New Algorithms for Discrete-Time Parameter Estimation

Cui, Yingnan; Gaudio, Joseph E.; Annaswamy, Anuradha M.

doi:10.48550/arxiv.2103.16653

Cited by 4 publications

(11 citation statements)

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“…where Γ is a gain matrix, and N k is a suitable normalization, an example of which is 1+φ T k φ k . In order to realize the learning goal, of convergence of θ k to θ * , the following property of excitation of the regressor φ k is needed [19,42,63]. We denote N + as the set of positive integers, and • as the Euclidean norm.…”

Section: Adaptive Approaches To Performance and Learningmentioning

confidence: 99%

“…When the regressors in ( 25) satisfy the PE condition, it can be shown using the methods in [19,42,63] that θ k converges to θ * uniformly in k. We note that if the gain matrix in ( 30) is time-varying and updated as…”

Section: Definition 1 ([72]) a Bounded Function φmentioning

confidence: 99%

“…Theorem 6. For the stochastic linear regression model in (56) and (57), if noise assumptions ( 22)-( 23) are satisfied, the adaptive law in (61)- (63)…”

Section: Stability Properties Of the Ht In The Presence Of Noisementioning

confidence: 99%

“…Preliminary versions of the results reported here can be found in peer-reviewed publications [50] and [52], and arXived publications [51,62,63]. Section 3 is a significant expansion of [62] which only addressed the single-input version of the result in Section 3.1.…”

Section: Introductionmentioning

confidence: 99%

“…Section 3 is a significant expansion of [62] which only addressed the single-input version of the result in Section 3.1. Section 4 is a significant expansion of [50] and [52], includes a comprehensive treatment of accelerated performance as well as accelerated learning in comparison to [51,63], and illustrates the central contribution of the corresponding algorithms and improvements compared to standard adaptive and ML approaches.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Integration of adaptive control and reinforcement learning for real-time control and learning

Annaswamy¹,

Guha²,

Cui³

et al. 2021

Preprint

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This paper considers the problem of real-time control and learning in dynamic systems subjected to uncertainties. Adaptive approaches are proposed to address the problem, which are combined with methods and tools in Reinforcement Learning (RL) and Machine Learning (ML). Algorithms are proposed in continuous-time that combine adaptive approaches with RL leading to online control policies that guarantee stable behavior in the presence of parametric uncertainties that occur in real-time. Algorithms are proposed in discrete-time that combine adaptive approaches proposed for parameter and output estimation and ML approaches proposed for accelerated performance that guarantee stable estimation even in the presence of time-varying regressors, and for accelerated learning of the parameters with persistent excitation. Numerical validations of all algorithms are carried out using a quadrotor landing task on a moving platform and benchmark problems in ML. All results clearly point out the advantage of the proposed integrative approaches for real-time control and learning.

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Section: Adaptive Approaches To Performance and Learningmentioning

confidence: 99%

Section: Definition 1 ([72]) a Bounded Function φmentioning

confidence: 99%

“…Theorem 6. For the stochastic linear regression model in (56) and (57), if noise assumptions ( 22)-( 23) are satisfied, the adaptive law in (61)- (63)…”

Section: Stability Properties Of the Ht In The Presence Of Noisementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Integration of adaptive control and reinforcement learning for real-time control and learning

Annaswamy¹,

Guha²,

Cui³

et al. 2021

Preprint

Self Cite

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Generation of New Exciting Regressors for Consistent Online Estimation of Unknown Constant Parameters

Bobtsov

Astolfi

2022

IEEE Trans. Automat. Contr.

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The problem of estimating constant parameters from a standard vector linear regression equation in the absence of sufficient excitation in the regressor is addressed. The first step to solve the problem consists in transforming this equation into a set of scalar ones using the well-known dynamic regressor extension and mixing technique. Then a novel procedure to generate new scalar exciting regressors is proposed. The superior performance of a classical gradient estimator using this new regressor, instead of the original one, is illustrated with comprehensive simulations.

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Accelerated Performance and Accelerated Learning with Discrete-Time High-Order Tuners

Cui¹,

Annaswamy²

2022

Preprint

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We consider two algorithms that have been shown to have accelerated performance, Polyak's heavy ball method and Nesterov's acceleration method. In the context of adaptive control, we show that both algorithms will present accelerated learning phenomenon under persistent excitation. Simulation results show that the two algorithms have very similar behavior and are both faster than normalized gradient descent.

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New Algorithms for Discrete-Time Parameter Estimation

Cited by 4 publications

References 0 publications

Integration of adaptive control and reinforcement learning for real-time control and learning

Integration of adaptive control and reinforcement learning for real-time control and learning

Generation of New Exciting Regressors for Consistent Online Estimation of Unknown Constant Parameters

Accelerated Performance and Accelerated Learning with Discrete-Time High-Order Tuners

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