Final Year Project
Final Year Project
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Overview
Overview
I am currently working on my Engineering Final Year Project (Honours). It is an individual project building on a paper published by my supervisor A/Prof Paranjape. I am applying control theory to a highly nonlinear ODE model of Mitogen Activated Protein Kinase (MAPK) cellular signalling cascades, aiming to maximise the amplitude of the limit cycle of the system by dynamically adjusting two input parameters which control the concentration of the enzyme kinase. When the limit cycle in this system deteriorates it can impact cellular function, and by affecting apoptosis it can increase cancer risk. Understanding how to optimally and robustly control this limit cycle could lead to progress in preventative medicine.
I am currently working on my Engineering Final Year Project (Honours). It is an individual project building on a paper published by my supervisor A/Prof Paranjape. I am applying control theory to a highly nonlinear ODE model of Mitogen Activated Protein Kinase (MAPK) cellular signalling cascades, aiming to maximise the amplitude of the limit cycle of the system by dynamically adjusting two input parameters which control the concentration of the enzyme kinase. When the limit cycle in this system deteriorates it can impact cellular function, and by affecting apoptosis it can increase cancer risk. Understanding how to optimally and robustly control this limit cycle could lead to progress in preventative medicine.
I began researching and studying nonlinear dynamics and nonlinear control in November 2025, and the project will be completed in October 2026. This project has required extensive self study, going far beyond what I had learnt in my degree so far. I have learned and applied many techniques from control and dynamical systems theory including Extremum Seeking Control (ESC), the centre manifold theorem and normal forms. The project is still in its early stages, but so far I have used python to conduct simulations and have successfully stabilised the system and achieved convergence of the input parameters to their optimal values.
I began researching and studying nonlinear dynamics and nonlinear control in November 2025, and the project will be completed in October 2026. This project has required extensive self study, going far beyond what I had learnt in my degree so far. I have learned and applied many techniques from control and dynamical systems theory including Extremum Seeking Control (ESC), the centre manifold theorem and normal forms. The project is still in its early stages, but so far I have used python to conduct simulations and have successfully stabilised the system and achieved convergence of the input parameters to their optimal values.
Course: ENG4701: Final Year Project
Course: ENG4701: Final Year Project
Collaborators: Solo project
Collaborators: Solo project
Date: November 2025 - October 2026
Date: November 2025 - October 2026
Key skills: Nonlinear Control, Extremum Seeking Control (ESC), Dynamical Systems Modeling, Python (SciPy/NumPy), LaTeX
Key skills: Nonlinear Control, Extremum Seeking Control (ESC), Dynamical Systems Modeling, Python (SciPy/NumPy), LaTeX
Preliminary Paper
Preliminary Paper
Below is my preliminary paper detailing the project and the research results so far. It is the main deliverable for the first half of the project, designed to be a brief overview, with a significant proportion consisting of a literature review. Code is attached at the bottom of the page.
Below is my preliminary paper detailing the project and the research results so far. It is the main deliverable for the first half of the project, designed to be a brief overview, with a significant proportion consisting of a literature review. Code is attached at the bottom of the page.
FYP_A_Preliminary_Paper - Control_of_Limit_Cycles_in_MAPK_Cascades.pdfLessons Learned
Lessons Learned
Applying this theoretical math to a real system through python simulations came with a big learning curve, and there were lots of hurdles along the way. Navigating these hurdles became a really valuable learning opportunity that taught me invaluable skills about the practical challenges of implementing control logic.
Applying this theoretical math to a real system through python simulations came with a big learning curve, and there were lots of hurdles along the way. Navigating these hurdles became a really valuable learning opportunity that taught me invaluable skills about the practical challenges of implementing control logic.
The importance of control timing
The importance of control timing
Implementing ESC reinforced that when you apply control is just as critical as how. Initially, applying the control logic right out of the gate led to erratic system behavior because the biological cascade hadn't settled into its natural limit cycle. By introducing an adjustable threshold variable that explicitly delayed the ESC application, the system had time to stabilize. This taught me the importance of allowing time for the transient to die out before readjusting the parameters, to make sure the signal being fed back into the control law is the steady state response.
Implementing ESC reinforced that when you apply control is just as critical as how. Initially, applying the control logic right out of the gate led to erratic system behavior because the biological cascade hadn't settled into its natural limit cycle. By introducing an adjustable threshold variable that explicitly delayed the ESC application, the system had time to stabilize. This taught me the importance of allowing time for the transient to die out before readjusting the parameters, to make sure the signal being fed back into the control law is the steady state response.
The importance of accurate state estimation
The importance of accurate state estimation
When estimating the amplitude of the Mpp limit cycle, my first instinct was to use the more mathematically sophisticated approach of fitting an ellipse to the phase portrait. Unfortunately, this often returned highly inaccurate state estimates. Aiming to improve the accuracy, I scaled this up to average the parameters of hundreds of fitted ellipses, but this still failed to solve the problem. Ultimately, the most reliable state estimate came from the absolute simplest solution: just calculating the difference between the maximum and minimum Mpp values over a 5000 time unit window. While this tradeoff introduced a delay, its accuracy ultimately improved the speed of convergence of the control law. This taught me the importance of accurate state estimation for successful control implementation.
When estimating the amplitude of the Mpp limit cycle, my first instinct was to use the more mathematically sophisticated approach of fitting an ellipse to the phase portrait. Unfortunately, this often returned highly inaccurate state estimates. Aiming to improve the accuracy, I scaled this up to average the parameters of hundreds of fitted ellipses, but this still failed to solve the problem. Ultimately, the most reliable state estimate came from the absolute simplest solution: just calculating the difference between the maximum and minimum Mpp values over a 5000 time unit window. While this tradeoff introduced a delay, its accuracy ultimately improved the speed of convergence of the control law. This taught me the importance of accurate state estimation for successful control implementation.
The crippling effect of measurement noise
The crippling effect of measurement noise
When I encountered the noisy estimates of the amplitude of Mpp, I saw firsthand how a noisy signal can derail a control law. This taught me the importance of managing and minimising noise, and the value of filtering to produce pure, accurate signals that accurately show the response of the system to a change in input parameters.
When I encountered the noisy estimates of the amplitude of Mpp, I saw firsthand how a noisy signal can derail a control law. This taught me the importance of managing and minimising noise, and the value of filtering to produce pure, accurate signals that accurately show the response of the system to a change in input parameters.
Code
Code
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