In this thesis, two separate problems are examines. First, sinusoidal signals are quite prevalent in practical applications. For example, any machine driven by a rotary shaft will exhibit periodic behaviour. For this reason, the estimation of sinusoidal parameters is studied extensively in the literature. Often in practical applications, there are unmodeled disturbances to the system, and the incoming measurements are noisy. Thus, estimation of the parameters of a sinusoidal signal in real-time for these conditions is of interest, calling for the use of a filter-based approach such as the Extended Kalman Filter. Considering the sinusoidal signal in its complex form, a novel approach is proposed resulting in a complex-valued filter. The resulting complex Extended Kalman Filter’s performance is evaluated in various test environments and is compared to standard approaches to the estimation problem using a Discrete Fourier Transform and standard Extended Kalman Filter. Results show that the complex Extended Kalman Filter outperforms the standard approaches in some cases in both accuracy and convergence rate. Second, research on hybrid systems has seen a large growth in interest in recent years. This is largely due to the increase of natural systems where discrete mode dynamics interact with continuous state dynamics. Switched systems are a subclass of hybrid systems that restrict their definition to continuous dynamic systems that interact with dis- crete switching events. Controller synthesis for such systems is no trivial task. Given the current trend in Artificial Intelligence and Machine Learning approaches, Dynamic Programming is explored as a means to approximate optimal control policies for switched systems. Discussions of discretization of the system’s state space are presented, followed by a high-level overview of an algorithm that leverages Dynamic Programming to find the approximated optimal control policies. Finally, the algorithm is applied to several examples to demonstrate its effectiveness. / Thesis / Master of Applied Science (MASc)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/27562 |
| Date | January 2022 |
| Creators | Elaghoury, Hassan |
| Contributors | Von Mohrenschildt, Martin, Computing and Software |
| Source Sets | McMaster University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
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