Optimal control on special Euclidean group via natural gradient algorithm

Li, Chunhui; Zhang, Erchuan; Jiu, Lin; Sun, Hongwei

doi:10.1007/s11432-015-0096-3

Cited by 9 publications

(6 citation statements)

References 20 publications

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“…According to Equation (29), the centre and width can be updated by the gradient descent [27,28]. The gradient descent linear function of eðkÞ can be expressed as…”

Section: International Journal Of Aerospace Engineeringmentioning

confidence: 99%

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Fuzzy Neural Network Q-Learning Method for Model Disturbance Change: A Deployable Antenna Panel Application

Liu

Bao

Xue

et al. 2019

International Journal of Aerospace Engineering

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This paper addresses the disturbance change control problem with an active deformation adjustment mechanism on a 5-meter deployable antenna panel. A fuzzy neural network Q-learning control (FNNQL) strategy is proposed in this paper for the disturbance change to improve the accuracy of the antenna panel. In the proposed method, the error of the model disturbance is reduced by introducing the fuzzy radial basis function (RBF) neural network into Q-learning, and the parameters of the fuzzy RBF neural network were optimized and adjusted by a Q-learning method. This allows the FNNQL controller to have a strong adaptability to deal with the disturbance change. Finally, the proposed method has been adopted in the middle plate of a 5-meter deployable antenna panel, and it was found that the method could successfully adapt the model disturbance change in the antenna panel. Results of the simulation also show that the whole control system meets the required accuracy requirements.

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“…According to Equation (29), the centre and width can be updated by the gradient descent [27,28]. The gradient descent linear function of eðkÞ can be expressed as…”

Section: International Journal Of Aerospace Engineeringmentioning

confidence: 99%

“…Part II: Fuzzy Parameter Adjustment. According to Equation (27), the new displacement X P ðk + 1Þ can be obtained. And then, the new error eðk + 1Þ and the rate of the error ecðk + 1Þ can be derived based on Equations (12) and (13).…”

mentioning

confidence: 99%

Fuzzy Neural Network Q-Learning Method for Model Disturbance Change: A Deployable Antenna Panel Application

Liu

Bao

Xue

et al. 2019

International Journal of Aerospace Engineering

View full text Add to dashboard Cite

show abstract

“…Research on optimal control has lasted for many decades, and various methods and strategies have emerged [1][2][3]. Receding horizon control (RHC), also called model predictive control (MPC), is a promising optimal control strategy and has had a tremendous impact on industrial applications [4,5].…”

Section: Introductionmentioning

confidence: 99%

Event-triggered receding horizon control via actor-critic design

Dong

Yuan

Sun

2020

Sci. China Inf. Sci.

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In this paper, we propose a novel event-triggered near-optimal control for nonlinear continuoustime systems. The receding horizon principle is utilized to improve the system robustness and obtain better dynamic control performance. In the proposed structure, we first decompose the infinite horizon optimal control into a series of finite horizon optimal problems. Then a learning strategy is adopted, in which an actor network is employed to approximate the cost function and an critic network is used to learn the optimal control law in each finite horizon. Furthermore, in order to reduce the computational cost and transmission cost, an event-triggered strategy is applied. We design an adaptive trigger condition, so that the signal transmissions and controller updates are conducted in an aperiodic way. Detailed stability analysis shows that the nonlinear system with the developed event-triggered optimal control policy is asymptotically stable. Simulation results on a single-link robot arm with different noise types have demonstrated the effectiveness of the proposed method.

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“…The natural gradient algorithm has been widely applied into, for instance neural network, optimal control, offering a new way to solve such problems more effectively, cf. [17,23,25,26].…”

Section: Introductionmentioning

confidence: 99%

Application of gradient descent algorithms based on geodesic distances

Duan

Sun

Peng

2020

Sci. China Inf. Sci.

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In this paper, the Riemannian gradient algorithm and the natural gradient algorithm are applied to solve descent direction problems on the manifold of positive definite Hermitian matrices, where the geodesic distance is considered as the cost function. The first proposed problem is control for positive definite Hermitian matrix systems whose outputs only depend on their inputs. The geodesic distance is adopted as the difference of the output matrix and the target matrix. The controller to adjust the input is obtained such that the output matrix is as close as possible to the target matrix. We show the trajectory of the control input on the manifold using the Riemannian gradient algorithm. The second application is to compute the Karcher mean of a finite set of given Toeplitz positive definite Hermitian matrices, which is defined as the minimizer of the sum of geodesic distances. To obtain more efficient iterative algorithm compared with traditional ones, a natural gradient algorithm is proposed to compute the Karcher mean. Illustrative simulations are provided to show the computational behavior of the proposed algorithms.

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Optimal control on special Euclidean group via natural gradient algorithm

Abstract: Natural gradient-based recursive least-squares algorithm for adaptive blind source separation Science in China Series F-Information Sciences 47, 55 (2004); Open-loop and optimal control of cylinder wake via electromagnetic fields

Cited by 9 publications

References 20 publications

Fuzzy Neural Network Q-Learning Method for Model Disturbance Change: A Deployable Antenna Panel Application

Fuzzy Neural Network Q-Learning Method for Model Disturbance Change: A Deployable Antenna Panel Application

Event-triggered receding horizon control via actor-critic design

Application of gradient descent algorithms based on geodesic distances

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