PhD Proposal Defense - Jhon Portella Delgado

Wed, 13 Nov 2024 11:30:40 -0500

Advisor: Dr. Ankit Goel

Title: Adaptive Control with Input and State Constraint: THEORY AND APPLICATIONS

Abstract:
Physical systems evolve as time progresses. A system’s temporal behavior depends on its internal characteristics and interactions with its surroundings. A control signal that affects the state of the system can be carefully designed to achieve the desired behavior of the system. However, this approach, called the open-loop control, requires a detailed apriori description, in the form of a mathematical model, of the interaction between the state and the control signals. Feedback interconnections, resulting in closed loops, can be used to alter the system’s behavior, enabling closed-loop feedback control to reduce the modeling fidelity required to design control systems and achieve the desired temporal behavior of the system.

If a sufficiently detailed, control-oriented model is available, optimal control strategies can be used to optimize relevant metrics such as time of operation, fuel consumption, etc. Robust control strategies can be used to design control laws that reduce the sensitivity of relevant metrics to parametric variations in the system. When parameters in the system model are unknown, uncertain, or vary with time, adaptive control strategies can be used to achieve and maintain the desired behavior of the system despite a lack of knowledge of system parameters. However, real-world effects such as actuator constraints, measurement uncertainty, conflicting and infeasible system commands, and the system’s mathematically unmodelable complexity pose considerable challenges to optimal, robust, and adaptive control synthesis and weaken the performance guarantees.

Motivated by these fundamental challenges, this thesis thus is focused on exploring and developing adaptive strategies that can guarantee performance in the presence of system uncertainties, actuator constraints, and lack of control-oriented models. In particular, model-based adaptive control designs based on a backstepping framework and input-output linearization technique are developed for systems where a control-oriented model is available but the parameters of the system are unknown, uncertain, or time-varying. Such systems include aircrafts, multicopters, pendulum systems, rigid multi-body systems, etc, where physics-based models are available, but systems’ inertial and geometric properties introduce parametric uncertainties.

Data-driven adaptive control strategies based on retrospective cost optimization, extremum seeking control, etc., are explored for systems where only discrete measurements from the system are available. Various adaptive control techniques developed in this thesis are validated in a numerical simulation framework for multicopter control problems, aircraft control problems, quantum systems control problems, etc.