Least Squares Based Adaptive Control and Extremum Seeking with Active Vehicle Safety System Applications
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On-line parameter estimation is one of the two key components of a typical adaptive control scheme, beside the particular control law to be used. Gradient and recursive least squares (RLS) based parameter estimation algorithms are the most widely used ones among others. Adaptive control studies in the literature mostly utilize gradient based parameter estimators for convenience in nonlinear analysis and Lyapunov analysis based constructive design. However, simulations and real-time experiments reveal that, compared to gradient based parameter estimators, RLS based parameter estimators, with proper selection of design parameters, exhibit better transient performance from the aspects of speed of convergence and robustness to measurement noise. One reason for the control theory researchers' preference of gradient algorithms to RLS ones is that there does not exist a well-established stability and convergence analysis framework for adaptive control schemes involving RLS based parameter estimation. Having this fact as one of the motivators, this thesis is on systematic design, formal stability and convergence analysis, and comparative numerical analysis of RLS parameter estimation based adaptive control schemes and extension of the same framework to adaptive extremum seeking, viz. adaptive search for (local) extremum points of a certain field. Extremum seeking designs apply to (i) finding locations of physical signal sources, (ii) minimum or maximum points of (vector) cost or potential functions for optimization, (iii) calculating optimal control parameters within a feedback control design. In this thesis, firstly, gradient and RLS based on-line parameter estimation schemes are comparatively analysed and a literature review on RLS estimation based adaptive control is provided. The comparative analysis is supported with a set of simulation examples exhibiting transient performance characteristics of RLS based parameter estimators, noting absence of such a detailed comparison study in the literature. The existing literature on RLS based adaptive control mostly follows the indirect adaptive control approach as opposed to the direct one, because of the difficulty in integrating an RLS based adaptive law within the direct approaches starting with a certain Lyapunov-like cost function to be driven to (a neighborhood) of zero. A formal constructive analysis framework for integration of RLS based estimation to direct adaptive control is proposed following the typical steps for gradient adaptive law based direct model reference adaptive control, but constructing a new Lyapunov-like function for the analysis. After illustration of the improved performance with RLS adaptive law via some simple numerical examples, the proposed RLS parameter estimation based direct adaptive control scheme is successfully applied to vehicle antilock braking system control and adaptive cruise control. The performance of the proposed scheme is numerically analysed and verified via Matlab/Simulink and CarSim based simulation tests. Similar to the direct adaptive control works, the extremum seeking approaches proposed in the literature commonly use gradient/Newton based search algorithms. As an alternative to these search algorithms, this thesis studies RLS based on-line estimation in extremum seeking aiming to enhance the transient performance compared to the existing gradient based extremum seeking. The proposed RLS estimation based extremum seeking approach is applied to active vehicle safety system control problems, including antilock braking system control and traction control, supported by Matlab/Simulink and CarSim based simulation results demonstrating the effectiveness of the proposed approach.
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Nursefa Zengin (2020). Least Squares Based Adaptive Control and Extremum Seeking with Active Vehicle Safety System Applications. UWSpace. http://hdl.handle.net/10012/15878