J.A. Fax

Bio: J.A. Fax is an academic researcher from California Institute of Technology. The author has contributed to research in topics: Optimal control & Affine connection. The author has an hindex of 2, co-authored 3 publications receiving 11 citations.

Finite-horizon optimal control and stabilization of time-scalable systems

Abstract: We consider the optimal control of time-scalable systems. The time-scaling property is shown to convert the PDE associated with the Hamilton-Jacobi-Bellman (HJB) equation to a purely spatial PDE. Solution of this PDE yields the value function at a fixed time, and that solution can be scaled to find the value function at any point in time. Furthermore, in certain cases the unscaled control law stabilizes the system, and the unscaled value function acts as a Lyapunov function for that system. The PDE is solved for the well-known example of the nonholonomic integrator.

Robustness analysis of accelerometry using an electrostatically suspended gyroscope

Abstract: The electrostatically suspended gyroscope (ESG) is a two-axis inertial orientation sensor manufactured by Boeing and currently in use on US Navy submarines. The additional ability of the ESG to act as an accelerometer is well known, but extraction of precision acceleration measurements from an ESG has not been achieved. The major obstacles to precision accelerometry are the nonlinear dynamics of the ESG rotor and parametric variation of the ESG electronics. We derive a model for the ESG dynamics with an eye toward efficient representation of the uncertainties in the model. We represent the model uncertainties and nonlinearities in a framework amenable to /spl mu/-analysis and analyze ESG accelerometer precision using /spl mu/-analysis tools. Finally, we discuss the implementation of a digital ESG control architecture for use in ESG system identification and testing of suspension control and accelerometer algorithms.

Optimal control of affine connection control systems: a variational approach

Abstract: We investigate the optimal control of affine connection control systems. The formalism of the affine connection can be used to describe geometrically the dynamics of mechanical systems, including those with nonholonomic constraints. In the standard variational approach to such problems, one converts an n-dimensional second-order system into a 2n-dimensional first-order system, and uses these equations as constraints on the optimization. An alternative approach, which we develop in this paper, is to include the system dynamics as second-order constraints of the optimization, and optimize relative to variations in the configuration space. Using the affine connection, its associated tensors, and the notion of covariant differentiation, we show how variations in the configuration space induce variations in the tangent space. In this setting, we derive second-order equations having a geometric formulation parallel to that of the system dynamics. They also specialize to results found in the literature.

Solutions of the optimal feedback control problem using Hamiltonian dynamics and generating functions

Abstract: We show that the optimal cost function that satisfies the Hamilton-Jacobi-Bellman (HJB) equation is a generating function for a class of canonical transformations for the Hamiltonian dynamical system defined by the necessary conditions for optimality. This result allows us to circumvent the final time singularity in the HJB equation for a finite time problem, and allows us to analytically construct a nonlinear optimal feedback control and cost function that satisfies the HJB equation for a large class of dynamical systems. It also establishes that the optimal cost function can be computed from a large class of solutions to the Hamilton-Jacobi (HJ) equation, many of which do not have singular boundary conditions at the terminal state.

Initial levitation of an electrostatic bearing system without bias

Abstract: The force analysis of a three-axis electrostatic bearing supporting a spherical rotor shows that classical linear control using linearization by a fixed bias necessitates the supporting lands due to highly nonlinear and coupled nature of electrostatic bearings. This paper proposes a suspension control without voltage bias to achieve a steady levitation of the rotor over the entire housing orientations for a class of electrostatic bearings without supports. A nonlinear controller which minimizes the cross-axis coupling is designed using a nonlinear model and feedback linearization techniques. A linear controller is then utilized for this linearized plant to stabilize the closed-loop system. The performance of the proposed nonlinear suspension control system is experimentally investigated on a three-degree freedom electrostatic bearing in the absence of supporting lands. The experimental results demonstrate that the rotor lift in an arbitrary orientation is realized with desired dynamic performance and global stability.

The Hamilton -Jacobi theory for solving optimal feedback control problems with general boundary conditions.

Abstract: THE HAMILTON-JACOBI THEORY FOR SOLVING OPTIMAL FEEDBACK CONTROL PROBLEMS WITH GENERAL BOUNDARY CONDITIONS