Survey of duality between linear quadratic regulation and linear estimation problems for discrete-time systems

Song, X.; Yan, Xuehua; Li, Xiaodi

doi:10.1186/s13662-019-2043-2

Cited by 6 publications

(3 citation statements)

References 97 publications

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“…When the process and the observation noise are Gaussian, the optimal solution separates into a Kalman filter and a linear-quadratic regulator, known as linear-quadratic-Gaussian control. However, given that EnKF is a linear variant of the Kalman filter and that TDE falls within the category of linear estimation (or optimal control), 38 and the separation principle is still valid for our proposed controller.…”

Section: Control Synthesismentioning

confidence: 99%

Position control for an autonomous underwater vehicle under noisy conditions

Liu

2022

Proceedings of the Institution of Mechanical Engineers, Part I:

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Position tracking of an autonomous underwater vehicle is not trivial as its accuracy is affected by process noise, measurement noise, and uncertain hydrodynamic parameters. Thus, in this article, we studied the position control of an autonomous underwater vehicle that operates under largely unbounded system uncertainties and large noise levels and proposed a method that reduces the interference and thereby enhances the overall autonomous underwater vehicle position estimation. Our technique extended the ensemble Kalman filter by combining it with a time-delay estimator to compensate against extended uncertainty of the system dynamics which cannot be solved by the traditional ensemble Kalman filter. Our synthetic simulations demonstrated the effectiveness of the proposed controller, highlighting its appealing position-control accuracy under simultaneous noise and uncertain hydrodynamics parameters. In addition, our simulation results showed that the proposed controller outperforms the conventional time-delay controller by a percentage range of approximately 30.8%–92.6% in terms of root-mean-square error and requires on average less than 88.2% calculation time than the conventional model predictive control.

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Section: Control Synthesismentioning

confidence: 99%

Position control for an autonomous underwater vehicle under noisy conditions

Liu

2022

Proceedings of the Institution of Mechanical Engineers, Part I:

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“…Given that the process and the observation noise are Gaussian, the optimal solution can be separated into a Kalman Filter and a linear quadratic regulator, known as linear-quadratic Gaussian control. In this work, EnKF is a linear variant of the Kalman Filter, and thus, TDE can be considered to be a linear estimation (or optimal control) [35]. Therefore, the separation principle is still available for the designed controller.…”

Section: The Modified Algorithm Based On Enkfmentioning

confidence: 99%

Discrete-Time Position Control for Autonomous Underwater Vehicle under Noisy Conditions

Liu

2021

Applied Sciences

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This paper deals with the discrete-time position control problem for an autonomous underwater vehicle (AUV) under noisy conditions. Due to underwater noise, the velocity measurements returned by the AUV’s on-board sensors afford low accuracy, downgrading its control quality. Additionally, most of the hydrodynamic parameters of the AUV model are uncertain, further degrading the AUV control accuracy. Based on these findings, a discrete-time control law that improves the position control for the AUV trajectory tracking is presented to reduce the impact of these two factors. The proposed control law extends the Ensemble Kalman Filter and solves the problem of the traditional Ensemble Kalman Filter that underperforms when the hydrodynamic parameters of the AUV model are uncertain. The effectiveness of the proposed discrete-time controller is tested on various simulated scenarios and the results demonstrate that the proposed controller has appealing precision for AUV position tracking under noisy conditions and hydrodynamic parameter uncertainty. The proposed controller outperforms the conventional time-delay controller in root-mean-square error by a percentage range of approximately 72.1–97.4% and requires at least 89.5% less average calculation time than the conventional model predictive control.

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“…Neural Networks (NNs) have attracted great attention in recent decades owing to their extensive application in many different fields, such as optimization and signal processing [1][2][3][4][5], pattern recognition [6][7][8][9][10], parallel computing [11][12][13][14][15], and so forth. In the implementation of such applications, the phenomenon of time-varying delays (TDs) is inevitably encountered due to the inherent communication time among neurons, the finite switching speed of the amplifier [16][17][18][19], and other reasons. Furthermore, the structure and parameters of NNs are often subject to random abrupt variations caused by the external environment sudden change, the information latching [20], and so on.…”

Section: Introductionmentioning

confidence: 99%

Stochastically exponential synchronization for Markov jump neural networks with time-varying delays via event-triggered control scheme

et al. 2021

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This paper focuses on the stochastically exponential synchronization problem for one class of neural networks with time-varying delays (TDs) and Markov jump parameters (MJPs). To derive a tighter bound of reciprocally convex quadratic terms, we provide an improved reciprocally convex combination inequality (RCCI), which includes some existing ones as its particular cases. We construct an eligible stochastic Lyapunov–Krasovskii functional to capture more information about TDs, triggering signals, and MJPs. Based on a well-designed event-triggered control scheme, we derive several novel stability criteria for the underlying systems by employing the new RCCI and other analytical techniques. Finally, we present two numerical examples to show the validity of our methods.

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Survey of duality between linear quadratic regulation and linear estimation problems for discrete-time systems

Cited by 6 publications

References 97 publications

Position control for an autonomous underwater vehicle under noisy conditions

Position control for an autonomous underwater vehicle under noisy conditions

Discrete-Time Position Control for Autonomous Underwater Vehicle under Noisy Conditions

Stochastically exponential synchronization for Markov jump neural networks with time-varying delays via event-triggered control scheme

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