Disturbance rejection with information constraints: Performance limitations of a scalar system for bounded and Gaussian disturbances

Shingin, Hidenori; Ohta, Yuichi

doi:10.1016/j.automatica.2012.02.040

Cited by 23 publications

(18 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Using these results, it was then established that the state of a noiseless LTI system can be estimated via such a channel with exponential uniform accuracy iff an inequality linking the unstable plant eigenvalues, the desired exponential rate of convergence and C 0 was satisfied. Though other nonstochastic information functionals had been previously proposed in [15], [16], these results indicate that I * may be particularly relevant when dynamical systems or erroneous channels are involved.…”

Section: Introductionmentioning

confidence: 69%

“…The main result of this section follows: Theorem 4.1: Consider a linear time-invariant plant (20)-(21), with plant matrix A ∈ R n×n , uncertain initial state X(0) and outputs that are coded and controlled (22)-(23) via a stationary memoryless uncertain channel (Def. 2.6) with zero-error feedback capacity C 0f (16). Assume that at any time t ∈ Z ≥0 , the channel output Q(t) is conditionally unrelated with (X(0), S(0 : t − 1)) given the channel input S(t) (Def.…”

Section: Controlling Lti Plants Via Erroneous Channelsmentioning

confidence: 99%

See 1 more Smart Citation

A nonstochastic information theory for feedback

Nair

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

This paper extends a recently proposed theory of nonstochastic maximin information to study feedback systems with erroneous channels. The concepts of conditional and directed maximin information are introduced, without assuming any statistical structure. It is proved that the zero-error feedback capacity of a stationary memoryless channel coincides with the largest rate of directed maximin information across it. This provides a nonstochastic counterpart to recent results in information theory. This characterization is then used to find a tight condition for exponential uniform stabilizability of a linear time-invariant plant over an erroneous channel, consistent with a result of Matveev and Savkin.

show abstract

Section: Introductionmentioning

confidence: 69%

Section: Controlling Lti Plants Via Erroneous Channelsmentioning

confidence: 99%

A nonstochastic information theory for feedback

Nair

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

show abstract

“…(13) This is essentially the approach proposed in [4], where its operational relevance was established for control problems involving errorless digital channels. Nonetheless, significant modifications of this definition are needed, stemming from the following two observations.…”

Section: Maximin Informationmentioning

confidence: 99%

“…This leads to the notions of Hartley entropy [2] for discrete-valued variables, and Rényi differential 0th-order entropy [3] for continuousvalued variables, neither of which require statistical structure. Using the latter entropy, a nonstochastic information index for continuous-valued, bounded rv's was introduced in [4] to study control over errorless digital channels. 1 A different construction had previously been proposed in [6].…”

Section: Introductionmentioning

confidence: 99%

A non-stochastic information theory for communication and state estimation over erroneous channels

Nair

2011

2011 9th IEEE International Conference on Control and Automation (ICCA)

View full text Add to dashboard Cite

In communications, unknown variables are usually modelled as random variables, with concepts such as independence, entropy and information given in terms of the underlying probability distributions. In contrast, control theory often treats uncertainties and disturbances as bounded unknowns having no statistical structure. The area of networked control combines both fields and raises the question of whether it is possible to construct meaningful analogues of important stochastic concepts such as independence, Markovianness, entropy, and information, without assuming a probability space. This paper introduces a framework for doing so, leading in particular to the construction of a maximin information functional for non-stochastic variables. It is shown that, in this framework, the largest maximin information rate through a memoryless, error-prone channel coincides exactly with its block-coding zero-error capacity. This leads to a tight condition for the achievability of uniform exponential convergence when estimating the state of an unperturbed linear system over such a channel, similar to recent results of Matveev and Savkin.

show abstract

“…The SNR limitation for Gaussian channels given in [13] is shown to be valid for nonlinear controllers by [14] using entropy. Our approach based on generalized entropy [18], [19] provides an unified method for deriving the limitations under bounded and Gaussian disturbances. As information measures adapted to dynamical systems, directed information [3], [4], [11], [16] and non-probabilistic information [9] are also effectively employed for limitation analyses.…”

Section: Introductionmentioning

confidence: 99%

SNR limitation for feedback control systems with amplitude-bounded noise

Shingin

Ohta

2014

2014 IEEE International Symposium on Intelligent Control (ISIC)

Self Cite

View full text Add to dashboard Cite

This paper presents an SNR limitation in control under amplitude-bounded noise. The SNR of feedback link in control system is evaluated with respect to amplitude and minimized over all causal control laws. The minimum SNR is represented by the absolute value of the product of unstable poles of the plant. This index is known to describe performance limitations in various control problems. The optimal control law minimizing the SNR is simply constructed as a combination of scaling factor and the state feedback gain for minimum energy control. This control law overcomes the drawback of computational complexity of the encoding scheme minimizing bit-rate, which is employed to minimize an amplitude-base SNR in our preceding work. This simplification is accomplished by relaxing the requirement of stability to the convergence of the state to near the origin and introducing a new criterion for evaluating SNR.

show abstract

Disturbance rejection with information constraints: Performance limitations of a scalar system for bounded and Gaussian disturbances

Cited by 23 publications

References 7 publications

A nonstochastic information theory for feedback

A nonstochastic information theory for feedback

A non-stochastic information theory for communication and state estimation over erroneous channels

SNR limitation for feedback control systems with amplitude-bounded noise

Contact Info

Product

Resources

About