arXiv subjects

Aditya Gahlawat

Publications and source records attributed to Aditya Gahlawat.

25 records · Page 2Linked to original sources

arXiv2020

$\mathcal{L}_1$-$\mathcal{GP}$: $\mathcal{L}_1$ Adaptive Control with Bayesian Learning

We present $\mathcal{L}_1$-$\mathcal{GP}$, an architecture based on $\mathcal{L}_1$ adaptive control and Gaussian Process Regression (GPR) for safe simultaneous control and learning. On one hand, the $\mathcal{L}_1$ adaptive control provides stability and transient performance guarantees, which allows for GPR to efficiently and safely learn the uncertain dynamics. On the other hand, the learned dynamics can be conveniently incorporated into the $\mathcal{L}_1$ control architecture without sacrificing robustness and tracking performance. Subsequently, the learned dynamics can lead to less conservative designs for performance/robustness tradeoff. We illustrate the efficacy of the proposed architecture via numerical simulations.

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arXiv2020

Learning Probabilistic Intersection Traffic Models for Trajectory Prediction

Autonomous agents must be able to safely interact with other vehicles to integrate into urban environments. The safety of these agents is dependent on their ability to predict collisions with other vehicles' future trajectories for replanning and collision avoidance. The information needed to predict collisions can be learned from previously observed vehicle trajectories in a specific environment, generating a traffic model. The learned traffic model can then be incorporated as prior knowledge into any trajectory estimation method being used in this environment. This work presents a Gaussian process based probabilistic traffic model that is used to quantify vehicle behaviors in an intersection. The Gaussian process model provides estimates for the average vehicle trajectory, while also capturing the variance between the different paths a vehicle may take in the intersection. The method is demonstrated on a set of time-series position trajectories. These trajectories are reconstructed by removing object recognition errors and missed frames that may occur due to data source processing. To create the intersection traffic model, the reconstructed trajectories are clustered based on their source and destination lanes. For each cluster, a Gaussian process model is created to capture the average behavior and the variance of the cluster. To show the applicability of the Gaussian model, the test trajectories are classified with only partial observations. Performance is quantified by the number of observations required to correctly classify the vehicle trajectory. Both the intersection traffic modeling computations and the classification procedure are timed. These times are presented as results and demonstrate that the model can be constructed in a reasonable amount of time and the classification procedure can be used for online applications.

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arXiv2018

Learning to Communicate: A Machine Learning Framework for Heterogeneous Multi-Agent Robotic Systems

We present a machine learning framework for multi-agent systems to learn both the optimal policy for maximizing the rewards and the encoding of the high dimensional visual observation. The encoding is useful for sharing local visual observations with other agents under communication resource constraints. The actor-encoder encodes the raw images and chooses an action based on local observations and messages sent by the other agents. The machine learning agent generates not only an actuator command to the physical device, but also a communication message to the other agents. We formulate a reinforcement learning problem, which extends the action space to consider the communication action as well. The feasibility of the reinforcement learning framework is demonstrated using a 3D simulation environment with two collaborating agents. The environment provides realistic visual observations to be used and shared between the two agents.

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arXiv2017

A Semi-Definite Programming Approach to Stability Analysis of Linear Partial Differential Equations

We consider the stability analysis of a large class of linear 1-D PDEs with polynomial data. This class of PDEs contains, as examples, parabolic and hyperbolic PDEs, PDEs with boundary feedback and systems of in-domain/boundary coupled PDEs. Our approach is Lyapunov based which allows us to reduce the stability problem to the verification of integral inequalities on the subspaces of Hilbert spaces. Then, using fundamental theorem of calculus and Green's theorem, we construct a polynomial problem to verify the integral inequalities. Constraining the solution of the polynomial problem to belong to the set of sum-of-squares polynomials subject to affine constraints allows us to use semi-definite programming to algorithmically construct Lyapunov certificates of stability for the systems under consideration. We also provide numerical results of the application of the proposed method on different types of PDEs.

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arXiv2016

A Convex Sum-of-Squares Approach to Analysis, State Feedback and Output Feedback Control of Parabolic PDEs

We present an optimization-based framework for analysis and control of linear parabolic partial differential equations (PDEs) with spatially varying coefficients without discretization or numerical approximation. For controller synthesis, we consider both full-state feedback and point observation (output feedback). The input occurs at the boundary (point actuation). We use positive matrices to parameterize positive Lyapunov functions and polynomials to parameterize controller and observer gains. We use duality and an invertible state-variable transformation to convexify the controller synthesis problem. Finally, we combine our synthesis condition with the Luenberger observer framework to express the output feedback controller synthesis problem as a set of LMI/SDP constraints. We perform an extensive set of numerical experiments to demonstrate accuracy of the conditions and to prove necessity of the Lyapunov structures chosen. We provide numerical and analytical comparisons with alternative approaches to control including Sturm Liouville theory and backstepping. Finally we use numerical tests to show that the method retains its accuracy for alternative boundary conditions.

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arXiv2015

Output Feedback Control of Inhomogeneous Parabolic PDEs with Point Actuation and Point Measurement using SOS and Semi-Separable Kernels

In this paper we use SOS and SDP to design output feedback controllers for a class of one-dimensional parabolic partial differential equations with point measurements and point actuation. Our approach is based on the use of SOS to search for positive quadratic Lyapunov functions, controllers and observers. These Lyapunov functions, controllers and observers are parameterized by linear operators which are defined by SOS polynomials. The main result of the paper is the development of an improved class of observer-based controllers and evidence which indicates that when the system is controllable and observable, these methods will find a observer-based controller for sufficiently high polynomial degree (similar to well-known results from backstepping).

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arXiv2014

A Convex Approach to Output Feedback Control of Parabolic PDEs Using Sum-of-Squares

In this paper we use optimization-based methods to design output-feedback controllers for a class of one-dimensional parabolic partial differential equations. The output may be distributed or point-measurements. The input may be distributed or boundary actuation. We use Lyapunov operators, duality, and the Luenberger observer framework to reformulate the synthesis problem as a convex optimization problem expressed as a set of Linear-Operator-Inequalities (LOIs). We then show how feasibility of these LOIs may be tested using Semidefinite Programming (SDP) and the Sum-of-Squares methodology.

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