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Adaptive Lyapunov redesign of model predictive powered descent guidance

Altıntaş, Oğuz
A new era of space systems is initiated with the development of reusable rocket systems. The experience gained from interplanetary landing missions shed a light upon the design of reusable rocket stages with vertical precision landing capabilities. For two decades, the descent guidance problem of interplanetary landers and reusable rocket stages are modeled and handled as computational optimal control problems which are usually solved as parametric optimization problems. Nevertheless, the precision of descent guidance highly relies on the robustness of the used solution procedure against unexpected subsystem faults occurring in sensors, thrusters and so on. In many engineering applications, particularly in descent guidance problems, the subsystem faults are inevitable due to drastically changing environments and subjecting to physical stress. There are plenty of precautions used for fault detection in such missions, however, very few of them consist of approximating the faults or, in control theoretic terms, the uncertainties in an online manner. On the other hand, there exists a well-established literature of adaptive control theory which particularly focuses on the estimation and approximation of physical uncertainties. In this thesis, the descent guidance problem of reusable rocket stages is solved via receding horizon optimal control strategy known as model predictive control in the presence of various physical uncertainty factors such as sensor faults, thruster losses and modelling errors. First, the formulation of model predictive control is explained with the various aspects such as estimation-based approach and feasibility issues. As a preliminary to estimation-based model predictive control, the globally adopted methods of Kalman filtering and the theory of quadratic programming are presented as the state estimator and the optimization solver used, respectively. Then, the state estimator used in optimal control formulation is redesigned to be adaptive to the disruptive effects of uncertainties, in the sense of discrete-time model reference adaptive control. Meanwhile, the approximate functional representations of uncertainties acting on the subsystems can be obtained. In the major part of the thesis, the proposed redesign methodology on the state estimation part of optimal control is given and proven with the mathematical analysis and control theoretical perspectives. In the proposed methods, the state estimator is redesigned with a regressor structure (e.g. neural networks) that learns to mimic the physical uncertainty up to some adequacy. The online tuning law (or training) of regressor is obtained from the necessary and sufficient conditions of Lyapunov stability theory and it is shown that the proposed methods are input-to-state stable when the structure of uncertainty is known. On the other hand, it is also shown that the methods are semiglobally practically asymptotically stable in the presence of bounded approximation errors when used along the convex projections. In either case, the proposed online tuning laws consist of some particular Kalman filter terms which build a novel bridge between optimal filtering and Lyapunov-based adaptive control.