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Affine Abstraction of Nonlinear Systems with Applications to Active Model Discrimination

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This work considers the design of separating input signals in order to discriminate among a finite number of uncertain nonlinear models. Each nonlinear model corresponds to a system operating mode,

This work considers the design of separating input signals in order to discriminate among a finite number of uncertain nonlinear models. Each nonlinear model corresponds to a system operating mode, unobserved intents of other drivers or robots, or to fault types or attack strategies, etc., and the separating inputs are designed such that the output trajectories of all the nonlinear models are guaranteed to be distinguishable from each other under any realization of uncertainties in the initial condition, model discrepancies or noise. I propose a two-step approach. First, using an optimization-based approach, we over-approximate nonlinear dynamics by uncertain affine models, as abstractions that preserve all its system behaviors such that any discrimination guarantees for the affine abstraction also hold for the original nonlinear system. Then, I propose a novel solution in the form of a mixed-integer linear program (MILP) to the active model discrimination problem for uncertain affine models, which includes the affine abstraction and thus, the nonlinear models. Finally, I demonstrate the effectiveness of our approach for identifying the intention of other vehicles in a highway lane changing scenario. For the abstraction, I explore two approaches. In the first approach, I construct the bounding planes using a Mixed-Integer Nonlinear Problem (MINLP) formulation of the given system with appropriately designed constraints. For the second approach, I solve a linear programming (LP) problem that over-approximates the nonlinear function at only the grid points of a mesh with a given resolution and then accounting for the entire domain via an appropriate correction term. To achieve a desired approximation accuracy, we also iteratively subdivide the domain into subregions. This method applies to nonlinear functions with different degrees of smoothness, including Lipschitz continuous functions, and improves on existing approaches by enabling the use of tighter bounds. Finally, we compare the effectiveness of this approach with the existing optimization-based methods in simulation and illustrate its applicability for estimator design.

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Date Created
  • 2018

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Modeling and H-Infinity Loop Shaping Control of a Vertical Takeoff and Landing Drone

Description

VTOL drones were designed and built at the beginning of the 20th century for military applications due to easy take-off and landing operations. Many companies like Lockheed, Convair, NASA and

VTOL drones were designed and built at the beginning of the 20th century for military applications due to easy take-off and landing operations. Many companies like Lockheed, Convair, NASA and Bell Labs built their own aircrafts but only a few from them came in to the market. Usually, flight automation starts from first principles modeling which helps in the controller design and dynamic analysis of the system.

In this project, a VTOL drone with a shape similar to a Convair XFY-1 is studied and the primary focus is stabilizing and controlling the flight path of the drone in
its hover and horizontal flying modes. The model of the plane is obtained using first principles modeling and controllers are designed to stabilize the yaw, pitch and roll rotational motions.

The plane is modeled for its yaw, pitch and roll rotational motions. Subsequently, the rotational dynamics of the system are linearized about the hover flying mode, hover to horizontal flying mode, horizontal flying mode, horizontal to hover flying mode for ease of implementation of linear control design techniques. The controllers are designed based on an H∞ loop shaping procedure and the results are verified on the actual nonlinear model for the stability of the closed loop system about hover flying, hover to horizontal transition flying, horizontal flying, horizontal to hover transition flying. An experiment is conducted to study the dynamics of the motor by recording the PWM input to the electronic speed controller as input and the rotational speed of the motor as output. A theoretical study is also done to study the thrust generated by the propellers for lift, slipstream velocity analysis, torques acting on the system for various thrust profiles.

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Date Created
  • 2018