Data-driven methods for statistical verification of uncertain nonlinear systems

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2018.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 277-290).Due to the increasing complexity of autonomous, adaptive, and nonlinear systems, engineers commonly rely upon statistical techniques to verify that the closed-loop system satisfies specified performance requirements at all possible operating conditions. However, these techniques require a large number of simulations or experiments to exhaustively search the set of possible parametric uncertainties for conditions that lead to failure. This work focuses on resource-constrained applications, such as preliminary control system design or experimental testing, which cannot rely upon exhaustive search to analyze the robustness of the closed-loop system to those requirements. This thesis develops novel statistical verification frameworks that combine data-driven statistical learning techniques and control system verification. First, two frameworks are introduced for verification of deterministic systems with binary and non-binary evaluations of each trajectory's robustness. These frameworks implement machine learning models to learn and predict the satisfaction of the requirements over the entire set of possible parameters from a small set of simulations or experiments. In order to maximize prediction accuracy, closed-loop verification techniques are developed to iteratively select parameter settings for subsequent tests according to their expected improvement of the predictions. Second, extensions of the deterministic verification frameworks redevelop these procedures for stochastic systems and these new stochastic frameworks achieve similar improvements. Lastly, the thesis details a method for transferring information between simulators or from simulators to experiments. Moreover, this method is introduced as part of a new failure-adverse closed-loop verification framework, which is shown to successfully minimize the number of failures during experimental verification without undue conservativeness. Ultimately, these data-driven verification frameworks provide principled approaches for efficient verification of nonlinear systems at all stages in the control system development cycle.by John Francis Quindlen.Ph. D

Output feedback concurrent learning model reference adaptive control

Concurrent learning model reference adaptive control has recently been shown to guarantee simultaneous state tracking and parameter estimation error convergence to zero without requiring the restrictive persistency of excitation condition of other adaptive methods. This simultaneous convergence drastically improves the transient performance of the adaptive system since the true model is learned, but prior results were limited to systems with full state feedback. This paper presents an output feedback form of the concurrent learning controller for a novel extension to partial state feedback systems. The approach modifies a baseline LQG/LTR adaptive law with a recorded data stack of output and state estimate vectors. This maintains the guaranteed stability and boundedness of the baseline adaptive method, while improving output tracking error response. Simulations of exible aircraft dynamics demonstrate the improvement of the concurrent learning system over a baseline output feedback adaptive method

Machine Learning for Efficient Sampling-Based Algorithms in Robust Multi-Agent Planning Under Uncertainty

Robust multi-agent planning algorithms have been developed to assign tasks to cooperative teams of robots operating under various uncertainties. Often, it is difficult to evaluate the robustness of potential task assignments analytically, so sampling-based approximations are used instead. In many applications, not only are sampling-based approximations the only solution, but these samples are computationally-burdensome to obtain. This paper presents a machine learning procedure for sampling-based approximations that actively selects samples in order to maximize the accuracy of the approximation with a limited number of samples. Gaussian process regression models are constructed from a small set of training samples and used to approximate the robustness evaluation. Active learning is then used to iteratively select samples that most improve this evaluation. Three example problems demonstrate that the new procedure achieves a similar level of accuracy as the existing sample-inefficient procedures, but with a significant reduction in the number of samples

Region-of-convergence estimation for learning-based adaptive controllers

Recent learning-based extensions to popular adaptive control procedures offer improved convergence, but at the cost of increased complexity. This complexity makes it difficult to analytically compute level sets that bound the system response. These level sets can be combined with the a priori known Lyapunov function for such systems to provide barrier certificates, verifying the safety of the system to maximum allowable error limits. This paper presents a complementary automated procedure for computing invariant level sets offline using simulation data. These level sets encompass combinations of safe initial conditions and parameters that will not cause the adaptive system's response to exceed constraints. First, conditions for the complete set of safe initial states and parameters, known as the region-of-convergence, are established. These conditions, coupled with the known Lyapunov functions describing the adaptation, are used to form an optimization procedure to construct verifiable level sets for the system response. These levels sets thus provide barrier certificates for safety and conservatively estimate the complete regionof-convergence. Lastly, the procedure is demonstrated on an adaptive control system