 

3 Multivariable feedback control : analysis and design. Skogestad, Sigurd. John Wiley, 2005
 

4 Linear optimal control Anderson, Brian D. O. Prentice-Hall, 1971