Randomized algorithms for robust controller synthesis using statistical learning theory

Vidyasagar, M.

doi:10.1016/s0005-1098(01)00122-4

Cited by 202 publications

(100 citation statements)

References 20 publications

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“…Thus, in finite time the control scheme is robust, and it progressively becomes better performing. The use of average control cost criteria was originally proposed in [11] in the context of robust control and then extended to the adaptive control context in [12]. In these references, randomized algorithms are used to make the minimization of the average control cost computationally tractable.…”

Section: ])mentioning

confidence: 99%

“…For many control objectives, the integrand function J(ϑ, γ) cannot be computed in a closed-form and even the evaluation of J(ϑ, γ) for a given pair (ϑ, γ) may be time consuming. The approach adopted here to overcome this difficulty follows to a large extent the ideas in [11,12] and is based on the use of randomized methods. The resulting minimizers are not rigorously optimal (i.e., they do not minimize E Pt [J(ϑ, γ)] with probability 1).…”

Section: Compute M T and V T Through The Kalman Filter Equationsmentioning

confidence: 99%

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Cautious hierarchical switching control of stochastic linear systems

Campi

Hespanha

Prandini

2004

Adaptive Control & Signal

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Standard switching control methods are based on the certainty equivalence philosophy in that, at each switching time, the supervisor selects the candidate controller that is better tuned to the currently estimated process model. If the estimated model does not appropriately describe the process, this procedure may result in the selection of a controller that is not appropriate for the actual process.In this paper, we propose a supervisory switching logic that takes into account the uncertainty on the process description when performing the controller selection. Specifically, a probability measure describing the likelihood of the different models is computed on-line based on the collected data and, at each switching time, the supervisor selects the candidate controller that, according to this probability measure, performs the best on the average. If the candidate controller set is hierarchically structured, the supervisor automatically selects the controller that appropriately compromises robustness and performance, given the actual level of uncertainty on the process description. The use of randomized algorithms makes the supervisor implementation computationally tractable.

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Section: ])mentioning

confidence: 99%

Section: Compute M T and V T Through The Kalman Filter Equationsmentioning

confidence: 99%

Cautious hierarchical switching control of stochastic linear systems

Campi

Hespanha

Prandini

2004

Adaptive Control & Signal

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“…Ray and Stengel (1993); Tempo and Dabbene (1999); Vidyasagar and Blondel (2001) and Vidyasagar (2001). The main idea behind randomized methods is to associate a probability distribution to the uncertainty set, and to assess system performance in terms of empirical probability.…”

Section: A Probabilistic Framework For Uncertain Systemsmentioning

confidence: 99%

“…E-mail addresses: calaÿore@polito.it (G. Calaÿore), dabbene@ polito.it (F. Dabbene). Blondel, 2001;Vidyasagar, 2001). It turns out that problems that are computationally hard in a deterministic setting may be e ciently solved using randomized algorithms, if a certain probability of performance degradation is accepted (Khargonekar & Tikku, 1996;Tempo, Bai, & Dabbene, 1997;Vidyasagar, 1997).…”

Section: Introductionmentioning

confidence: 99%

A probabilistic framework for problems with real structured uncertainty in systems and control

Calafiore

Dabbene

2002

Automatica

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The objective of this paper is twofold. First, the problem of generation of real random matrix samples with uniform distribution in structured (spectral) norm bounded sets is studied. This includes an analysis of the distribution of the singular values of uniformly distributed real matrices, and an e cient (i.e. polynomial-time) algorithm for their generation. Second, it is shown how the developed techniques may be used to solve in a probabilistic setting several hard problems involving systems subject to real structured uncertainty. ?

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“…Classical robustness analysis usually considers the worst-case scenario of uncertainties, meaning that the stability and desired performance characteristics should always be satisfied with the parameters within the largest uncertain range. However, in practice, if the worst case occurs quite rarely, the designed controller is often too conservative and its performance is not satisfactory [10], [12]. On the other hand, by assuming a probabilistic distribution of the parameter uncertainties, the probability that a specific performance is satisfied can be evaluated by randomized algorithms.…”

Section: Algorithms For Jump Linear Systemsmentioning

confidence: 99%

Analysis of fault tolerant control by using randomized algorithms

Zhao

Proceedings of the 2005, American Control Conference, 2005.

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Abstract-Active Fault Tolerant Control Systems (FTCS)can be modeled as stochastic systems with Markovian parameters. This paper addresses the modeling and analysis of such systems by using the randomized algorithms. Such algorithms are usually used to perform the robustness analysis or robust control synthesis based on a probabilistic notion. This paper extends the methods to Jump Linear Systems (JLS) and stochastic FTCS for performance verification. It discusses how to set up a model for FTCS from the imperfect FDI parameters and how to transform it into a JLS model. Then, by combining the stationary distribution of the Markov process and specific performance at each state, it presents two algorithms to estimate probability given the performance requirement or estimate performance given the probability requirement. The performance analysis can reveal some valuable results on the influence of imperfect FDI and properties of integrated design, as illustrated in the examples.

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Randomized algorithms for robust controller synthesis using statistical learning theory

Cited by 202 publications

References 20 publications

Cautious hierarchical switching control of stochastic linear systems

Cautious hierarchical switching control of stochastic linear systems

A probabilistic framework for problems with real structured uncertainty in systems and control

Analysis of fault tolerant control by using randomized algorithms

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