Retrospective Cost Adaptive Control: Pole Placement, Frequency Response, and Connections with LQG Control

Rahman, Yousaf; Xie, Antai; Bernstein, Dennis S.

doi:10.1109/mcs.2017.2718825

Cited by 61 publications

(13 citation statements)

References 74 publications

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“…3) e, θ → 0 exponentially, ∀t ≥ 0 when PE in Definition 1 exists for certain constants τ d , σ ∈ R + . Theorem 2 extends the adaptive estimation results in Theorem 1 regarding the convergence of the prediction error ε and the estimation error θ to the control problem that considers the extra convergence of the tracking error e. The PE requirement of the CAC scheme in Theorem 2 to achieve exponential stability with the convergence of θ results from the fact that only instantaneous data at the current time t are utilized to update the parameter estimate θ in (7). In the following sections, we will review four MRE schemes 3 for parameter estimation in adaptive systems, where all of them can achieve the exponential convergence of θ without the classical PE condition in Definition 1.…”

Section: Composite Adaptive Controlmentioning

confidence: 79%

“…which is a SE condition in Definition 3 with respect to Φ f . The parameter update law ( 15) is questionable because the setting ξ(0) = λΘ(0) θ(0) is impossible due to Θ 0 ̸ = 0 and θ(0) being unknown 7 . In [42], the method in [39] was extended to the system (1) without the above drawback, in which finitetime parameter convergence is achieved under the SE condition, and robust parameter estimation is demonstrated under bounded perturbations.…”

Section: Full Data-driven Mrementioning

confidence: 99%

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Adaptive Estimation and Control With Online Data Memory: A Historical Perspective

Pan,

Shi

2024

IEEE Control Syst. Lett.

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Online data memory is essential for adaptive estimation and control as it can enhance the performance and robustness of adaptive systems compared to adaptive systems without data memory. We provide an overview of four data memory-driven parameter estimation schemes for adaptive systems from a historical perspective, including forgetting-data memory regression extension (MRE), full-data MRE, discrete-data MRE, and interval-data MRE. For clear presentation and better understanding, a general class of nonlinear systems with linear-in-the-parameter uncertainties is applied as a unifying framework to demonstrate the motivation, synthesis, and characteristics of each MRE scheme for parameter estimation in adaptive control. Intensive comparisons of the four MRE schemes are provided to reveal their technical natures, and real-world applications are discussed to show their practicability. It is concluded that all the MRE schemes can achieve exponential parameter convergence under relaxed excitation conditions rather than the classical condition of persistent excitation which is too stringent to satisfy in practice. The distinctive features of intervaldata MRE termed composite learning are highlighted with respect to computational simplicity, estimation accuracy, robustness against perturbations, and widespread real-world applications to robot learning and control. Possible directions for future research in this area are suggested to conclude this survey.

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Section: Composite Adaptive Controlmentioning

confidence: 79%

Section: Full Data-driven Mrementioning

confidence: 99%

Adaptive Estimation and Control With Online Data Memory: A Historical Perspective

Pan,

Shi

2024

IEEE Control Syst. Lett.

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“…Then in order to obtain a basic estimate on the maximum number of iterations needed for convergence, the Schulz algorithm (1), (2) was executed for each resulting matrix above in order to obtain a basic estimate. The above results are presented in Figure 8 where, out of the 636 elements of the pseudo-inverse solution, the evolution of elements (59,8), (60,9), (13,27) and (14,28) is indicatively shown in the first four graphs of the figure. In addition, the last graph Figure 8 shows the evolution of the convergenceexpression (32).…”

Section: Example 5 ; 2 × 2 Interval Matrix Matrix a =mentioning

confidence: 87%

“…The falsification approach above is illustrated with the following example. In the numerical experiments matrix elements (8,59) and (9,60) were varied within the interval [0, 2] and elements (27,13) and (28,14) within the interval [−2, 0] . The above element variation corresponds to a ±100% range of their original values.…”

Section: Example 5 ; 2 × 2 Interval Matrix Matrix a =mentioning

confidence: 99%

“…The impact of contributions of the paper can be foreseen within the area of software certification standards DO178C [63], based on its formal methods supplement DO333 [62], targeting aerospace applications where embedded systems reliability is of primary importance. Furthermore, it is evident that adaptive system control and machine intelligence technologies [60] are emerging in modern cyber-physical system applications. Many of such developments are using advanced matrix iterative algorithms, comparable to Schulz algorithm (1), the operational assurance of which is significant for real time embedded systems applications.…”

mentioning

confidence: 99%

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Formal analysis of the Schulz matrix inversion algorithm: A paradigm towards computer aided verification of general matrix flow solvers

Tsachouridis¹,

Giantamidis²,

Basagiannis³

et al. 2020

Numerical Algebra, Control &Amp; Optimization

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This paper pilots Schulz generalised matrix inverse algorithm as a paradigm in demonstrating how computer aided reachability analysis and theoretical numerical analysis can be combined effectively in developing verification methodologies and tools for matrix iterative solvers. It is illustrated how algorithmic convergence to computed solutions with required accuracy is mathematically quantified and used within computer aided reachability analysis tools to formally verify convergence over predefined sets of multiple problem data. In addition, some numerical analysis results are used to form computational reliability monitors to escort the algorithm on-line and monitor the numerical performance, accuracy and stability of the entire computational process. For making the paper self-contained, formal verification preliminaries and background on tools and approaches are reported together with the detailed numerical analysis in basic mathematical language. For demonstration purposes, a custom made reachability analysis program based on affine arithmetic is applied to numerical examples.

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Retrospective‐cost‐based model reference adaptive control of nonminimum‐phase systems

Mohseni,

Bernstein

2024

Adaptive Control & Signal

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This paper presents a novel approach to model reference adaptive control inspired by the adaptive pole‐placement controller (APPC) of Elliot and based on retrospective cost optimization. Retrospective cost model reference adaptive control (RC‐MRAC) is applicable to nonminimum‐phase (NMP) systems assuming that the NMP zeros are known. Under this assumption, the advantage of RC‐MRAC is a reduced need for persistency. The present paper compares APPC and RC‐MRAC under various levels of persistency in the command for minimum‐phase and NMP systems. It is shown numerically that the model‐following performance of RC‐MRAC is less sensitive to the persistency of the command compared to APPC at the cost of knowledge of the NMP zeros. RC‐MRAC is also shown to be applicable for disturbance rejection under unknown harmonic disturbances.

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Retrospective Cost Adaptive Control: Pole Placement, Frequency Response, and Connections with LQG Control

Cited by 61 publications

References 74 publications

Adaptive Estimation and Control With Online Data Memory: A Historical Perspective

Adaptive Estimation and Control With Online Data Memory: A Historical Perspective

Formal analysis of the Schulz matrix inversion algorithm: A paradigm towards computer aided verification of general matrix flow solvers

Retrospective‐cost‐based model reference adaptive control of nonminimum‐phase systems

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