Generalized Linear Quadratic Control

Gattami, Ather

doi:10.1109/tac.2009.2033736

Cited by 44 publications

(49 citation statements)

References 8 publications

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“…The constraint (6) is related to the energy of the state trajectories, and (7) corresponds to the energy of the input trajectories. The constraint (8) is a state-dependent input constraint.…”

Section: Semidefinite Programming Algorithmsmentioning

confidence: 99%

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Primal-Dual Q-Learning Framework for LQR Design

Lee

2019

IEEE Trans. Automat. Contr.

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Recently, reinforcement learning (RL) is receiving more and more attentions due to its successful demonstrations outperforming human performance in certain challenging tasks. In our recent paper 'primal-dual Q-learning framework for LQR design,' we study a new optimization formulation of the linear quadratic regulator (LQR) problem via the Lagrangian duality theories in order to lay theoretical foundations of potentially effective RL algorithms. The new optimization problem includes the Qfunction parameters so that it can be directly used to develop Q-learning algorithms, known to be one of the most popular RL algorithms. In the paper, we prove relations between saddle-points of the Lagrangian function and the optimal solutions of the Bellman equation. As an application, we propose a model-free primal-dual Q-learning algorithm to solve the LQR problem and demonstrate its validity through examples. It is meaningful to consider additional potential applications of the proposed analysis.Various SDP formulations of Problem 5 or Problem 2 of the paper can be derived, and they can be used to develop new analysis and control design approaches. For example, an SDP-based optimal control design with energy and input constraints can be derived. Another direction is algorithms for structured controller designs. These approaches are included in this supplemental material.

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Section: Semidefinite Programming Algorithmsmentioning

confidence: 99%

“…The constraint (8) is a state-dependent input constraint. We note that similar energy constraints were considered in [7] as well. However, the SDP condition in [7] cannot address the state-dependent input constraint.…”

Section: Semidefinite Programming Algorithmsmentioning

confidence: 99%

Primal-Dual Q-Learning Framework for LQR Design

Lee

2019

IEEE Trans. Automat. Contr.

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“…Historically, this problem was first investigated in the case of white Gaussian noise [5], [6], and has been recently extended to arbitrary correlated noise [7]. The study of LQC still motivates the interest of the research community, as testified by the big number of works that are published about this subject [8]- [12].…”

Section: Introductionmentioning

confidence: 99%

Linear quadratic control of LPV systems using static and shifting specifications

Rotondo

Puig

Nejjari

2015

2015 European Control Conference (ECC)

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Abstract-This paper extends some recent results about linear quadratic control (LQC) using linear matrix inequalities (LMIs) to linear parameter varying (LPV) systems. At first, static specifications, where the weighting matrices are constant, are considered. Later, the concept of shifting linear quadratic control (SLQC), where some varying parameters are introduced and used to schedule not only the controller, but the weighting matrices too, is considered. A numerical example is used to illustrate the application of the proposed theory.

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“…In this section we will show how to solve a stochastic LQ control problem with power constraints recursively [29]. The problem we are trying to solve is…”

Section: Generalized Linear Quadratic Controlmentioning

confidence: 99%

“…In other words, although the method is powerful it is not easy to be applied to other similar problems. For more details, please refer to [29].…”

Section: Constrained Stochastic Linear Quadratic Controlmentioning

confidence: 99%

Stochastic LQ Control with Probabilistic Constraints

Zhou¹

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In this thesis we focus on stochastic LQ control problems with probabilistic constraints. We will briefly review the history of LQ control and the related classical results for constrained and unconstrained cases. Then we formulate the problem studied, where the system has linear dynamics and a quadratic cost, and states are required to satisfy a probabilistic constraint. We sample the most recent techniques for such probability constrained control problems and propose our own approach. We consider two types of probability constraints:all-stage and per-stage. In the first case, there is a joint probabilistic constraint on all the system states over the whole predicting horizon while in the second one the states are restricted by individual probability constraints at each stage. The contribution of this thesis has two parts: first we develop a recursive state feedback control algorithm for a special class of state constrained stochastic LQR, and a disturbance feedback controller for the general case using quadratic programming for the all-stage problems. Second, we design a recursive algorithm for the per-stage problem based on sub-gradient method. We also implement a practical Model Predictive Control algorithm for such problems. The control algorithm is tested on a simple temperature control problem for analysis.ii The last but not the least I am grateful to the staff members at the International Student Office and the language development center. As an international student I feel at home with their help.Four years can change much about a person, I sincerely thank you all for being part of this crucial change of my life.

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Generalized Linear Quadratic Control

Cited by 44 publications

References 8 publications

Primal-Dual Q-Learning Framework for LQR Design

Primal-Dual Q-Learning Framework for LQR Design

Linear quadratic control of LPV systems using static and shifting specifications

Stochastic LQ Control with Probabilistic Constraints

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