On the Stability and Robustness of Discrete Uncertain Systems

<p>Model reference adaptive control (MRAC) is a well-established control design framework for ensuring closed-loop system stability and reference tracking performance in dynamical systems with uncertainties. Nominal, fixed-gain controllers rely on accurate mathematical models to guarantee desired stability and performance. However, uncertainty in system modeling is unavoidable. MRAC provides flexibility in system modeling, allowing modeling inaccuracies to exist under certain conditions. The learning mechanism of MRAC allows gains or uncertain parameters to be estimated online to ensure that the reference tracking objective is achieved. As with any control architecture, MRAC is theoretically sound. However, these theoretical guarantees are not always directly translatable to implementation because of the need for continuous-time to discrete-time transformations. Continuous-time control algorithms are usually sampled at very high frequencies to preserve accuracy, which requires high-performance hardware. In many real-world embedded systems, many factors contribute to the limitations of low-performance hardware, which pose a challenge for accurately implementing continuous-time controllers. Alternatively, control design can be accomplished in the discrete-time domain using an approach referred to as digital control. In digital control, system dynamics are discretized before the control design, resulting in an inherently sampled control algorithm that is readily implementable on hardware and preserves theoretical stability guarantees. Due to this advantage, the sampling frequency is allowed to be much lower than that required for continuous-time implementations. While advantageous from an implementation point of view, digital control design comes with the major drawback of difficulties in the stability analysis. This dissertation investigates several digital control design approaches for MRAC algorithms originally developed in the continuous-time settings. A rigorous Lyapunov stability analysis accompanies the solution to each control design problem, and numerical simulations provide illustrations of the control designs' capabilities.</p>

Name thesis:degree_name

Doctor of Philosophy in Aerospace Engineering

Level thesis:degree_level

Dissertation - Open Access

Discipline thesis:degree_discipline

Aerospace Engineering

Year dc:date.available

2026

Author dc:creator

• Sisson, Nathaniel

• Adaptive control
• discrete systems
• Navigation, Guidance, Control and Dynamics

Repository record dc:identifier

https://commons.erau.edu/edt/989

OAI identifier oai:identifier

oai:commons.erau.edu:edt-2037