http://www-personal.umich.edu/~dsbaero/library/BhatTopObstrSCL2000.pdf

A topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon

Allee effects: population growth, critical density, and the chance of extinction

Rigid-body attitude control is motivated by aerospace applications that involve attitude maneuvers or attitude stabilization The set of attitudes of a rigid body is the set of 3 X 3 orthogonal matrices whose determinant is one This set is the configuration space of rigid-body attitude motion; however, this configuration space is not Euclidean Since the set of attitudes is not a Euclidean space, attitude control is typically studied using various attitude parameterizations Motivated by the desire to represent attitude both globally and uniquely in the analysis of rigid-body rotational motion, this article uses orthogonal matrices exclusively to represent attitude and to develop results on rigid-body attitude control An advantage of using orthogonal matrices is that these control results, which include open-loop attitude control maneuvers and stabilization using continuous feedback control, do not require reinterpretation on the set of attitudes viewed as orthogonal matrices The main objec tive of this article is to demonstrate how to characterize properties of attitude control systems for arbitrary attitude maneuvers without using attitude parameterizations

Rigid-Body Attitude Control

Quarternion feedback regulator for spacecraft eigenaxis rotations

This paper presents the stability and control analysis for large angle feedback reorientation maneuvers using reaction jets. The strapdown inertial reference system provides spacecraft attitude changes in terms of quaternions. Reaction jets with pulse-width pulse-frequency modulation provide nearly proportional control torques. The use of quaternions as attitude errors for large angle feedback control is investigated. Closed-loop stability analysis for the three-axis maneuvers is performed using the Liapunov stability theorem. Unique characteristics of the quaternion feedback are discussed for single-axis motion using a phase-plane plot. The practical feasibility of a three-axis large angle feedback maneuver is demonstrated by digital simulations.

Quaternion feedback for spacecraft large angle maneuvers

The purpose of this report is to introduce the engineer to the area of stochastic differential equations, and to point out the mathematical techniques and pitfalls in this area Topics discussed include continuous-time Markov processes, the Fokker-Planck-Kolmogorov equations, the Ito and Stratonovich stochastic calculi, and the problem of modeling physical systems

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Mathematical problems of modeling stochastic nonlinear dynamic systems

The problem considered in this paper is that of designing an attitude regulator for an arbitrary rigid body. The design criterion is that, in the presence of no disturbance torques on the body, the system should have only one equilibrium point, and this point should be asymptotically stable for arbitrary initial conditions. By use of Lyapunov techniques and an appropriate choice of state variables, it is shown that this criterion can be satisfied by employing a linear feedback law with constant coefficients.

A globally stable linear attitude regulator

Discussion of Probability and Stochastic Processes The Gaussian Distribution in One and Two Dimensions The Multidimensional Gaussian Distribution Finite Random Sequences Stationary Random Sequences Continuous-time Stationary Gaussian and Second-order Processes Nonstationary Continuous-time Processes Additional Topics in the Study of Continuous-time Processes Linear Systems in Conjunction with Memoryless Nonlinear Devices Nonstationary Random Sequences Discrete-time Kalman Filtering Appendixes References Index.

Random Signals and Systems

This paper is presented, not so much as an end in itself concerning the solution of a definite engineering problem, but as an exploratory step toward the solution of the problem of optimal control of continuous time stochastic non-linear systems when only noisy observations of the state are available. In this paper, the problem of determining the optimal open loop control, when no observations at all are available, is treated by dynamic programming. The main results of the paper are to obtain the functional equation of dynamic programming and to present a quasi-linearization type of algorithm for its solution. The author's intention was to illustrate by these results that infinite dimensional function space is the most natural setting for stochastic non-linear problems. The results obtained give some insight into what can be expected in the more general case of noisy observations. In the Appendices an argument is presented to justify the proposed algorithm and an example is given for which an exa...

A Priori Open Loop Optimal Control of Continuous Time Stochastic Systems

The problem of how to model a physical system which is subject to random disturbance has been the subject of much debate. In the continuous-time case, attempts to construct models which employ the formal concept of white noise as inputs or forcing terms have encountered difficulties. One formalism which has been advocated for dealing with this situation is the Ito stochastic calculus. In this paper, an example is considered in which the Ito formalism appears to be lacking in merit when the issue of performing actual numerical computation is introduced. There is described an alternative formalism, called the Balakrishnan white noise model, which is claimed to exhibit more merit in the given example.

Richard E. Mortensen

Papers

Mathematical problems of modeling stochastic nonlinear dynamic systems

A globally stable linear attitude regulator

Random Signals and Systems

A Priori Open Loop Optimal Control of Continuous Time Stochastic Systems

Balakrishnan's white noise model versus the Wiener process model