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Prerequisites: Basic course in Linear Systems/Control Systems/Dynamics or permission of the instructor. Objectives: To learn about concepts and advances in estimation theory and relate them to modern dynamic systems found in mechanical and aerospace disciplines. Emphasis will be on modeling of physical problems (aerospace, robotics) into mathematical terms.(More)
The stationary Fokker-Planck Equation (FPE) is solved for nonlinear dynamic systems using a local numerical technique based on the meshless Partition of Unity Finite Element Method (PUFEM). The method is applied to the FPE for two-dimensional dynamical systems , and argued to be an excellent candidate for higher dimensional systems and the transient(More)
In this paper a novel approach is developed for relative state estimation of spacecraft flying in formation. The approach uses information from an optical sensor to provide multiple line-of-sight vectors from one spacecraft to another. The line-of-sight measurements are coupled with gyro measurements and dynamical models in an extended Kalman filter to(More)
A new family of orientation parameters derived from the Euler parameters is presented. They are found by a general stereographic projection of the Euler parameter constraint surface, a four-dimensional unit sphere, onto a three-dimensional hyperplane. The resulting set of three stereographic parameters have a low degree polynomial non-linearity in the(More)
In this paper an optimal solution to the problem of determining both vehicle attitude and position using line-of-sight measurements is presented. The new algorithm is derived from a generalized predictive filter for nonlinear systems. This uses a one time-step ahead approach to propagate a simple kinematics model for attitude and position determination. The(More)
Introduction E IGENSTRUCTURE assignment algorithms are widely used to design control systems. Most of the available eigenstructure assignment algorithms assign all of the eigenvalues to the desired values. The eigenstructureassignmentalgorithmcan be divided into two groups, that is, the null space approach and Sylvester equation approach.The null space(More)
The optimal control of nonlinear stochastic systems is considered in this paper. The central role played by the Fokker-Planck-Kolmogorov equation in the stochastic control problem is shown under the assumption of asymptotic stability. A computational approach for the problem is devised based on policy iteration/ successive approximations, and a finite(More)
A semianalytic partition of unity finite element method (PUFEM) is presented to solve the transient Fokker-Planck equation (FPE) for high-dimensional nonlinear dynamical systems. Meshless spatial discretization of the PUFEM is employed to develop linear ordinary differential equations for the time varying coefficients of the local shape functions. A(More)
Autonomous in-flight aerial refueling is an important capability for the future deployment of unmanned aerial vehicles, because they will likely be ferried in flight to overseas theaters of operation instead of being shipped unassembled in containers. A reliable sensor, capable of providing accurate relative position measurements of sufficient bandwidth, is(More)
In this paper we generalize some previous results on attitude representations using Cayley transforms. First, we s h o w that proper orthogonal matrices, that naturally represent rotations, can be generated by a form of \conformal" analytic mappings in the space of matrices. Using a natural parallelism between the elements of the complex plane and the real(More)