Controller Synthesis for Discrete-time Hybrid Polynomial Systems via Occupation Measures

Han, Weiqiao; Tedrake, Russ

doi:10.1109/icra.2019.8793881

Cited by 4 publications

(3 citation statements)

References 62 publications

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“…The computational complexity of these methods grows exponentially with respect to the number of time steps. Lyapunov-based approaches [43]- [45] and occupation measure approaches [46], [47] do not depend on the number of time steps, but are quite conservative and may not always find solutions. Sampling-based methods [15], [48] suffer from the issue of scalability.…”

Section: Related Workmentioning

confidence: 99%

Local Trajectory Stabilization for Dexterous Manipulation via Piecewise Affine Approximations

Han

Tedrake

2019

Preprint

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We propose a model-based approach to design feedback policies for dexterous robotic manipulation. The manipulation problem is formulated as reaching the target region from an initial state for some non-smooth nonlinear system. First, we use trajectory optimization to find a feasible trajectory. Next, we characterize the local multi-contact dynamics around the trajectory as a piecewise affine system, and build a funnel around the linearization of the nominal trajectory using polytopes. We prove that the feedback controller at the vicinity of the linearization is guaranteed to drive the nonlinear system to the target region. During online execution, we solve linear programs to track the system trajectory. We validate the algorithm on hardware, showing that even under large external disturbances, the controller is able to accomplish the task.

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Section: Related Workmentioning

confidence: 99%

Local Trajectory Stabilization for Dexterous Manipulation via Piecewise Affine Approximations

Han

Tedrake

2019

Preprint

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“…In [14], occupation measure based feedback controllers are designed to maximize the backward reachable sets of control-affine polynomial systems. This technique, in [15], is extended to design stabilizing controllers for hybrid polynomial systems.…”

Section: Introductionmentioning

confidence: 99%

Sequential Chance Optimization For Flow-Tube Based Control Of Probabilistic Nonlinear Systems

Jasour¹,

Williams²

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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In this paper, we address the problem of closed-loop control of nonlinear dynamical systems subjected to probabilistic uncertainties. More precisely, we design time-varying polynomial feedback controllers to follow the given nominal trajectory and also, for safety purposes, remain in the tube around the nominal trajectory, despite all uncertainties. We formulate this problem as a chance optimization problem where we maximize the probability of achieving control objectives. To address control problems with long planning horizons, we formulate the single large chance optimization problem as a sequence of smaller chance optimization problems. To solve the obtained chance optimization problems, we leverage the theory of measures and moments and obtain convex relaxations in the form of semidefinite programs. We provide numerical examples on stabilizing controller design and motion planning of uncertain nonlinear systems to illustrate the performance of the proposed approach.

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“…The control and reachability set programs in [119,120,124] define measures ρ e supported over the guard M + (S e ) for each transition e ∈ E. For subsets A ⊂ [0, T ], C e ⊂ S e and an initial condition x 0 , the counting measure ρ e records the number of times the trajectory, starting from location src(e), enters the patch C e of the guard S e with…”

Section: Measures For Hybrid Systemsmentioning

confidence: 99%

Safety quantification for nonlinear and time-delay systems using occupation measures

Miller

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To my parents, Wayne and Debbie. i I would like to begin by thanking my parents, Debbie Mitzner and Wayne Miller, for all of their advice and support. Wayne Miller voluntarily acted as a copy-editor for all of my publications, including this thesis. My next thanks go to my advisor, Mario Sznaier, at the Robust Systems Laboratory in Northeastern. I met Mario in Fall of 2016 as a BS/MS student, when I asked him for an override in order to attend his Spring 2017 special topics course in Big Data, Sparsity, and Control. During the opening lecture, he gave a survey of sparse methods in robust regression, computer vision, and system identification. At the close of this first lecture, I asked him how I could learn more and join his lab, and he responded by giving me the door code. I officially joined the lab as a PhD student in Fall of 2018, and then acted as a teaching assistant for his Sparsity course in 2019, 2021, and 2022. Mario introduced me to topics such as rank-minimization, sparsity, Frank-Wolfe methods, measures, polynomial optimization, and data-driven control. Mario's wealth of experience allows him to draw connections between different disciplines and rapidly determine if ideas have promise, have been done before, and/or are marginal/intractable. His discussions with myself and other members of the laboratory help us refine our approaches and experiments, providing guidance in sometimes unexpected ways, and leading us into new directions of research. I would like to thank Octavia Camps (co-director of the Robust Systems Laboratory) for the discussions and application of my methods towards computer vision. I would like to thank all of my colleagues in the Robust Systems Lab over the course of my ∼6 years there. Specific recognition goes to my collaborators Tianyu Dai, Rajiv Singh, Jian Zheng, Armand Comas, Biel Roig-Solvas, and Zachary Walker-Liang. There are many other students and professors at Northeastern (outside the Robust Systems Laboratory) to thank. Students in research include

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Controller Synthesis for Discrete-time Hybrid Polynomial Systems via Occupation Measures

Cited by 4 publications

References 62 publications

Local Trajectory Stabilization for Dexterous Manipulation via Piecewise Affine Approximations

Local Trajectory Stabilization for Dexterous Manipulation via Piecewise Affine Approximations

Sequential Chance Optimization For Flow-Tube Based Control Of Probabilistic Nonlinear Systems

Safety quantification for nonlinear and time-delay systems using occupation measures

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