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Learning the model-free linear quadratic regulator via random search

Hesameddin Mohammadi, Mihailo R. Jovanovic, Mahdi Soltanolkotabi
2020 Conference on Learning for Dynamics & Control  
We provide theoretical bounds on the convergence rate and sample complexity of a random search method.  ...  In this paper, we examine the standard infinite-horizon linear quadratic regulator problem for continuous-time systems with unknown state-space parameters.  ...  For the discrete-time LQR problem, global convergence guarantees were recently provided in Fazel et al. (2018) for gradient decent and the random search method with one-point gradient estimates.  ... 
dblp:conf/l4dc/MohammadiJS20 fatcat:654duzegs5d7him6tepoo4nmwi

Randomly Sampling Actions In Dynamic Programming

Christopher G. Atkeson
2007 2007 IEEE International Symposium on Approximate Dynamic Programming and Reinforcement Learning  
We present results on finding time invariant control laws for two, four, and six dimensional deterministic swing up problems with up to 480 million discretized states.  ...  We describe an approach towards reducing the curse of dimensionality for deterministic dynamic programming with continuous actions by randomly sampling actions while computing a steady state value function  ...  ACKNOWLEDGMENT This material is based upon work supported in part by the National Science Foundation under NSF Grant ECS-0325383 and the DARPA Learning Locomotion Program.  ... 
doi:10.1109/adprl.2007.368187 fatcat:ozbqd3vl65bx3byxu6l6uuzt4a

Design of hybrid regrouping PSO–GA based sub-optimal networked control system with random packet losses

Indranil Pan, Saptarshi Das
2013 Memetic Computing  
other time domain performance criteria like expected value of the set-point tracking error with optimum weight selection based LQR design for the nominal system.  ...  The optimal regulator gains, producing guaranteed stability are designed with the nominal discrete time model of a plant using Lyapunov technique which produces a few set of Bilinear Matrix Inequalities  ...  Acknowledgement The authors thank the anonymous reviewers for providing helpful and constructive comments which has helped to increase the quality of the paper.  ... 
doi:10.1007/s12293-013-0107-5 fatcat:vpa3vtoifzfn7jrr7a3ks7mhxu

Stochastic Extended LQR for Optimization-Based Motion Planning Under Uncertainty

Wen Sun, Jur van den Berg, Ron Alterovitz
2016 IEEE Transactions on Automation Science and Engineering  
We introduce a novel optimization-based motion planner, Stochastic Extended LQR (SELQR), which computes a trajectory and associated linear control policy with the objective of minimizing the expected value  ...  In each iteration, SELQR uses a combination of forward and backward value iteration to estimate the cost-to-come and the cost-to-go for each state along a trajectory.  ...  His research focuses on motion planning for medical and assistive robots. Prof.  ... 
doi:10.1109/tase.2016.2517124 pmid:28163662 pmcid:PMC5287415 fatcat:kdtqazzbl5dfhgsmymo6fkrnae

A Relaxed Projection Control in the Context of Inverse Optimal Control for Discrete Nonlinear Systems

Ethan King, Hien Tran
2019 2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
We show that the proposed family of controls are globally exponentially stable for linear systems, and test the controls on both a linear and nonlinear example.  ...  We present a nonlinear discrete time feedback control design by searching over a family of controls and associated candidate quadratic control Lyapunov functions parameterized by the symmetric positive  ...  ACKNOWLEDGMENT This work was supported by the Center for Research in Scientific Computation at North Carolina State University.  ... 
doi:10.1109/allerton.2019.8919882 dblp:conf/allerton/KingT19 fatcat:52n7t5pxp5hytjm6hladfh7ssm

Synthesis of Feedback Controller for Nonlinear Control Systems with Optimal Region of Attraction [article]

Ayan Chakraborty, Indranil Saha
2020 arXiv   pre-print
Our synthesis technique relies on stochastic optimization, which involves computation of an objective function capturing the ROA for a feedback control law.  ...  We employ a machine learning technique based on deep neural network to estimate the ROA for a given feedback controller.  ...  The iteration continues until convergence or for a pre-specified number of times.  ... 
arXiv:1911.03870v3 fatcat:iqjdhsjprnespk2jyandcqqchi

LQR-RRT*: Optimal sampling-based motion planning with automatically derived extension heuristics

Alejandro Perez, Robert Platt, George Konidaris, Leslie Kaelbling, Tomas Lozano-Perez
2012 2012 IEEE International Conference on Robotics and Automation  
We propose automatically deriving these two heuristics for RRT * by locally linearizing the domain dynamics and applying linear quadratic regulation (LQR).  ...  However, like RRT, RRT * is difficult to apply in problems with complicated or underactuated dynamics because it requires the design of a two domain-specific extension heuristics: a distance metric and  ...  This work was supported in part by the NSF under Grant No. 019868, ONR MURI grant N00014-09-1-1051, AFOSR grant AOARD-104135, and the Singapore Ministry of Education under a grant to the Singapore-MIT  ... 
doi:10.1109/icra.2012.6225177 dblp:conf/icra/PerezPKKL12 fatcat:gsrjv3ebb5gmjh77s6myli6jfu

Iterated LQR smoothing for locally-optimal feedback control of systems with non-linear dynamics and non-quadratic cost

Jur van den Berg
2014 2014 American Control Conference  
for the linear-quadratic optimal control problem.  ...  , and show that our approach converges in only about a third of the number of iterations required by existing approaches such as Iterative LQR.  ...  EXPERIMENTS We implemented a discrete-time variant of our approach (see [23] for details on the discrete-time variant of Iterated LQR Smoothing), and experimented on two systems; a physical iRobot Create  ... 
doi:10.1109/acc.2014.6859404 dblp:conf/amcc/Berg14 fatcat:m4riq2ovxrcytf7ln3hliujmom

Extended LQR: Locally-Optimal Feedback Control for Systems with Non-Linear Dynamics and Non-Quadratic Cost [chapter]

Jur van den Berg
2016 Springer Tracts in Advanced Robotics  
Our results indicate that Extended LQR converges quickly and reliably to a locally-optimal solution of the non-linear, non-quadratic optimal control problem.  ...  Our formulation is conceptually different from existing approaches, and is based on the novel concept of LQR-smoothing, which is an LQR-analogue of Kalman smoothing.  ...  Therefore, we averaged the computation time and the number of iterations for both methods over the same 100 random queries for each value of the time-step, which we let range from τ = 1 40 s to τ = 1 10  ... 
doi:10.1007/978-3-319-28872-7_3 fatcat:d7f6zc7lfndchpkjgc3xi6twlu

Algorithms for LQR via Static Output Feedback for Discrete-Time LTI Systems [chapter]

Yossi Peretz
2019 Discrete Time Control Systems [Working Title]  
Randomized and deterministic algorithms for the problem of LQR optimal control via static-output-feedback (SOF) for discrete-time systems are suggested in this chapter.  ...  The randomized algorithm presented here has a proof of convergence in probability to the global optimum.  ...  The RS algorithm is one of the few, dealing with the problem of LQR via SOF for discrete-time systems. 6.  ... 
doi:10.5772/intechopen.89319 fatcat:7xqls2rtvrejpofxsiqsnfb24i

Stochastic Extended LQR: Optimization-Based Motion Planning Under Uncertainty [chapter]

Wen Sun, Jur van den Berg, Ron Alterovitz
2015 Springer Tracts in Advanced Robotics  
We introduce a novel optimization-based motion planner, Stochastic Extended LQR (SELQR), which computes a trajectory and associated linear control policy with the objective of minimizing the expected value  ...  In each iteration, SELQR uses a combination of forward and backward value iteration to estimate the cost-to-come and the cost-togo for each state along a trajectory.  ...  This research was supported in part by the National Science Foundation (NSF) under awards IIS-1117127 and IIS-1149965 and by the National Institutes of Health (NIH) under award R21EB017952.  ... 
doi:10.1007/978-3-319-16595-0_35 fatcat:433kwl326bceba35f2uzkfnfu4

Towards Planning and Control of Hybrid Systems with Limit Cycle using LQR Trees [article]

Ramkumar Natarajan, Siddharthan Rajasekaran, Jonathan D. Taylor
2017 arXiv   pre-print
We leverage the idea of LQR trees to plan with a continuous control set, unlike methods that rely on discretization like dynamic programming to plan for hybrid dynamical systems where it is hard to capture  ...  The original LQR Tree algorithm builds such trees for non-linear static and non-hybrid systems like a pendulum or a cart-pole.  ...  Russ Tedrake for his quick responses to our queries regarding DRAKE simulator [20] . We also thank Prof. Dmitry Berenson for his motivation behind exploring this area of research.  ... 
arXiv:1711.04063v1 fatcat:irongrhubneg3fijh7vwuyxxza

LQR-trees: Feedback Motion Planning via Sums-of-Squares Verification

Russ Tedrake, Ian R. Manchester, Mark Tobenkin, John W. Roberts
2010 The international journal of robotics research  
Advances in the direct computation of Lyapunov functions using convex optimization make it possible to efficiently evaluate regions of attraction for smooth nonlinear systems.  ...  We numerically investigate the properties of this systematic nonlinear feedback design algorithm on simple nonlinear systems, prove the property of probabilistic coverage, and discuss extensions and implementation  ...  Acknowledgements The authors wish to thank Alexandre Megretski and Pablo Parrilo for their invaluable assistance on the formulations and numerical implementations of the sums-of-squares methods.  ... 
doi:10.1177/0278364910369189 fatcat:fmdeklhuwrcpziez4ykzjcjm24

Synthesis of Minimal Error Control Software [article]

Rupak Majumdar, Indranil Saha, Majid Zamani
2012 arXiv   pre-print
Using synthesis, the need for formal verification can be considerably reduced thereby reducing the design time as well as design cost of embedded control software.  ...  Our technique is a combination of static analysis to estimate quantization errors for specific controller implementations and stochastic local search over the space of possible controllers using particle  ...  Consider the discrete-time linear system in (2.6).  ... 
arXiv:1204.2857v1 fatcat:eviva37edjgazayrck3vuf3iki

Synthesis of minimal-error control software

Rupak Majumdar, Indranil Saha, Majid Zamani
2012 Proceedings of the tenth ACM international conference on Embedded software - EMSOFT '12  
Our technique uses static analysis to estimate quantization-related errors for specific controller implementations, and performs stochastic local search over the space of possible controllers using particle  ...  Software implementations of controllers for physical systems are at the core of many embedded systems.  ...  Consider the discrete-time linear system in (2.6).  ... 
doi:10.1145/2380356.2380380 dblp:conf/emsoft/MajumdarSZ12 fatcat:t7fuungku5azdon5rs7uk2rc2u
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