Date of Completion
Adaptive Control, Neural Networks, Optimization, Air Management Systems, Satellite
Field of Study
Doctor of Philosophy
Over the past decade, L1 adaptive control has emerged as viable control architecture for systems with unmodeled dynamics and time-varying uncertainties. L1 control uses a concept known as "fast adaptation" to estimate uncertainties. This means the controller relies on high sampling rates. However, in any real-world application, sampling speed is limited by hardware capabilities. Thus the question of how to obtain better performance at slower sampling rates in fast adaptation-based algorithms has become an important research topic. This dissertation presents two methods of online modeling to solve this problem. The first of these is function approximation using artificial neural networks. This removes the burden of estimating state-dependent nonlinearities from the adaptive law. The second method is a memorizing mechanism which uses an integrator to store estimations from previous time-steps. The benefits of each of these methods are shown analytically and in simulation by comparing performance to an unmodified L1 controller.
Additionally, a technique for using fast adaptation to perform online optimization is discussed. Engineering systems are often designed to optimize some criteria, but in practice, manufacturing variability and component age cause deviations from the optimal design. Performance-seeking control can be used to re-optimize a system online by changing control inputs based on adaptation. This is useful when two control inputs are implicitly related such that an optimum point exists in the cost function. One input is updated via a gradient search while the other is updated via a Lyapunov-based controller using adaptive parameters for feedback. Simulation results are presented.
Finally, the dissertation contains two case studies: pressure control in aircraft air management systems and satellite orbit stabilization. In air management systems, the relationship between valve angle and downstream pressure is highly nonlinear, and the dynamics are subject to effects of hysteresis due to dry friction. Man-made satellites are subject to a number of difficult-to-measure disturbance forces such as variations in Earth's gravitational and magnetic fields, aerodynamic drag, and solar radiation pressure. These characteristics lend themselves well to the use of adaptive control. Each case study contains simulation examples and comparisons of different control strategies.
Cooper, John R., "Improving Effects of Sampling Time in Fast Adaptation-Based Control Algorithms with Applications" (2017). Doctoral Dissertations. 1355.