Abstract: Systems and methods for solving multivariate state-estimation problems in accordance with numerous embodiments of the invention are illustrated. One embodiment includes a method that develops a characteristic function associated with a state-estimation problem. The method collects, for a set including at least one time point, from a sensory instrument, a set of measurements reflecting the state corresponding to the most recent time point. The method derives, from the set of measurements, new parameters corresponding to the state of the system at the most recent time point. The method updates a hyperplane arrangement based on the new parameters. The method runs a cell-enumeration algorithm based on the hyperplane arrangement to obtain sign vectors for each cell of the hyperplane arrangement. The method determines, based at least in part on the sign vectors, function parameters for the updated characteristic function, wherein the updated characteristic function includes a linear combination of sign vectors.

Abstract: A vehicle lifting system comprising a mechanism fixedly disposed within a center pillar at the side of a vehicle, for extending out of the pillar and exerting a downward force onto the surface on which the vehicle is positioned. When the force is exerted on the surface, the side of the vehicle is lifted above the surface. A control device is utilized for selectively extending the mechanism out of the pillar and retracting the mechanism back into the pillar.

Abstract: A vehicle lifting system comprising a mechanism fixedly disposed within a center pillar at the side of a vehicle, for extending out of the pillar and exerting a downward force onto the surface on which the vehicle is positioned. When the force is exerted on the surface, the side of the vehicle is lifted above the surface. A control device is utilized for selectively extending the mechanism out of the pillar and retracting the mechanism back into the pillar.

Abstract: An adaptive control system (ACS) uses direct output feedback to control a plant. The ACS uses direct adaptive output feedback control developed for highly uncertain nonlinear systems, that does not rely on state estimation. The approach is also applicable to systems of unknown, but bounded dimension, whose output has known, but otherwise arbitrary relative degree. This includes systems with both parameter uncertainty and unmodeled dynamics. The result is achieved by extending the universal function approximation property of linearly parameterized neural networks to model unknown system dynamics from input/output data. The network weight adaptation rule is derived from Lyapunov stability analysis, and guarantees that the adapted weight errors and the tracking error are bounded.

Abstract: An adaptive control system (ACS) uses direct output feedback to control a plant. The ACS uses direct adaptive output feedback control developed for highly uncertain nonlinear systems, that does not rely on state estimation. The approach is also applicable to systems of unknown, but bounded dimension, whose output has known, but otherwise arbitrary relative degree. This includes systems with both parameter uncertainty and unmodeled dynamics. The result is achieved by extending the universal function approximation property of linearly parameterized neural networks to model unknown system dynamics from input/output data. The network weight adaptation rule is derived from Lyapunov stability analysis, and guarantees that the adapted weight errors and the tracking error are bounded.

Abstract: An adaptive control system (ACS) uses direct output feedback to control a plant. The ACS uses direct adaptive output feedback control developed for highly uncertain nonlinear systems, that does not rely on state estimation. The approach is also applicable to systems of unknown, but bounded dimension, whose output has known, but otherwise arbitrary relative degree. This includes systems with both parameter uncertainty and unmodeled dynamics. The result is achieved by extending the universal function approximation property of linearly parameterized neural networks to model unknown system dynamics from input/output data. The network weight adaptation rule is derived from Lyapunov stability analysis, and guarantees that the adapted weight errors and the tracking error are bounded.

Abstract: An adaptive control system (ACS) uses direct output feedback to control a plant. The ACS uses direct adaptive output feedback control developed for highly uncertain nonlinear systems, that does not rely on state estimation. The approach is also applicable to systems of unknown, but bounded dimension, whose output has known, but otherwise arbitrary relative degree. This includes systems with both parameter uncertainty and unmodeled dynamics. The result is achieved by extending the universal function approximation property of linearly parameterized neural networks to model unknown system dynamics from input/output data. The network weight adaptation rule is derived from Lyapunov stability analysis, and guarantees that the adapted weight errors and the tracking error are bounded.