arXiv subjects

Nikolai Matni

Publications and source records attributed to Nikolai Matni.

At least 109 records · Page 6Linked to original sources

arXiv2020

An Adversarial Objective for Scalable Exploration

Model-based curiosity combines active learning approaches to optimal sampling with the information gain based incentives for exploration presented in the curiosity literature. Existing model-based curiosity methods look to approximate prediction uncertainty with approaches which struggle to scale to many prediction-planning pipelines used in robotics tasks. We address these scalability issues with an adversarial curiosity method minimizing a score given by a discriminator network. This discriminator is optimized jointly with a prediction model and enables our active learning approach to sample sequences of observations and actions which result in predictions considered the least realistic by the discriminator. We demonstrate progressively increasing advantages as compute is restricted of our adversarial curiosity approach over leading model-based exploration strategies in simulated environments. We further demonstrate the ability of our adversarial curiosity method to scale to a robotic manipulation prediction-planning pipeline where we improve sample efficiency and prediction performance for a domain transfer problem.

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arXiv2020

Learning Control Barrier Functions from Expert Demonstrations

Inspired by the success of imitation and inverse reinforcement learning in replicating expert behavior through optimal control, we propose a learning based approach to safe controller synthesis based on control barrier functions (CBFs). We consider the setting of a known nonlinear control affine dynamical system and assume that we have access to safe trajectories generated by an expert - a practical example of such a setting would be a kinematic model of a self-driving vehicle with safe trajectories (e.g., trajectories that avoid collisions with obstacles in the environment) generated by a human driver. We then propose and analyze an optimization-based approach to learning a CBF that enjoys provable safety guarantees under suitable Lipschitz smoothness assumptions on the underlying dynamical system. A strength of our approach is that it is agnostic to the parameterization used to represent the CBF, assuming only that the Lipschitz constant of such functions can be efficiently bounded. Furthermore, if the CBF parameterization is convex, then under mild assumptions, so is our learning process. We end with extensive numerical evaluations of our results on both planar and realistic examples, using both random feature and deep neural network parameterizations of the CBF. To the best of our knowledge, these are the first results that learn provably safe control barrier functions from data.

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arXiv2020

Learning Hybrid Control Barrier Functions from Data

Motivated by the lack of systematic tools to obtain safe control laws for hybrid systems, we propose an optimization-based framework for learning certifiably safe control laws from data. In particular, we assume a setting in which the system dynamics are known and in which data exhibiting safe system behavior is available. We propose hybrid control barrier functions for hybrid systems as a means to synthesize safe control inputs. Based on this notion, we present an optimization-based framework to learn such hybrid control barrier functions from data. Importantly, we identify sufficient conditions on the data such that feasibility of the optimization problem ensures correctness of the learned hybrid control barrier functions, and hence the safety of the system. We illustrate our findings in two simulations studies, including a compass gait walker.

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arXiv2020

Robust, Perception Based Control with Quadrotors

Traditionally, controllers and state estimators in robotic systems are designed independently. Controllers are often designed assuming perfect state estimation. However, state estimation methods such as Visual Inertial Odometry (VIO) drift over time and can cause the system to misbehave. While state estimation error can be corrected with the aid of GPS or motion capture, these complementary sensors are not always available or reliable. Recent work has shown that this issue can be dealt with by synthesizing robust controllers using a data-driven characterization of the perception error, and can bound the system's response to state estimation error using a robustness constraint. We investigate the application of this robust perception-based approach to a quadrotor model using VIO for state estimation and demonstrate the benefits and drawbacks of using this technique in simulation and hardware. Additionally, to make tuning easier, we introduce a new cost function to use in the control synthesis which allows one to take an existing controller and "robustify" it. To the best of our knowledge, this is the first robust perception-based controller implemented in real hardware, as well as one utilizing a data-driven perception model. We believe this as an important step towards safe, robust robots that explicitly account for the inherent dependence between perception and control.

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arXiv2020

Learning Stability Certificates from Data

Many existing tools in nonlinear control theory for establishing stability or safety of a dynamical system can be distilled to the construction of a certificate function that guarantees a desired property. However, algorithms for synthesizing certificate functions typically require a closed-form analytical expression of the underlying dynamics, which rules out their use on many modern robotic platforms. To circumvent this issue, we develop algorithms for learning certificate functions only from trajectory data. We establish bounds on the generalization error - the probability that a certificate will not certify a new, unseen trajectory - when learning from trajectories, and we convert such generalization error bounds into global stability guarantees. We demonstrate empirically that certificates for complex dynamics can be efficiently learned, and that the learned certificates can be used for downstream tasks such as adaptive control.

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arXiv2020

Distributed and Localized Model Predictive Control via System Level Synthesis

We present the Distributed and Localized Model Predictive Control (DLMPC) algorithm for large-scale structured linear systems, wherein only local state and model information needs to be exchanged between subsystems for the computation and implementation of control actions. We use the System Level Synthesis (SLS) framework to reformulate the MPC problem as an optimization problem over closed loop system responses, and show that this allows us to naturally impose localized communication constraints between sub-controllers, such that only local state and system model information needs to be exchanged for both computation and implementation of closed loop MPC control policies. In particular, we show that the structure of the resulting optimization problem can be exploited to develop an Alternating Direction Method of Multipliers (ADMM) based algorithm that allows for distributed and localized computation of control decisions. Moreover, our approach can accommodate constraints and objective functions that couple the behavior of different subsystems, so long as the coupled systems are able to communicate directly with each other, allowing for a broader class of MPC problems to be solved via distributed optimization. We conclude with numerical simulations to demonstrate the usefulness of our method, and in particular, we demonstrate that the computational complexity of the subproblems solved by each subsystem in DLMPC is independent of the size of the global system.

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arXiv2020

Robust Closed-loop Model Predictive Control via System Level Synthesis

In this paper, we consider the robust closed-loop model predictive control (MPC) of a linear time-variant (LTV) system with norm bounded disturbances and LTV model uncertainty, wherein a series of constrained optimal control problems (OCPs) are solved. Guaranteeing robust feasibility of these OCPs is challenging due to disturbances perturbing the predicted states, and model uncertainty, both of which can render the closed-loop system unstable. As such, a trade-off between the numerical tractability and conservativeness of the solutions is often required. We use the System Level Synthesis (SLS) framework to reformulate these constrained OCPs over closed-loop system responses, and show that this allows us to transparently account for norm bounded additive disturbances and LTV model uncertainty by computing robust state feedback policies. We further show that by exploiting the underlying linear fractional structure of the resulting robust OCPs, we can significantly reduce the conservativeness of existing SLS-based and tube-MPC-based robust control methods while also improving computational efficiency. We conclude with numerical examples demonstrating the effectiveness of our methods.

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arXiv2020

Explicit Distributed and Localized Model Predictive Control via System Level Synthesis

An explicit Model Predictive Control algorithm for large-scale structured linear systems is presented. We base our results on Distributed and Localized Model Predictive Control (DLMPC), a closed-loop model predictive control scheme based on the System Level Synthesis (SLS) framework wherein only local state and model information needs to be exchanged between subsystems for the computation and implementation of control actions. We provide an explicit solution for each of the subproblems resulting from the distributed MPC scheme. We show that given the separability of the problem, the explicit solution is only divided into three regions per state and input instantiation, making the point location problem very efficient. Moreover, given the locality constraints, the subproblems are of much smaller dimension than the full problem, which significantly reduces the computational overhead of explicit solutions. We conclude with numerical simulations to demonstrate the computational advantages of our method, in which we show a large improvement in runtime per MPC iteration as compared with the results of computing the optimization with a solver online.

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arXiv2020

Robust Performance Guarantees for System Level Synthesis

We generalize the system level synthesis framework to systems defined by bounded causal linear operators, and use this parameterization to make connections between robust system level synthesis and classical results from the robust control literature. In particular, by leveraging results from L1 robust control, we show that necessary and sufficient conditions for robust performance with respect to causal bounded linear uncertainty in the system dynamics can be translated into convex constraints on the system responses. We exploit this connection to show that these conditions naturally allow for the incorporation of delay, sparsity, and locality constraints on the system responses and resulting controller implementation, allowing these methods to be applied to large-scale distributed control problems -- to the best of our knowledge, these are the first such robust performance guarantees for distributed control systems.

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arXiv2020

Sample Complexity of Kalman Filtering for Unknown Systems

In this paper, we consider the task of designing a Kalman Filter (KF) for an unknown and partially observed autonomous linear time invariant system driven by process and sensor noise. To do so, we propose studying the following two step process: first, using system identification tools rooted in subspace methods, we obtain coarse finite-data estimates of the state-space parameters and Kalman gain describing the autonomous system; and second, we use these approximate parameters to design a filter which produces estimates of the system state. We show that when the system identification step produces sufficiently accurate estimates, or when the underlying true KF is sufficiently robust, that a Certainty Equivalent (CE) KF, i.e., one designed using the estimated parameters directly, enjoys provable sub-optimality guarantees. We further show that when these conditions fail, and in particular, when the CE KF is marginally stable (i.e., has eigenvalues very close to the unit circle), that imposing additional robustness constraints on the filter leads to similar sub-optimality guarantees. We further show that with high probability, both the CE and robust filters have mean prediction error bounded by $\tilde O(1/\sqrt{N})$, where $N$ is the number of data points collected in the system identification step. To the best of our knowledge, these are the first end-to-end sample complexity bounds for the Kalman Filtering of an unknown system.

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arXiv2020

PAC Confidence Sets for Deep Neural Networks via Calibrated Prediction

We propose an algorithm combining calibrated prediction and generalization bounds from learning theory to construct confidence sets for deep neural networks with PAC guarantees---i.e., the confidence set for a given input contains the true label with high probability. We demonstrate how our approach can be used to construct PAC confidence sets on ResNet for ImageNet, a visual object tracking model, and a dynamics model for the half-cheetah reinforcement learning problem.

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arXiv2019

Robust Guarantees for Perception-Based Control

Motivated by vision-based control of autonomous vehicles, we consider the problem of controlling a known linear dynamical system for which partial state information, such as vehicle position, is extracted from complex and nonlinear data, such as a camera image. Our approach is to use a learned perception map that predicts some linear function of the state and to design a corresponding safe set and robust controller for the closed loop system with this sensing scheme. We show that under suitable smoothness assumptions on both the perception map and the generative model relating state to complex and nonlinear data, parameters of the safe set can be learned via appropriately dense sampling of the state space. We then prove that the resulting perception-control loop has favorable generalization properties. We illustrate the usefulness of our approach on a synthetic example and on the self-driving car simulation platform CARLA.

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arXiv2019

Efficient Learning of Distributed Linear-Quadratic Controllers

In this work, we propose a robust approach to design distributed controllers for unknown-but-sparse linear and time-invariant systems. By leveraging modern techniques in distributed controller synthesis and structured linear inverse problems as applied to system identification, we show that near-optimal distributed controllers can be learned with sub-linear sample complexity and computed with near-linear time complexity, both measured with respect to the dimension of the system. In particular, we provide sharp end-to-end guarantees on the stability and the performance of the designed distributed controller and prove that for sparse systems, the number of samples needed to guarantee robust and near optimal performance of the designed controller can be significantly smaller than the dimension of the system. Finally, we show that the proposed optimization problem can be solved to global optimality with near-linear time complexity by iteratively solving a series of small quadratic programs.

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arXiv2019

From self-tuning regulators to reinforcement learning and back again

Machine and reinforcement learning (RL) are increasingly being applied to plan and control the behavior of autonomous systems interacting with the physical world. Examples include self-driving vehicles, distributed sensor networks, and agile robots. However, when machine learning is to be applied in these new settings, the algorithms had better come with the same type of reliability, robustness, and safety bounds that are hallmarks of control theory, or failures could be catastrophic. Thus, as learning algorithms are increasingly and more aggressively deployed in safety critical settings, it is imperative that control theorists join the conversation. The goal of this tutorial paper is to provide a starting point for control theorists wishing to work on learning related problems, by covering recent advances bridging learning and control theory, and by placing these results within an appropriate historical context of system identification and adaptive control.

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arXiv2019

A Tutorial on Concentration Bounds for System Identification

We provide a brief tutorial on the use of concentration inequalities as they apply to system identification of state-space parameters of linear time invariant systems, with a focus on the fully observed setting. We draw upon tools from the theories of large-deviations and self-normalized martingales, and provide both data-dependent and independent bounds on the learning rate.

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arXiv2019

Safely Learning to Control the Constrained Linear Quadratic Regulator

We study the constrained linear quadratic regulator with unknown dynamics, addressing the tension between safety and exploration in data-driven control techniques. We present a framework which allows for system identification through persistent excitation, while maintaining safety by guaranteeing the satisfaction of state and input constraints. This framework involves a novel method for synthesizing robust constraint-satisfying feedback controllers, leveraging newly developed tools from system level synthesis. We connect statistical results with cost sub-optimality bounds to give non-asymptotic guarantees on both estimation and controller performance.

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arXiv2019

A System Level Approach to Controller Synthesis

Biological and advanced cyberphysical control systems often have limited, sparse, uncertain, and distributed communication and computing in addition to sensing and actuation. Fortunately, the corresponding plants and performance requirements are also sparse and structured, and this must be exploited to make constrained controller design feasible and tractable. We introduce a new "system level" (SL) approach involving three complementary SL elements. System Level Parameterizations (SLPs) generalize state space and Youla parameterizations of all stabilizing controllers and the responses they achieve, and combine with System Level Constraints (SLCs) to parameterize the largest known class of constrained stabilizing controllers that admit a convex characterization, generalizing quadratic invariance (QI). SLPs also lead to a generalization of detectability and stabilizability, suggesting the existence of a rich separation structure, that when combined with SLCs, is naturally applicable to structurally constrained controllers and systems. We further provide a catalog of useful SLCs, most importantly including sparsity, delay, and locality constraints on both communication and computing internal to the controller, and external system performance. The resulting System Level Synthesis (SLS) problems that arise define the broadest known class of constrained optimal control problems that can be solved using convex programming. An example illustrates how this system level approach can systematically explore tradeoffs in controller performance, robustness, and synthesis/implementation complexity.

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arXiv2019

Learning Sparse Dynamical Systems from a Single Sample Trajectory

This paper addresses the problem of identifying sparse linear time-invariant (LTI) systems from a single sample trajectory generated by the system dynamics. We introduce a Lasso-like estimator for the parameters of the system, taking into account their sparse nature. Assuming that the system is stable, or that it is equipped with an initial stabilizing controller, we provide sharp finite-time guarantees on the accurate recovery of both the sparsity structure and the parameter values of the system. In particular, we show that the proposed estimator can correctly identify the sparsity pattern of the system matrices with high probability, provided that the length of the sample trajectory exceeds a threshold. Furthermore, we show that this threshold scales polynomially in the number of nonzero elements in the system matrices, but logarithmically in the system dimensions --- this improves on existing sample complexity bounds for the sparse system identification problem. We further extend these results to obtain sharp bounds on the $\ell_{\infty}$-norm of the estimation error and show how different properties of the system---such as its stability level and \textit{mutual incoherency}---affect this bound. Finally, an extensive case study on power systems is presented to illustrate the performance of the proposed estimation method.

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