Invitation: PhD Dissertation Defense of Jhon Portella Delgado
Friday, December 19, 2025 · 10 AM - 12 PM
Hello ME Community,
Advisor: Dr. Ankit GoelYou are invited to join the PhD Dissertation Defense of Jhon Portella Delgado, on Friday, December 19, beginning at 10:00am. The defense will be presented in person in the Engineering Building room 210-I. (the Mechanical Engineering Conference room)
Title: Adaptive and Safe Nonlinear Control: Fundamental Theory and Applications
Abstract:
The demand for reliable and safe control has increased dramatically in recent decades, driven by growing performance requirements across a wide range of engineering domains, including robotics, aerospace, nuclear systems, and emerging quantum technologies. However, state-of-the-art control techniques that offer rigorous performance guarantees are still limited in scope. Even with recent advances, a significant class of systems and problem formulations remains beyond the reach of current methodologies. This thesis focuses on two such distinct but related classes of systems and control problems. The first problem is motivated by the need to control rigid bodies whose inertial properties are uncertain. Because these inertial parameters enter the dynamics multiplicatively with the control input, the classical adaptive backstepping framework becomes impractical or inapplicable. This class of problems encompasses a broad range of applications in robotics, aerospace, and mechanical systems. The second problem is motivated by the need to design control systems that simultaneously stabilize the dynamics, regulate the output, and ensure that the states remain within a user-prescribed safe set, all without relying on online optimization. This problem is driven by the need to implement safety-enforcing controllers on resource-constrained platforms, where real-time optimization may be impractical or infeasible.
The first part develops an adaptive controller for pure-feedback systems with multiplicative uncertainties, which commonly arise in mechanical and aerospace applications due to unknown actuation gains, aerodynamic coefficients, or inertial properties. Standard adaptive backstepping often requires inverting parameter estimates, which can lead to potential singularities when these estimates approach zero. The proposed approach circumvents this issue by directly estimating the inverse parameters, eliminating the need for inversion and preventing unbounded internal signals. The resulting controller preserves the recursive backstepping structure while ensuring robustness to multiplicative uncertainties. A Lyapunov-based analysis guarantees boundedness of all closed-loop signals and asymptotic convergence of the tracking error. Furthermore, when the final state equation is non-affine in the control input, a dynamic extension renders the system suitable for adaptive design, thereby broadening the class of systems to which the method applies.
The second part addresses the problem of safe nonlinear control for systems subject to state constraints. To enforce these bounds without online optimization, a constraint-lifting framework is introduced that maps the constrained state space into an unconstrained domain using smooth, invertible sigmoid functions. In this lifted space, the system evolves freely while its projection automatically satisfies the original constraints. To avoid the ill-conditioning that arises with classical barrier Lyapunov functions near constraint boundaries, a new Lyapunov function, which we refer to as the sigmoid integral function, is proposed. This function exhibits quadratic growth near equilibrium and linear growth for large deviations, ensuring smooth and well-conditioned behavior across the entire state space. The resulting controller ensures closed-loop stability and constraint satisfaction without relying on predictive solvers or barrier terms, making it suitable for real-time implementation on resource-limited platforms.
Together, these two studies advance nonlinear control in complementary directions: adaptive design for uncertain pure-feedback systems and safe control for constrained dynamics. Although developed independently, their connection reveals that constraint-lifting transformations often yield pure-feedback structures, suggesting opportunities for future integration of adaptive and safety-critical control methodologies. By avoiding parameter inversion, enforcing constraints through smooth transformations, and providing rigorous stability guarantees, this dissertation offers practical and theoretically grounded tools for controlling uncertain and safety-critical nonlinear systems.
Abstract:
The demand for reliable and safe control has increased dramatically in recent decades, driven by growing performance requirements across a wide range of engineering domains, including robotics, aerospace, nuclear systems, and emerging quantum technologies. However, state-of-the-art control techniques that offer rigorous performance guarantees are still limited in scope. Even with recent advances, a significant class of systems and problem formulations remains beyond the reach of current methodologies. This thesis focuses on two such distinct but related classes of systems and control problems. The first problem is motivated by the need to control rigid bodies whose inertial properties are uncertain. Because these inertial parameters enter the dynamics multiplicatively with the control input, the classical adaptive backstepping framework becomes impractical or inapplicable. This class of problems encompasses a broad range of applications in robotics, aerospace, and mechanical systems. The second problem is motivated by the need to design control systems that simultaneously stabilize the dynamics, regulate the output, and ensure that the states remain within a user-prescribed safe set, all without relying on online optimization. This problem is driven by the need to implement safety-enforcing controllers on resource-constrained platforms, where real-time optimization may be impractical or infeasible.
The first part develops an adaptive controller for pure-feedback systems with multiplicative uncertainties, which commonly arise in mechanical and aerospace applications due to unknown actuation gains, aerodynamic coefficients, or inertial properties. Standard adaptive backstepping often requires inverting parameter estimates, which can lead to potential singularities when these estimates approach zero. The proposed approach circumvents this issue by directly estimating the inverse parameters, eliminating the need for inversion and preventing unbounded internal signals. The resulting controller preserves the recursive backstepping structure while ensuring robustness to multiplicative uncertainties. A Lyapunov-based analysis guarantees boundedness of all closed-loop signals and asymptotic convergence of the tracking error. Furthermore, when the final state equation is non-affine in the control input, a dynamic extension renders the system suitable for adaptive design, thereby broadening the class of systems to which the method applies.
The second part addresses the problem of safe nonlinear control for systems subject to state constraints. To enforce these bounds without online optimization, a constraint-lifting framework is introduced that maps the constrained state space into an unconstrained domain using smooth, invertible sigmoid functions. In this lifted space, the system evolves freely while its projection automatically satisfies the original constraints. To avoid the ill-conditioning that arises with classical barrier Lyapunov functions near constraint boundaries, a new Lyapunov function, which we refer to as the sigmoid integral function, is proposed. This function exhibits quadratic growth near equilibrium and linear growth for large deviations, ensuring smooth and well-conditioned behavior across the entire state space. The resulting controller ensures closed-loop stability and constraint satisfaction without relying on predictive solvers or barrier terms, making it suitable for real-time implementation on resource-limited platforms.
Together, these two studies advance nonlinear control in complementary directions: adaptive design for uncertain pure-feedback systems and safe control for constrained dynamics. Although developed independently, their connection reveals that constraint-lifting transformations often yield pure-feedback structures, suggesting opportunities for future integration of adaptive and safety-critical control methodologies. By avoiding parameter inversion, enforcing constraints through smooth transformations, and providing rigorous stability guarantees, this dissertation offers practical and theoretically grounded tools for controlling uncertain and safety-critical nonlinear systems.
