Nicholas Gioia

* Developed in collaboration with two peers as part of the Optimal Control and Reinforcement Learning course at the University of Bologna.

This project focuses on the trajectory generation and tracking of a planar gymnast robot, modeled as an Acrobot (an underactuated double pendulum with torque applied only at the second joint).

The control architecture was decoupled into two main phases. First, an offline trajectory generation phase was implemented using Newton's Method to mathematically optimize the system's movement between different equilibrium points.

Second, to track the generated reference, I applied optimal feedback controllers. While a Linear Quadratic Regulator (LQR) proved efficient for nominal operations, a receding horizon Model Predictive Control (MPC) strategy was implemented to handle hard constraints on both inputs and states. This successfully allowed the robot to recover from initial disturbances while strictly respecting physical limits (e.g., maximum torque), ensuring the absolute safety of the mechanical system.

This project addresses two core challenges in Automation Engineering: Dynamical System Estimation and Data Classification, implemented entirely from scratch in MATLAB.

In the first part, I developed algorithms to identify mathematical models (ARX vs FIR) from input-output datasets. I estimated the optimal model complexity using advanced criteria such as Akaike Information Criterion (AIC), Final Prediction Error (FPE), and Minimum Description Length (MDL). The chosen ARX model was then rigorously validated through Whiteness and Cross-Correlation statistical hypothesis tests on the residuals.

The second part focuses on a multi-class Machine Learning problem. I implemented a One-vs-All Logistic Regression classifier using the Gradient Descent optimization algorithm to define linear decision boundaries. The custom-built model successfully clustered the data, achieving an outstanding Error Rate of just 0.53% on the test set, matching the performance of built-in MATLAB linear discriminant analysis tools.

This project tackles a complex recursive parsing problem: translating mathematical expressions from Infix to Postfix notation. Unlike standard sequence-to-sequence tasks, it requires managing deep syntactic structures and long-distance dependencies, where traditional RNNs typically fail due to the vanishing gradient problem.

To overcome this, I designed and implemented a custom Encoder-Decoder Transformer architecture entirely from scratch using TensorFlow and Keras. By leveraging the Self-Attention mechanism, the model successfully maintains its internal state across deep sequences. The network was highly optimized to operate efficiently with under 2 million parameters.

I also experimented with different training strategies, demonstrating how Curriculum Learning (progressive training on gradually increasing complexity) builds a more robust internal latent space and improves Out-of-Distribution generalization compared to standard methods, achieving a flawless 100% accuracy on deep recursion tasks.