Value function approximation for the control of multiscale dynamical systems

Zhu, Pingping; Morelli, Julian; Ferrari, Silvia

doi:10.1109/cdc.2016.7799109

Cited by 3 publications

(3 citation statements)

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“…Although the functional control law C k is an operator as described before and the functional operator learning has been studied in [30], [31], it is still challenging to approximate this operator online and approximate ℘ k+1 according to (9). Thus, in this paper, the critic-only Q-learning (CoQL) method is applied to obtain the optimal control where the approximation of control law C k is not required [32].…”

Section: B Derivation Of Optimal Functional Control Lawmentioning

confidence: 99%

“…By applying Ck (•, m k ), an upper bound of the optimal value functional V * k (℘ k+1 , m k ) is provided in the following theorem. Theorem 2 (Upper bound of optimal value functional): Given the robot PDF ℘ k+1 and the target robot PDF ℘ targ defined in ( 29) and (30), respectively, there exists an upper bound of the optimal value functional V * k (℘ k+1 , m k ), which is denoted by Ṽk (℘ k+1 , m k ), such that…”

Section: B Approximation Of Optimal Value Functional In Wasserstein-g...mentioning

confidence: 99%

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Adaptive Online Distributed Optimal Control of Very-Large-Scale Robotic Systems

Zhu

Liu

Ferrari

2020

Preprint

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This paper presents an adaptive online distributed optimal control approach that is applicable to optimal planning for very-large-scale robotics systems in highly uncertain environments. This approach is developed based on the optimal mass transport theory. It is also viewed as an online reinforcement learning and approximate dynamic programming approach in the Wasserstein-GMM space, where a novel value functional is defined based on the probability density functions of robots and the time-varying obstacle map functions describing the changing environmental information. The proposed approach is demonstrated on the path planning problem of very-largescale robotic systems where the approximated layout of obstacles in the workspace is incrementally updated by the observations of robots, and compared with some existing state-of-the-art approaches. The numerical simulation results show that the proposed approach outperforms these approaches in aspects of the average traveling distance and the energy cost.

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Section: B Derivation Of Optimal Functional Control Lawmentioning

confidence: 99%

Section: B Approximation Of Optimal Value Functional In Wasserstein-g...mentioning

confidence: 99%

Adaptive Online Distributed Optimal Control of Very-Large-Scale Robotic Systems

Zhu

Liu

Ferrari

2020

Preprint

Self Cite

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“…Approximating a function from its samples is a fundamental problem with rich theory developed in areas such as numerical analysis and statistics, and which also has numerous practical applications such as in systems biology [19], solving PDEs [11], control systems [50], optimization [39] etc. Concretely, for an unknown d-variate function f : G → R, one is given information about f in the form of samples (x i , f (x i )) n i=1 .…”

Section: Introductionmentioning

confidence: 99%

Learning General Sparse Additive Models from Point Queries in High Dimensions

Tyagi

Vybíral

2019

Constr Approx

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We consider the problem of learning a d-variate function f defined on the cube [−1, 1] d ⊂ R d , where the algorithm is assumed to have black box access to samples of f within this domain. Denote S r ⊂ [d] r ; r = 1, . . . , r 0 to be sets consisting of unknown r-wise interactions amongst the coordinate variables. We then focus on the setting where f has an additive structure, i.e., it can be represented aswhere each φ j ; j ∈ S r is at most r-variate for 1 ≤ r ≤ r 0 . We derive randomized algorithms that query f at carefully constructed set of points, and exactly recover each S r with high probability.In contrary to the previous work, our analysis does not rely on numerical approximation of derivatives by finite order differences.

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