1,016 research outputs found

    Episodic Learning with Control Lyapunov Functions for Uncertain Robotic Systems

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    Many modern nonlinear control methods aim to endow systems with guaranteed properties, such as stability or safety, and have been successfully applied to the domain of robotics. However, model uncertainty remains a persistent challenge, weakening theoretical guarantees and causing implementation failures on physical systems. This paper develops a machine learning framework centered around Control Lyapunov Functions (CLFs) to adapt to parametric uncertainty and unmodeled dynamics in general robotic systems. Our proposed method proceeds by iteratively updating estimates of Lyapunov function derivatives and improving controllers, ultimately yielding a stabilizing quadratic program model-based controller. We validate our approach on a planar Segway simulation, demonstrating substantial performance improvements by iteratively refining on a base model-free controller

    Towards Robust Data-Driven Control Synthesis for Nonlinear Systems with Actuation Uncertainty

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    Modern nonlinear control theory seeks to endow systems with properties such as stability and safety, and has been deployed successfully across various domains. Despite this success, model uncertainty remains a significant challenge in ensuring that model-based controllers transfer to real world systems. This paper develops a data-driven approach to robust control synthesis in the presence of model uncertainty using Control Certificate Functions (CCFs), resulting in a convex optimization based controller for achieving properties like stability and safety. An important benefit of our framework is nuanced data-dependent guarantees, which in principle can yield sample-efficient data collection approaches that need not fully determine the input-to-state relationship. This work serves as a starting point for addressing important questions at the intersection of nonlinear control theory and non-parametric learning, both theoretical and in application. We validate the proposed method in simulation with an inverted pendulum in multiple experimental configurations

    Bayesian Nonparametric Adaptive Control using Gaussian Processes

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    This technical report is a preprint of an article submitted to a journal.Most current Model Reference Adaptive Control (MRAC) methods rely on parametric adaptive elements, in which the number of parameters of the adaptive element are fixed a priori, often through expert judgment. An example of such an adaptive element are Radial Basis Function Networks (RBFNs), with RBF centers pre-allocated based on the expected operating domain. If the system operates outside of the expected operating domain, this adaptive element can become non-effective in capturing and canceling the uncertainty, thus rendering the adaptive controller only semi-global in nature. This paper investigates a Gaussian Process (GP) based Bayesian MRAC architecture (GP-MRAC), which leverages the power and flexibility of GP Bayesian nonparametric models of uncertainty. GP-MRAC does not require the centers to be preallocated, can inherently handle measurement noise, and enables MRAC to handle a broader set of uncertainties, including those that are defined as distributions over functions. We use stochastic stability arguments to show that GP-MRAC guarantees good closed loop performance with no prior domain knowledge of the uncertainty. Online implementable GP inference methods are compared in numerical simulations against RBFN-MRAC with preallocated centers and are shown to provide better tracking and improved long-term learning.This research was supported in part by ONR MURI Grant N000141110688 and NSF grant ECS #0846750
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