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Pontryagin's principle is applied to several significant problems associated with optimal large angle spacecraft rotational maneuvers. Both rigid and flexible body dynamical models for these vehicles are considered. Three relaxation/analytic continuation methods are developed for iteratively solving the two-point-boundary value problem which results in the treatment of these problems. The solutions obtained are required to rigorously satisfy the necessary conditions derived from Pontryagin's principle. These methods include: (1) boundary condition relaxation processes; (2) differential equation relaxation processes; and (3) hybrid relaxation processes, combining (1) and (2) above. In the literature these relaxation processes are closely related to a number of methods for solving nonlinear equations, known as Davidenko's method, imbedding, and homotopy chain methods. For rigid vehicles a general nonsingular optimal maneuver formulation is obtained, treating all kinematic and dynamical nonlinearities, for general orientation and angular velocity boundary conditions. For flexible vehicles restricted to single axis maneuvers and anti-symmetric elastic deflection modes, a general optimal maneuver formulation is obtained; treating all kinematic, dynamical, and first order structural nonlinearities. In the case of general motion for a flexible vehicle a general formulation is provided, though a solution is not obtained; due to a previously unidentified and as yet unresolved computational difficulty associated symmetry in the dynamical model for the spacecraft. / Ph. D.

Polynomial feedback controls are developed for large angle, nonlinear spacecraft attitude maneuvers. Scalar and two-state systems are presented as simple examples to demonstrate the method, and several systems of state variables to parameterize spacecraft motion are considered. Both external and internal control torques are treated; in the latter, attention is restricted to momentum transfer maneuvers that permit several order reductions. Several stability theorems with their application to polynomial feedback systems are discussed. / Ph. D.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1979. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERONAUTICS. / Bibliography: leaf 72. / by Yuji Hanawa. / M.S.

Jia Peng. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 85-87). / Abstracts in English and Chinese. / Abstract --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Overview of Output Regulation Problem --- p.2 / Chapter 1.2 --- Attitude Tracking Control of Rigid Spacecraft --- p.3 / Chapter 1.3 --- Overview of Continuous-time Nonlinear H∞ Control --- p.4 / Chapter 1.4 --- Overview of Discrete-time Nonlinear Hq∞ Control --- p.6 / Chapter 1.5 --- Flight Control in Windshears --- p.8 / Chapter 1.6 --- Nonlinear Benchmark System --- p.9 / Chapter 1.7 --- Outline of the Work --- p.11 / Chapter 2 --- Attitude Control and Asymptotic Disturbance Rejection of Rigid Spacecraft --- p.12 / Chapter 2.1 --- Model Description --- p.12 / Chapter 2.2 --- Problem Formulation --- p.16 / Chapter 2.3 --- Preliminaries of General Framework for Global Robust Output Regulation --- p.17 / Chapter 2.4 --- Application of Global Robust Output Regulation --- p.21 / Chapter 2.4.1 --- Case I: without unknown parameters --- p.21 / Chapter 2.4.2 --- Case II: with unknown parameters --- p.26 / Chapter 2.5 --- Simulation --- p.34 / Chapter 2.5.1 --- Case I: without unknown parameters --- p.34 / Chapter 2.5.2 --- Case II: with unknown parameters --- p.36 / Chapter 2.6 --- Conclusions --- p.38 / Chapter 3 --- Application of Approximation Continuous-time Nonlinear H∞ Control Law --- p.45 / Chapter 3.1 --- Preliminaries of Approximation Continuous-time Nonlinear Hq∞ Control Law --- p.45 / Chapter 3.2 --- Disturbance Attenuation of Flight Control System in Windshears --- p.50 / Chapter 3.2.1 --- Design of Control Law --- p.51 / Chapter 3.2.2 --- Computer Simulation --- p.56 / Chapter 3.3 --- Conclusions --- p.57 / Chapter 4 --- Application of Approximation Discrete-time Nonlinear H∞ Control Law --- p.65 / Chapter 4.1 --- Preliminaries of Approximation Discrete-time Nonlinear H∞ Control Law --- p.66 / Chapter 4.2 --- Explicit Expression of u --- p.69 / Chapter 4.3 --- Disturbance Attenuation of RTAC System --- p.73 / Chapter 4.4 --- Computer Simulation --- p.78 / Chapter 4.5 --- Conclusions --- p.80 / Chapter 5 --- Conclusions --- p.83 / Bibliography --- p.85 / A Programs --- p.88 / Vita --- p.112

Adaptive control has long focused on establishing stable adaptive control methods for various nonlinear systems. Existing methods are mostly based on the certainty equivalence principle which states that the controller structure developed in the deterministic case (without uncertain system parameters) can be used for controlling the uncertain system along by adopting a carefully determined parameter estimator. Thus, the overall performance of the regulating/tracking control depends on the performance of the parameter estimator, which often results in the poor closed-loop performance compared with the deterministic control because the parameter estimate can exhibit wide variations compared to their true values in general. In this dissertation we introduce a new adaptive control method for nonlinear systems where unknown parameters are estimated to within an attracting manifold and the proposed control method always asymptotically recovers the closed-loop error dynamics of the deterministic case control system. Thus, the overall performance of this new adaptive control method is comparable to that of the deterministic control method, something that is usually impossible to obtain with the certainty equivalent control method. We apply the noncertainty equivalent adaptive control to study application arising in the n degree of freedom (DOF) robot control problem and spacecraft attitude control. Especially, in the context of the spacecraft attitude control problem, we developed a new attitude observer that also utilizes an attracting manifold, while ensuring that the estimated attitude matrix confirms at all instants to the special group of rotation matrices SO(3). As a result, we demonstrate for the first time a separation property of the nonlinear attitude control problem in terms of the observer/controller based closed-loop system. For both the robotic and spacecraft attitude control problems, detailed derivations for the controller design and accompanying stability proofs are shown. The attitude estimator construction and its stability proof are presented separately. Numerical simulations are extensively performed to highlight closed-loop performance improvement vis-a-vis adaptive control design obtained through classical certainty equivalence based approaches. / text

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERO. / Includes bibliographical references. / by Edward Gregory Taylor. / Ph.D.

Numerical schemes for the solution of two-point boundary value problems arising from the application of optimal control theory to mathematical models of dynamic systems, are discussed. Optimal control problems are formulated for rotational maneuvers of multiple rigid body, asymmetric spacecraft configurations with both external torques and/or internal torques. Necessary conditions for optimality are derived through Pontryagin’s principle; solutions to the problems are obtained numerically. Comparison studies using competing numerical methods and various choices of performance indices are reported. / Ph. D.

Thesis. 1978. M.S.--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERONAUTICS. / Includes bibliographical references. / M.S.