Computational adaptive optimal control for continuous-time linear systems with completely unknown dynamics

Jiang, Yu; Jiang, Zhong‐Ping

doi:10.1016/j.automatica.2012.06.096

Cited by 830 publications

(446 citation statements)

References 25 publications

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“…This last condition, called excitability of the pair (S, ω(0)), is a geometric characterization of the property that the signals generated by (3) are persistently exciting, see [38]. The excitability of the pair (S, ω(0)) can be also connected to the notion of exploration noise used in the data-driven dynamic programming problem, see [39]- [41]. However, note that while it is not clear how to select the exploration noise in optimal control problems, the excitability condition provides a precise characterization of the frequencies that have to be present in the excitation signal.…”

Section: A Model Reduction By Moment Matching -Recalledmentioning

confidence: 99%

Constrained optimal reduced-order models from input/output data

Scarciotti

Jiang

Astolfi

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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Abstract-Model reduction by moment matching does not preserve, in a systematic way, the transient response of the system to be reduced, thus limiting the use of this model reduction technique in control problems. With the final goal of designing reduced-order models which can effectively be used (not just for analysis but also) for control purposes, we determine, using a data-driven approach, an estimate of the moments and of the transient response of an unknown system. We compute the unique, up to a change of coordinates, reducedorder model which possesses the estimated transient and, simultaneously, achieves moment matching at the prescribed interpolation points. The error between the output of the system and the output of the reduced-order model is minimized and we show that the resulting system is a constrained optimal (in a sense to be specified) reduced-order model. The results of the paper are illustrated by means of a simple numerical example.

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Section: A Model Reduction By Moment Matching -Recalledmentioning

confidence: 99%

Constrained optimal reduced-order models from input/output data

Scarciotti

Jiang

Astolfi

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

Self Cite

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“…In this case p can be taken larger than nν and, as well-known from linear algebra and remarked in [25] and [34], the solution of equation (11) is the least squares solution of (10).…”

Section: A Preliminary Analysismentioning

confidence: 99%

“…However, in practice a model of the system to be reduced is not always available. In this paper, inspired by the learning algorithm given in [25] to solve a model-free adaptive dynamic programming problem (see also the references therein, e.g. [26], [27]), we propose an on-line algorithm for the model reduction of linear systems and linear time-delay systems from data.…”

Section: Introductionmentioning

confidence: 99%

Model reduction for linear systems and linear time-delay systems from input/output data

Scarciotti

Astolfi

2015

2015 European Control Conference (ECC)

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Abstract-An algorithm for the estimation of the moments of linear single-input, single-output (SISO) systems and linear time-delay SISO systems from input/output data is proposed. It is proved that the estimate converges to the moments of the system. The estimate is exploited to construct a family of reduced order models. These models asymptotically match the moments of the unknown system to be reduced. Conditions to enforce additional properties, e.g. matching with prescribed eigenvalues or matching with prescribed zeros, upon the reduced order model are provided and discussed. The computational complexity of the algorithm is analyzed and the use of the algorithm is illustrated by a benchmark example.

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“…In [19], the algorithm of policy improvement with path integrals is integrated with reinforcement learning to achieve variable impedance control. In [20], impedance adaptation for robot control is developed based on adaptive dynamic programming proposed in [21]. Literature reviews of reinforcement learning can be found in [22,23], which introduce the use of reinforcement learning in feedback control and state open challenges of developing a reinforcement learning control.…”

Section: Introductionmentioning

confidence: 99%

Reinforcement learning control for coordinated manipulation of multi-robots

Chen

Tee

et al. 2015

Neurocomputing

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In this paper, coordination control is investigated for multi-robots to manipulate an object with a common desired trajectory. Both trajectory tracking and control input minimization are considered for each individual robot manipulator, such that possible disagreement between different manipulators can be handled. Reinforcement learning is employed to cope with the problem of unknown dynamics of both robots and the manipulated object. It is rigorously proven that the proposed method guarantees the coordination control of the multi-robots system under study. The validity of the proposed method is verified through simulation studies.

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Computational adaptive optimal control for continuous-time linear systems with completely unknown dynamics

Cited by 830 publications

References 25 publications

Constrained optimal reduced-order models from input/output data

Constrained optimal reduced-order models from input/output data

Model reduction for linear systems and linear time-delay systems from input/output data

Reinforcement learning control for coordinated manipulation of multi-robots

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