PhD Oral Exam - Geovana França dos Santos, Information and Systems Engineering

When studying for a doctoral degree (PhD), candidates submit a thesis that provides a critical review of the current state of knowledge of the thesis subject as well as the student’s own contributions to the subject. The distinguishing criterion of doctoral graduate research is a significant and original contribution to knowledge.

Once accepted, the candidate presents the thesis orally. This oral exam is open to the public.

Abstract

Output feedback tracking control for systems subject to state and input constraints is a fundamental challenge in control engineering. In practical applications, full state measurement is often unavailable, while physical limitations impose strict operational boundaries. When tracking persistent exogenous references, unmodeled constraints lead to performance degradation and closed-loop instability. This thesis designs systematic output feedback controllers that guarantee offset-free tracking, local stability, and constraint satisfaction by bridging the Internal Model Principle with Set Invariance theory. The contributions are established across two complementary paradigms. In the first paradigm, polyhedral Robust Positive Invariance and the Extended Farkas' Lemma are leveraged to cast controller synthesis as an offline bilinear optimization program under asymmetric constraints. This architecture progresses from set-point tracking via PI-like control to ramps and sinusoids using second-order internal models, culminating in a unified dynamic output feedback framework capable of tracking a broad family of trajectories (steps, ramps, sinusoids, and parabolas) in multivariable settings. The formulation concurrently synthesizes feedback gains, internal model bounds, and domains of attraction. In the second paradigm, computational scalability in high-order multivariable systems is addressed through a convex two-stage Linear Matrix Inequality and semidefinite programming framework for static output feedback PID control, using Riccati-parameterized Lyapunov functions to enforce state and actuator limits and determine contractive ellipsoidal invariant domains. The proposed methodologies are validated across diverse benchmarks, demonstrating rigorous constraint fulfillment, stabilization, and tracking performance.