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Benjamin Recht - One of the best experts on this subject based on the ideXlab platform.

  • On the Sample Complexity of the Linear Quadratic Regulator
    Foundations of Computational Mathematics, 2019
    Co-Authors: Sarah Dean, Horia Mania, Nikolai Matni, Benjamin Recht, Stephen Tu
    Abstract:

    This paper addresses the optimal control problem known as the Linear Quadratic Regulator in the case when the dynamics are unknown. We propose a multistage procedure, called Coarse-ID control , that estimates a model from a few experimental trials, estimates the error in that model with respect to the truth, and then designs a controller using both the model and uncertainty estimate. Our technique uses contemporary tools from random matrix theory to bound the error in the estimation procedure. We also employ a recently developed approach to control synthesis called System Level Synthesis that enables robust control design by solving a quasi-convex optimization problem. We provide end-to-end bounds on the relative error in control cost that are optimal in the number of parameters and that highlight salient properties of the system to be controlled such as closed-loop sensitivity and optimal control magnitude. We show experimentally that the Coarse-ID approach enables efficient computation of a stabilizing controller in regimes where simple control schemes that do not take the model uncertainty into account fail to stabilize the true system.

  • ACC - Safely Learning to Control the Constrained Linear Quadratic Regulator
    2019 American Control Conference (ACC), 2019
    Co-Authors: Sarah Dean, Nikolai Matni, Benjamin Recht
    Abstract:

    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.

  • Safely Learning to Control the Constrained Linear Quadratic Regulator
    arXiv: Optimization and Control, 2018
    Co-Authors: Sarah Dean, Nikolai Matni, Benjamin Recht
    Abstract:

    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.

  • regret bounds for robust adaptive control of the Linear Quadratic Regulator
    arXiv: Learning, 2018
    Co-Authors: Sarah Dean, Horia Mania, Nikolai Matni, Benjamin Recht
    Abstract:

    We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown Linear system is controlled subject to Quadratic costs. Leveraging recent developments in the estimation of Linear systems and in robust controller synthesis, we present the first provably polynomial time algorithm that provides high probability guarantees of sub-Linear regret on this problem. We further study the interplay between regret minimization and parameter estimation by proving a lower bound on the expected regret in terms of the exploration schedule used by any algorithm. Finally, we conduct a numerical study comparing our robust adaptive algorithm to other methods from the adaptive LQR literature, and demonstrate the flexibility of our proposed method by extending it to a demand forecasting problem subject to state constraints.

  • regret bounds for robust adaptive control of the Linear Quadratic Regulator
    Neural Information Processing Systems, 2018
    Co-Authors: Sarah Dean, Horia Mania, Nikolai Matni, Benjamin Recht
    Abstract:

    We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown Linear system is controlled subject to Quadratic costs. Leveraging recent developments in the estimation of Linear systems and in robust controller synthesis, we present the first provably polynomial time algorithm that achieves sub-Linear regret on this problem. We further study the interplay between regret minimization and parameter estimation by proving a lower bound on the expected regret in terms of the exploration schedule used by any algorithm. Finally, we conduct a numerical study comparing our robust adaptive algorithm to other methods from the adaptive LQR literature, and demonstrate the flexibility of our proposed method by extending it to a demand forecasting problem subject to state constraints.

Sarah Dean - One of the best experts on this subject based on the ideXlab platform.

  • On the Sample Complexity of the Linear Quadratic Regulator
    Foundations of Computational Mathematics, 2019
    Co-Authors: Sarah Dean, Horia Mania, Nikolai Matni, Benjamin Recht, Stephen Tu
    Abstract:

    This paper addresses the optimal control problem known as the Linear Quadratic Regulator in the case when the dynamics are unknown. We propose a multistage procedure, called Coarse-ID control , that estimates a model from a few experimental trials, estimates the error in that model with respect to the truth, and then designs a controller using both the model and uncertainty estimate. Our technique uses contemporary tools from random matrix theory to bound the error in the estimation procedure. We also employ a recently developed approach to control synthesis called System Level Synthesis that enables robust control design by solving a quasi-convex optimization problem. We provide end-to-end bounds on the relative error in control cost that are optimal in the number of parameters and that highlight salient properties of the system to be controlled such as closed-loop sensitivity and optimal control magnitude. We show experimentally that the Coarse-ID approach enables efficient computation of a stabilizing controller in regimes where simple control schemes that do not take the model uncertainty into account fail to stabilize the true system.

  • ACC - Safely Learning to Control the Constrained Linear Quadratic Regulator
    2019 American Control Conference (ACC), 2019
    Co-Authors: Sarah Dean, Nikolai Matni, Benjamin Recht
    Abstract:

    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.

  • Safely Learning to Control the Constrained Linear Quadratic Regulator
    arXiv: Optimization and Control, 2018
    Co-Authors: Sarah Dean, Nikolai Matni, Benjamin Recht
    Abstract:

    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.

  • regret bounds for robust adaptive control of the Linear Quadratic Regulator
    arXiv: Learning, 2018
    Co-Authors: Sarah Dean, Horia Mania, Nikolai Matni, Benjamin Recht
    Abstract:

    We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown Linear system is controlled subject to Quadratic costs. Leveraging recent developments in the estimation of Linear systems and in robust controller synthesis, we present the first provably polynomial time algorithm that provides high probability guarantees of sub-Linear regret on this problem. We further study the interplay between regret minimization and parameter estimation by proving a lower bound on the expected regret in terms of the exploration schedule used by any algorithm. Finally, we conduct a numerical study comparing our robust adaptive algorithm to other methods from the adaptive LQR literature, and demonstrate the flexibility of our proposed method by extending it to a demand forecasting problem subject to state constraints.

  • regret bounds for robust adaptive control of the Linear Quadratic Regulator
    Neural Information Processing Systems, 2018
    Co-Authors: Sarah Dean, Horia Mania, Nikolai Matni, Benjamin Recht
    Abstract:

    We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown Linear system is controlled subject to Quadratic costs. Leveraging recent developments in the estimation of Linear systems and in robust controller synthesis, we present the first provably polynomial time algorithm that achieves sub-Linear regret on this problem. We further study the interplay between regret minimization and parameter estimation by proving a lower bound on the expected regret in terms of the exploration schedule used by any algorithm. Finally, we conduct a numerical study comparing our robust adaptive algorithm to other methods from the adaptive LQR literature, and demonstrate the flexibility of our proposed method by extending it to a demand forecasting problem subject to state constraints.

Nikolai Matni - One of the best experts on this subject based on the ideXlab platform.

  • On the Sample Complexity of the Linear Quadratic Regulator
    Foundations of Computational Mathematics, 2019
    Co-Authors: Sarah Dean, Horia Mania, Nikolai Matni, Benjamin Recht, Stephen Tu
    Abstract:

    This paper addresses the optimal control problem known as the Linear Quadratic Regulator in the case when the dynamics are unknown. We propose a multistage procedure, called Coarse-ID control , that estimates a model from a few experimental trials, estimates the error in that model with respect to the truth, and then designs a controller using both the model and uncertainty estimate. Our technique uses contemporary tools from random matrix theory to bound the error in the estimation procedure. We also employ a recently developed approach to control synthesis called System Level Synthesis that enables robust control design by solving a quasi-convex optimization problem. We provide end-to-end bounds on the relative error in control cost that are optimal in the number of parameters and that highlight salient properties of the system to be controlled such as closed-loop sensitivity and optimal control magnitude. We show experimentally that the Coarse-ID approach enables efficient computation of a stabilizing controller in regimes where simple control schemes that do not take the model uncertainty into account fail to stabilize the true system.

  • ACC - Safely Learning to Control the Constrained Linear Quadratic Regulator
    2019 American Control Conference (ACC), 2019
    Co-Authors: Sarah Dean, Nikolai Matni, Benjamin Recht
    Abstract:

    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.

  • Safely Learning to Control the Constrained Linear Quadratic Regulator
    arXiv: Optimization and Control, 2018
    Co-Authors: Sarah Dean, Nikolai Matni, Benjamin Recht
    Abstract:

    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.

  • regret bounds for robust adaptive control of the Linear Quadratic Regulator
    arXiv: Learning, 2018
    Co-Authors: Sarah Dean, Horia Mania, Nikolai Matni, Benjamin Recht
    Abstract:

    We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown Linear system is controlled subject to Quadratic costs. Leveraging recent developments in the estimation of Linear systems and in robust controller synthesis, we present the first provably polynomial time algorithm that provides high probability guarantees of sub-Linear regret on this problem. We further study the interplay between regret minimization and parameter estimation by proving a lower bound on the expected regret in terms of the exploration schedule used by any algorithm. Finally, we conduct a numerical study comparing our robust adaptive algorithm to other methods from the adaptive LQR literature, and demonstrate the flexibility of our proposed method by extending it to a demand forecasting problem subject to state constraints.

  • regret bounds for robust adaptive control of the Linear Quadratic Regulator
    Neural Information Processing Systems, 2018
    Co-Authors: Sarah Dean, Horia Mania, Nikolai Matni, Benjamin Recht
    Abstract:

    We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown Linear system is controlled subject to Quadratic costs. Leveraging recent developments in the estimation of Linear systems and in robust controller synthesis, we present the first provably polynomial time algorithm that achieves sub-Linear regret on this problem. We further study the interplay between regret minimization and parameter estimation by proving a lower bound on the expected regret in terms of the exploration schedule used by any algorithm. Finally, we conduct a numerical study comparing our robust adaptive algorithm to other methods from the adaptive LQR literature, and demonstrate the flexibility of our proposed method by extending it to a demand forecasting problem subject to state constraints.

Horia Mania - One of the best experts on this subject based on the ideXlab platform.

  • On the Sample Complexity of the Linear Quadratic Regulator
    Foundations of Computational Mathematics, 2019
    Co-Authors: Sarah Dean, Horia Mania, Nikolai Matni, Benjamin Recht, Stephen Tu
    Abstract:

    This paper addresses the optimal control problem known as the Linear Quadratic Regulator in the case when the dynamics are unknown. We propose a multistage procedure, called Coarse-ID control , that estimates a model from a few experimental trials, estimates the error in that model with respect to the truth, and then designs a controller using both the model and uncertainty estimate. Our technique uses contemporary tools from random matrix theory to bound the error in the estimation procedure. We also employ a recently developed approach to control synthesis called System Level Synthesis that enables robust control design by solving a quasi-convex optimization problem. We provide end-to-end bounds on the relative error in control cost that are optimal in the number of parameters and that highlight salient properties of the system to be controlled such as closed-loop sensitivity and optimal control magnitude. We show experimentally that the Coarse-ID approach enables efficient computation of a stabilizing controller in regimes where simple control schemes that do not take the model uncertainty into account fail to stabilize the true system.

  • regret bounds for robust adaptive control of the Linear Quadratic Regulator
    arXiv: Learning, 2018
    Co-Authors: Sarah Dean, Horia Mania, Nikolai Matni, Benjamin Recht
    Abstract:

    We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown Linear system is controlled subject to Quadratic costs. Leveraging recent developments in the estimation of Linear systems and in robust controller synthesis, we present the first provably polynomial time algorithm that provides high probability guarantees of sub-Linear regret on this problem. We further study the interplay between regret minimization and parameter estimation by proving a lower bound on the expected regret in terms of the exploration schedule used by any algorithm. Finally, we conduct a numerical study comparing our robust adaptive algorithm to other methods from the adaptive LQR literature, and demonstrate the flexibility of our proposed method by extending it to a demand forecasting problem subject to state constraints.

  • regret bounds for robust adaptive control of the Linear Quadratic Regulator
    Neural Information Processing Systems, 2018
    Co-Authors: Sarah Dean, Horia Mania, Nikolai Matni, Benjamin Recht
    Abstract:

    We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown Linear system is controlled subject to Quadratic costs. Leveraging recent developments in the estimation of Linear systems and in robust controller synthesis, we present the first provably polynomial time algorithm that achieves sub-Linear regret on this problem. We further study the interplay between regret minimization and parameter estimation by proving a lower bound on the expected regret in terms of the exploration schedule used by any algorithm. Finally, we conduct a numerical study comparing our robust adaptive algorithm to other methods from the adaptive LQR literature, and demonstrate the flexibility of our proposed method by extending it to a demand forecasting problem subject to state constraints.

Wolfgang Marquardt - One of the best experts on this subject based on the ideXlab platform.

  • on computing solutions to the continuous time constrained Linear Quadratic Regulator
    IEEE Transactions on Automatic Control, 2010
    Co-Authors: Gabriele Pannocchia, James B. Rawlings, David Q. Mayne, Wolfgang Marquardt
    Abstract:

    We propose in this note a method for computing the solution to the infinite horizon continuous-time constrained Linear Quadratic Regulator. The method is based on two main ingredients: a multigrid method for placing a finite number of time intervals, and a piece-wise Linear parameterization of the input within the intervals. The input values at the decision-time points and slopes within the time intervals are computed via Quadratic programs (QPs). The grids are gradually refined to efficiently improve the accuracy of the solution, and the required matrices and vectors for all QPs are computed offline and stored to improve the online efficiency. Two examples are presented to show the main characteristics of the proposed method.

  • Addendum to the paper \On computing solutions to the continuous time constrained Linear Quadratic Regulator"
    2010
    Co-Authors: Gabriele Pannocchia, James B. Rawlings, David Q. Mayne, Wolfgang Marquardt
    Abstract:

    In this report we present detailed proofs of the results presented in the paper \On Computing Solutions to the Continuous Time Constrained Linear Quadratic Regulator" [1], which were omitted in the nal published paper due to space limitations.