Asymptotic Recovery for Discrete-Time Systems

Maciejowski, Jan M.; Westaway, Peter

doi:10.23919/acc.1983.4788212

Cited by 22 publications

(61 citation statements)

References 2 publications

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“…The results show that the smoother of Method 1 provided the best overall performance. Variants of these one-step smoothing algorithms have been used in conjunction with IMM filtering algorithms to develop techniques for the alignment of asynchronous sensors [ 6 ] . Finally, approaches similar to the ones presented in this paper have been applied to the fixed-interval smoothing problem for Markovian switching systems ~71.…”

Section: Discussionmentioning

confidence: 99%

LTR design of discrete-time proportional-integral observers

Shafai

Beale

Niemann

et al. 1996

IEEE Trans. Automat. Contr.

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A Monte Carlo simulation with 500 experiments was executed, and the results are presented in Fig. 3. In each experiment, the measurement model in effect at each point of time was randomly chosen according to (65). In Fig. 3(a), the root-mean-square-error (RMSE) in the state estimate versus time is presented. Averaging the RMSE's over the time interval gives an average error of 10.75 for the IMM filter, 9.32 for the smoother of Method 1, and 9.42 for Method 2. Fig. 3(b) presents the probability of error in the system-stmcture detection versus time (i.e., the probability of choosing the incorrect measurement model at each point of time). Averaging the probabilities over the time interval gives an average probability of error of 0.19 for the IMM filter, 0.15 for Method 1, and 0.16 for Method 2.The two smoothers provided noticeably better performances than the IMM filter, while the smoother of Method 1 provided slightly better performance than Method 2. The smoother of Method 1 provided the best overall performance because it considered the most hypotheses.A simulation example comparing the performances of these algorithms in reconstructing the trajectory of a maneuvering target has also been performed. Detailed results are not presented because of space limitations. Both smoothers provided significantly better performance than the IMM filter in estimating the system state. However, unlike the system-structure simulation results above, the Method 1 smoother provided significantly better mode estimates than the Method 2 smoother. The mode estimates from the Method 2 smoother and the IMM filter were comparable. V. SUMMARYSuboptimal approaches to the one-step fixed-lag smoothing problem for Markovian switching systems were examined in this paper. Two algorithms for generating one-step fixed-lag smoothed estimates were presented. In the first algorithm, the models over the two most recent sampling periods were considered. For n models, there are n2 possible ways of conditioning on models in two sampling periods, and this algorithm evaluated the n2 hypotheses using n2 parallel one-step smoothers. In the second algorithm, only the models in the most recent sampling period were considered, and it evaluated 72 hypotheses using n parallel one-step smoothers. A simulation of a system-structure detection problem was used to compare the performances of the two smoothers and an IMM filter. The results show that the smoother of Method 1 provided the best overall performance. Variants of these one-step smoothing algorithms have been used in conjunction with IMM filtering algorithms to develop techniques for the alignment of asynchronous sensors [ 6 ] . Finally, approaches similar to the ones presented in this paper have been applied to the fixed-interval smoothing problem for Markovian switching systems ~71. Abstract-This paper applies the proportional-integral (PI) observer in connection with loop-transfer recovery (LTR) design for discrete-time systems. Both the prediction and the filtering versions of the PI observer are consid...

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Section: Discussionmentioning

confidence: 99%

LTR design of discrete-time proportional-integral observers

Shafai

Beale

Niemann

et al. 1996

IEEE Trans. Automat. Contr.

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“…Under appropriate hypotheses, the solution to the cheap control problem has appealing special properties [6].…”

Section: The Discrete Time Lqg Control Problemmentioning

confidence: 99%

Stabilization with disturbance attenuation over a Gaussian channel

Freudenberg

Middleton

Braslavsky

2007

2007 46th IEEE Conference on Decision and Control

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Abstract-We propose a linear control and communication scheme for the purposes of stabilization and disturbance attenuation when a discrete Gaussian channel is present in the feedback loop. Specifically, the channel input is amplified by a constant gain before transmission and the channel output is processed through a linear time invariant filter to produce the control signal. We show how the gain and filter may be chosen to minimize the variance of the plant output. For an order one plant, our scheme achieves the theoretical minimum taken over a much broader class of compensators.

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“…The fact that the Riccati equation for discrete-time cheap optimal control has a parametric solutionX = c T c may be not well-known, I suppose, but can be seen in the literature published in the middle of 80s [29], [30]. As mentioned above, nonuniqueness of positive semi-definite solution is the most significant contrast to the standard case.…”

Section: Theoremmentioning

confidence: 99%

“…From (18), one can computeR,Ā and v by (11), (23) and (14), respectively. This gives the coefficient matrices in (29). A numerical computation shows that (29) for γ = 0.009 is feasible 3 .…”

Section: Lemma 1 Letmentioning

confidence: 99%

On Internal Stabilizing Mechanism of Passive Dynamic Walking

Hirata

2011

SICE Journal of Control, Measurement, and System Integration

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: In this paper, the relationship between the internal stabilizing mechanism of passive dynamic walking and linear optimal control is investigated. In contrast to existing results, it is shown that the stabilizing mechanism can be characterized as a special type of optimal control. After verifying the feasibility of such a formulation numerically, it is proved that the internal stabilizing feedback coincides with a cheap optimal control law.

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Asymptotic Recovery for Discrete-Time Systems

Cited by 22 publications

References 2 publications

LTR design of discrete-time proportional-integral observers

LTR design of discrete-time proportional-integral observers

Stabilization with disturbance attenuation over a Gaussian channel

On Internal Stabilizing Mechanism of Passive Dynamic Walking

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