Neural Lyapunov Control

We propose new methods for learning control policies and neural network Lyapunov functions for nonlinear control problems, with provable guarantee of stability. The framework consists of a learner that attempts to find the control and Lyapunov functions, and a falsifier that finds counterexamples to quickly guide the learner towards solutions. The procedure terminates when no counterexample is found by the falsifier, in which case the controlled nonlinear system is provably stable. The approach significantly simplifies the process of Lyapunov control design, provides end-to-end correctness guarantee, and can obtain much larger regions of attraction than existing methods such as LQR and SOS/SDP. We show experiments on how the new methods obtain high-quality solutions for challenging control problems.Comment: NeurIPS 201

Linear Parameter-Varying Control of a Ducted Fan Engine

Parameter-dependent control techniques are applied to a vectored thrust, ducted fan engine. The synthesis technique is based on the solution of Linear Matrix Inequalities and produces a controller which achieves specified performance against the worst-case time variation of measurable parameters entering the plant in a linear fractional manner. Thus the plant can have widely varying dynamics over the operating range. The controller designed performs extremely well, and is compared to an ℋ∞ controller

Receding horizon control of vectored thrust flight experiment

Abstract: The application of a constrained receding horizon control technique to stabilise an indoor vectored-thrust flight experiment, known as the Caltech ducted fan, is given. The receding horizon control problem is formulated as a constrained optimal control problem and solved in real time with an efficient, computational method that combines nonlinear control theory, B-spline basis functions, and nonlinear programming. Characteristic issues, including non-zero computational times, convergence properties, choice of horizon length and terminal cost are discussed. The study validates the applicability of real-time receding horizon control for constrained systems with fast dynamics

The Whirling Blade and the Steaming Cauldron

Ths dissertation applies recent theoretical developments in control to two practical examples. The first example is control of the primary circuit of a pressurized water nuclear reactor. This is an interesting example because the plant is complex and its dynamics vary greatly over the operating range of interest. The second example is a thrust-vectored ducted fan engine, a nonlinear flight control experiment at Caltech. The main part of this dissertation is the application of linear parameter-dependent control techniques to the examples. The synthesis technique is based on the solution of linear matrix inequalities (LMIs) and produces a controller whch acheves specified performance against the worst-case time variation of measurable parameters entering the plant in a linear fractional manner. Thus the plant can have widely varying dynamics over the operating range, a quality possessed by both examples. The controllers designed with these methods perform extremely well and are compared to H∞, gain-scheduled, and nonlinear controllers. Additionally, an in-depth examination of the model of the ducted fan is performed, including system identification. From this work, we proceed to apply various techniques to examine what they can tell us in the context of a practical example. The primary technique is LMI-based model validation. The contribution ths dissertation makes is to show that parameter-dependent control techniques can be applied with great effectiveness to practical applications. Moreover, the trade-off between modelling and controller performance is examined in some detail. Finally, we demonstrate the applicability of recent model validation techruques in practice, and discuss stabilizability issues

Modeling and flight testing of differential thrust and thrust vectoring on a small UAV

The primary objectives of this research are to mathematically model the propulsion forces applied to the aircraft during nominal, differential thrust, and thrust vectored flight configurations, and verify this modeling through simulation and flight testing experiments. This thesis outlines the modeling process, simulator development, design, and implementation of a propulsion assisted control system for the WVU Flight Control Systems Lab (FCSL) research aircraft. Differential thrust and thrust vectoring introduce additional propulsive terms in the aircraft force equations that are not present when the thrust line passes through the center of gravity. These additional forces were modeled and incorporated into a simulator of the research aircraft. The effects from differential thrust were small and difficult to quantify. The thrust vectoring effects were also found to be small with the elevator having significantly more pitch control over the vectored motors at the simulated flight conditions.;Differential thrust was implemented using the on-board computer to command a different thrust level to each motor. The desired thrust differential was programed into a flight scheme based on simulation data, and activated during flight via a control switch on the transmitter. The thrust vectoring mechanism was designed using SolidWorksRTM, built and tested outside of the aircraft, and finally incorporated into the aircraft. A high torque servo was used to rotate the motor mounting bar and vector the motors to a desired deflection. Utilizing this mechanism, the thrust vectoring was flight tested, mimicking scenarios tested in simulation. The signal to noise ratio was very low, making it difficult to identify the small changes in the aircraft parameters caused by the vectored thrust

Receding horizon control of vectored thrust flight experiment

Abstract: The application of a constrained receding horizon control technique to stabilise an indoor vectored-thrust flight experiment, known as the Caltech ducted fan, is given. The receding horizon control problem is formulated as a constrained optimal control problem and solved in real time with an efficient, computational method that combines nonlinear control theory, B-spline basis functions, and nonlinear programming. Characteristic issues, including non-zero computational times, convergence properties, choice of horizon length and terminal cost are discussed. The study validates the applicability of real-time receding horizon control for constrained systems with fast dynamics