Stability robustness of the discrete-time LQG system under plant perturbation and noise uncertainty

Luo, J. S.; Johnson, A.

doi:10.1080/00207179208934296

Cited by 12 publications

(4 citation statements)

References 7 publications

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“…The approach proposed in this work is based on the separation principle of LQG. However, when we consider the uncertainty of model parameters, the separation principle will be invalid [48]. Therefore, there is no theoretical analysis of the effect of model parameters uncertainty and this uncertainty is not considered in the planning stage.…”

Section: B Planning Under Various Spatially Varying Noise 1) Holonommentioning

confidence: 99%

Speeding up Gaussian Belief Space Planning for Underwater Robots Through a Covariance Upper Bound

Liu

et al. 2019

IEEE Access

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Existing belief space motion planning methods are not efficient for underwater robots that are subject to spatially varying motion and sensing uncertainties arising from the non-uniform current disturbances and landmark populations, respectively. Based on a closed-loop stochastic control framework, we propose a fast Gaussian belief space planning approach for coupled optimization of trajectory, localization and control, resulting in a non-linear programming problem (NLP). In particular, as opposed to advancing the covariance by a Kalman filter in the existing literature, we utilize an upper bound of the trace propagation of the covariance, thereby avoiding to solve Riccati equations and thus, reducing the computational complexity. The NLP is then efficiently solved by sequential quadratic programming based on the initial solutions obtained from RRT-connect. These initials lie in multiple homotopy classes guaranteed by H-signature discrimination, leading to global optimality with probability one as the number of samples in RRT-connect goes to infinity. Numerical simulations on holonomic and non-holonomic autonomous underwater vehicles (AUVs) and an Intervention-AUV with a manipulator in cluttered underwater environments demonstrate that optimal and collision-free trajectories with low localization uncertainty are obtained efficiently.

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Section: B Planning Under Various Spatially Varying Noise 1) Holonommentioning

confidence: 99%

Speeding up Gaussian Belief Space Planning for Underwater Robots Through a Covariance Upper Bound

Liu

et al. 2019

IEEE Access

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“…But unfortunately both the plant parameters and the noise covariances are often approximations and subject to changes or are slowly varying [1]. The parameter perturbations and noise uncertainties may destroy the system performance or even destabilize the controlled system.…”

Section: Introductionmentioning

confidence: 99%

“…The parameter perturbations and noise uncertainties may destroy the system performance or even destabilize the controlled system. Recently, the stability robustness of the discrete-time LQG problem has studied by Luo and Johnson [1] and Chen and Chou [2]. Luo and Johnson [1] gave a simple method to prove the saddle point inequality [3,4] of the closed-loop system performance to cope with the noise uncertainties, and they derived a sufficient condition for the stability robustness of the discrete-time LQG problem with linear time-varying plant perturbations.…”

Section: Introductionmentioning

confidence: 99%

“…Luo and Johnson [1] gave a simple method to prove the saddle point inequality [3,4] of the closed-loop system performance to cope with the noise uncertainties, and they derived a sufficient condition for the stability robustness of the discrete-time LQG problem with linear time-varying plant perturbations. Chen and Chou [2] have proposed a new sufficient condition and gave an example to show numerically that their proposed new sufficient condition is less conservative than the previous condition proposed by Luo and Johnson [1].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust stability analysis for discrete-time LQG system under finite wordlength effects, noise uncertainties and time-varying structured parameter perturbations

Chen

Chou

2004

Mathematics and Computers in Simulation

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Robust LQG control system under parameter uncertainty

Maki¹,

Hagino²

1994

Electron Comm Jpn Pt III

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This paper presents a method of designing a robust linear quadratic Gaussian (LQG) controller for systems with unknown parameters when an accurate model is not available. The proposed robust LQG control scheme results in the prevention of the system performance deterioration caused by the parameter uncertainty without estimating unknown parameters explicitly. First, an approximate model is introduced to describe the uncertain parts of the plant and a target model which the controlled system should track is constructed based on the known nominal system and the approximate signal generated by this approximate model. Next, this tracking problem is changed to the LQG control one for an augmented system. This target trajectory is determined automatically in control operation for the augmented system. Further, both the controller and filter gain are determined as a solution of a deterministic suboptimal control problem.

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Stability robustness of the discrete-time LQG system under plant perturbation and noise uncertainty

Cited by 12 publications

References 7 publications

Speeding up Gaussian Belief Space Planning for Underwater Robots Through a Covariance Upper Bound

Speeding up Gaussian Belief Space Planning for Underwater Robots Through a Covariance Upper Bound

Robust stability analysis for discrete-time LQG system under finite wordlength effects, noise uncertainties and time-varying structured parameter perturbations

Robust LQG control system under parameter uncertainty

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