Episodic Learning with Control Lyapunov Functions for Uncertain Robotic Systems

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

Parameter estimation in softmax decision-making models with linear objective functions

With an eye towards human-centered automation, we contribute to the development of a systematic means to infer features of human decision-making from behavioral data. Motivated by the common use of softmax selection in models of human decision-making, we study the maximum likelihood parameter estimation problem for softmax decision-making models with linear objective functions. We present conditions under which the likelihood function is convex. These allow us to provide sufficient conditions for convergence of the resulting maximum likelihood estimator and to construct its asymptotic distribution. In the case of models with nonlinear objective functions, we show how the estimator can be applied by linearizing about a nominal parameter value. We apply the estimator to fit the stochastic UCL (Upper Credible Limit) model of human decision-making to human subject data. We show statistically significant differences in behavior across related, but distinct, tasks.Comment: In pres

Multi-Parametric Extremum Seeking-based Auto-Tuning for Robust Input-Output Linearization Control

We study in this paper the problem of iterative feedback gains tuning for a class of nonlinear systems. We consider Input-Output linearizable nonlinear systems with additive uncertainties. We first design a nominal Input-Output linearization-based controller that ensures global uniform boundedness of the output tracking error dynamics. Then, we complement the robust controller with a model-free multi-parametric extremum seeking (MES) control to iteratively auto-tune the feedback gains. We analyze the stability of the whole controller, i.e. robust nonlinear controller plus model-free learning algorithm. We use numerical tests to demonstrate the performance of this method on a mechatronics example.Comment: To appear at the IEEE CDC 201

Control Regularization for Reduced Variance Reinforcement Learning

Dealing with high variance is a significant challenge in model-free reinforcement learning (RL). Existing methods are unreliable, exhibiting high variance in performance from run to run using different initializations/seeds. Focusing on problems arising in continuous control, we propose a functional regularization approach to augmenting model-free RL. In particular, we regularize the behavior of the deep policy to be similar to a policy prior, i.e., we regularize in function space. We show that functional regularization yields a bias-variance trade-off, and propose an adaptive tuning strategy to optimize this trade-off. When the policy prior has control-theoretic stability guarantees, we further show that this regularization approximately preserves those stability guarantees throughout learning. We validate our approach empirically on a range of settings, and demonstrate significantly reduced variance, guaranteed dynamic stability, and more efficient learning than deep RL alone.Comment: Appearing in ICML 201