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Fixed-Final-Time-Constrained Optimal Control of Nonlinear Systems Using Neural Network HJB Approach
2007
IEEE Transactions on Neural Networks
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In this paper, fixed-final time-constrained optimal control laws using neural networks (NNS) to solve Hamilton-Jacobi-Bellman (HJB) equations for general affine in the constrained nonlinear systems are ...
Index Terms-Constrained input systems, finite-horizon optimal control, Hamilton-Jacobi-Bellman (HJB), neural network (NN) control. ...
Lewis, Fellow, IEEE, and Murad Abu-Khalaf Abstract-In this paper, fixed-final time-constrained optimal control laws using neural networks (NNS) to solve Hamilton-Jacobi-Bellman (HJB) equations for general ...
doi:10.1109/tnn.2007.905848
fatcat:glkjxxsjevagzgq6hjl43khy6q
Fixed-Final Time Constrained Optimal Control of Nonlinear Systems Using Neural Network HJB Approach
2006
Proceedings of the 45th IEEE Conference on Decision and Control
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In this paper, fixed-final time-constrained optimal control laws using neural networks (NNS) to solve Hamilton-Jacobi-Bellman (HJB) equations for general affine in the constrained nonlinear systems are ...
Index Terms-Constrained input systems, finite-horizon optimal control, Hamilton-Jacobi-Bellman (HJB), neural network (NN) control. ...
Lewis, Fellow, IEEE, and Murad Abu-Khalaf Abstract-In this paper, fixed-final time-constrained optimal control laws using neural networks (NNS) to solve Hamilton-Jacobi-Bellman (HJB) equations for general ...
doi:10.1109/cdc.2006.377523
dblp:conf/cdc/ChengL06
fatcat:bg54cfnz7vcztg7wwuojfvhxny
Constrained optimal control for a class of nonlinear systems with uncertainties
2011
Proceedings of the 2011 American Control Conference
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This approach is applicable to a wide class of nonlinear systems in engineering. Many real-life problems have controller limits. ...
A benchmark nonlinear system is used to illustrate the working of the proposed technique. Extensions to optimal controlconstrained problems in the presence of uncertainties are also considered. ...
The views of the authors do not necessarily represent the views of the NSF and NASA. ...
doi:10.1109/acc.2011.5990893
fatcat:y3tk3hle5vcchjyijkelpuv5h4
Neural Optimal Control using Learned System Dynamics
[article]
2023
arXiv
pre-print
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Our approach is to represent the controller and the value function with neural networks, and to train them using loss functions adapted from the Hamilton-Jacobi-Bellman (HJB) equations. ...
We study the problem of generating control laws for systems with unknown dynamics. ...
We use the Adam optimizer [39] with exponentially decaying learning rate starting from 0.01 to train the networks. L = α cost L cost + α HJB L HJB + α final L final + α hamil L hamil
VI. ...
arXiv:2302.09846v1
fatcat:ralz2zvrzfb5jda7p7pmnbpafm
Machine Learning in Event-Triggered Control: Recent Advances and Open Issues
[article]
2022
arXiv
pre-print
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Networked control systems have gained considerable attention over the last decade as a result of the trend towards decentralised control applications and the emergence of cyber-physical system applications ...
However, real-world wireless networked control systems suffer from limited communication bandwidths, reliability issues, and a lack of awareness of network dynamics due to the complex nature of wireless ...
EVENT-TRIGGERED AND SELF-TRIGGERED CONTROL Traditional time-triggered networked control approaches use a fixed sampling period, leading to time-periodic communication between the agents in the system. ...
arXiv:2009.12783v2
fatcat:o55wr4pedzah7c2ddqjn6ur4km
A Neural Network Approach Applied to Multi-Agent Optimal Control
[article]
2021
arXiv
pre-print
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We propose a neural network approach for solving high-dimensional optimal control problems. In particular, we focus on multi-agent control problems with obstacle and collision avoidance. ...
We train our model using the objective function and optimality conditions of the control problem. ...
We propose a machine learning framework to overcome the curse of dimensionality by approximating the value function with a neural network (NN). Our approach is a fusion of PMP and HJB. ...
arXiv:2011.04757v2
fatcat:xcirfue27zderc67wkhyr42wua
Neural Lyapunov and Optimal Control
[article]
2024
arXiv
pre-print
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We use the Hamilton-Jacobi-Bellman (HJB) and first-order gradients to learn optimal time-varying value functions and therefore, policies. ...
We show the relaxation of our objective results in time-varying Lyapunov functions, further verifying our approach by providing guarantees over a compact set of initial conditions. ...
Optimal Control: Optimal control is grounded within the Hamilton-Jacobi-Bellman (HJB) equation. ...
arXiv:2305.15244v4
fatcat:om7q7qvvj5dypmfjobocx6j2um
Extensions of the Deep Galerkin Method
[article]
2022
arXiv
pre-print
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Secondly, we tackle a number of Hamilton-Jacobi-Bellman (HJB) equations that appear in stochastic optimal control problems. ...
We extend the DGM algorithm to solve for the value function and the optimal control \simultaneously by characterizing both as deep neural networks. ...
These approaches often involve characterizing the unknown function using a deep neural network. ...
arXiv:1912.01455v3
fatcat:2trhb6ndqbd4ricmek6ktztxdu
Intelligent Constrained Optimal Control of Aerospace Vehicles with Model Uncertainties
2012
Journal of Guidance Control and Dynamics
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L., and Abu-Khalaf, M., “Discrete-Time Design Methodology for Nonlinear-in-Control Systems in Aircraft Nonlinear HJB Solution Using Approximate Dynamic Programming: Applications,” Journal of Guidance, ...
Lyashevskiy [25,26] outlined a constrained
optimization framework to solve optimization problems for nonlinear time-varying systems with state and control bounds. ...
doi:10.2514/1.54505
fatcat:d6su7ram2zb65akmbz6546nk7q
GrAVITree: Graph-based Approximate Value Function In a Tree
[article]
2023
arXiv
pre-print
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deep neural network model of its dynamics. ...
nonlinear optimal control problems. ...
Optimal control problem Consider the following optimal control problem which is terminal state constrained and has unspecified final time: J(x 0 ; x) = min u,t ≥0 t t=0 g(x t , u t ) (1) subject to u t ...
arXiv:2301.07822v1
fatcat:cevsclpbcbgehpb2buffv6ln6e
QRnet: optimal regulator design with LQR-augmented neural networks
[article]
2020
arXiv
pre-print
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Concretely, we augment linear quadratic regulators with neural networks to handle nonlinearities. ...
In this paper we propose a new computational method for designing optimal regulators for high-dimensional nonlinear systems. ...
In recent years, neural networks (NNs) have gained considerable attention as a promising tool for high-dimensional problems since they can avoid the use of spatial grids. ...
arXiv:2009.05686v1
fatcat:7ghmvpzagbgobotc3waaic5fku
Adaptive Dynamic Programming: An Introduction
2009
IEEE Computational Intelligence Magazine
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It is generally believed that the latter one has less computation at the cost of missing the guarantee of system stability during iteration process. ...
In this article, we introduce some recent research trends within the field of adaptive/approximate dynamic programming (ADP), including the variations on the structure of ADP schemes, the development of ...
Next, the fixed-final-time-constrained optimal control of nonlinear systems is studied in [22] , [23] based on the neural network solution of the GHJB equation. ...
doi:10.1109/mci.2009.932261
fatcat:qop5dvkdbbecxcn73u4i2smkvi
Statistical Control for Performance Shaping Using Cost Cumulants
2014
IEEE Transactions on Automatic Control
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In addition, we utilize neural networks to numerically solve HJB partial differential equations. Finally, we provide simulation results for an oscillator system to demonstrate our method. ...
For a stochastic system, a typical optimal control method minimizes the mean (first cumulant) of the cost function. ...
For discrete time nonlinear system, Chen and Jagannathan solved the HJB equation using neural networks [16] . ...
doi:10.1109/tac.2013.2270838
fatcat:x4uistkbdjekbpcfacpnvtcjze
Deep Learning for Efficient and Optimal Motion Planning for AUVs with Disturbances
2021
Sensors
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the Hamilton–Jacobi–Bellman PDE that can be used to solve continuous time and state optimal control problems. ...
We use the recent advances in Deep Learning to solve an underwater motion planning problem by making use of optimal control tools—namely, we propose using the Deep Galerkin Method (DGM) to approximate ...
Conflicts of Interest: The authors declare no conflict of interest. ...
doi:10.3390/s21155011
fatcat:zpiyxqabibajvkvw3xymuvqnqq
Adaptive Reinforcement Learning-Enhanced Motion/Force Control Strategy for Multirobot Systems
2021
Mathematical Problems in Engineering
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Finally, simulation studies are conducted on a system of three manipulators to validate the physical realization of the proposed optimal tracking control design. ...
The tracking effectiveness of the ARL-based optimal control is verified in the closed-loop system by theoretical analysis. ...
Acknowledgments is research was supported by the Ministry of Education and Training, Vietnam, under Grant B2020-BKA-05. ...
doi:10.1155/2021/5560277
fatcat:6heh4ja7xzctxjzf4zcp6q6l7e
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