Exponential stabilisability of finite-dimensional linear systems with limited data rates

Nair, Girish N.; Evans, R.J.

doi:10.1016/s0005-1098(02)00285-6

Cited by 438 publications

(262 citation statements)

References 14 publications

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“…Observe that the minimum cost → ∞ as |S| − |a| → 0, agreeing with results from (Nair and Evans, 2000;Nair and Evans, 2003). As a further check, note that since the quantisation errors become negligible as the channel alphabet size |S| grows, the channel-constrained optimal cost should approach the unconstrained mean classical optimal LQR cost.…”

Section: Proof: Omittedsupporting

confidence: 80%

“…The definitions of the coder, channel and controller below are nearly identical to (Nair and Evans, 2003). Suppose that the sensor which observes the states of the system is connected to the controller via a digital channel onto which one symbol s t from a fixed, finite alphabet S is transmitted during the (t + 1)th sampling interval.…”

Section: Formulationmentioning

confidence: 99%

“…Note that an average over the initial state pdf is taken because the controller here does not know the exact initial state, whereas the unaveraged LQR-optimal policy would not necessarily be independent of x 0 as in the classical case, due to the nonlinearity induced by the digital channel. It can be shown using (Nair and Evans, 2003) that, unlike the deterministic classical LQR problem, a finite cost here is possible iff |S| > max{|a|, 1}, provided also that X 0 has a finite absolute moment E{|X 0 | 2+ε } < ∞ for some ε > 2. Assuming throughout this paper that these conditions hold, the infimum cost…”

Section: Formulationmentioning

confidence: 99%

“…It is well-known now that at low data rates, control performance degrades drastically and even the most basic objective such as stability can become impossible. Much of the theoretical research in this area has focused on determining minimum feedback data rates for various notions of stabilisability (Wong and Brockett, 1999;Baillieul, 2001;Nair and Evans, 2000;Tatikonda and Mitter, 2000;Nair and Evans, 2003;Nair and Evans, 2004;Li and Baillieul, 2004), and precise expressions have been derived in terms of the unstable open-loop eigenvalues of the plant.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Infinite Horizon Control Under a Low Data Rate 2

Nair

Huang

Evans

2006

IFAC Proceedings Volumes

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This paper considers the optimal control of linear systems where measurement data is transmitted from the plant output to the controller over a noiseless communication channel with limited instantaneous data rate. The cost is defined to be the average, over a random initial state, of the usual infinite horizon quadratic regulation criterion, and the number of bits transported by the channel during each sampling interval is bounded. Several fundamental properties of the optimal cost functional are derived for initial state densities that satisfy a mild moment condition. Using these properties, precise expressions for the optimal cost and policy are obtained assuming a uniformly distributed initial state. These expressions agree with the classical optimal LQR results in the high data rate limit and with recent minimum rate results in the low rate regime. Extensions to the case of non-uniform densities and vector-valued states are discussed.

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Section: Proof: Omittedsupporting

confidence: 80%

Section: Formulationmentioning

confidence: 99%

Section: Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal Infinite Horizon Control Under a Low Data Rate 2

Nair

Huang

Evans

2006

IFAC Proceedings Volumes

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“…The research on stabilization of linear time-invariant systems with limited data rate was addressed. The fundamental problem of finding the lower bound on the data rate for stabilization was solved in [8][9][10]. There has been a lot of new interest in quantized feedback control where the measurements are quantized, coded and transmitted over a digital communication channel.…”

mentioning

confidence: 99%

Stabilization of Unmanned Air Vehicles over Wireless Communication Channels

Liu

2013

TELKOMNIKA

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Abstrak IntroductionThe research on networked control systems has received resurgent interests in recent years [1][2][3]. Some salient examples include unmanned air vehicles (UAVs), unmanned ground vehicles (UGVs), and unmanned underwater vehicles (UUVs) [4][5][6]. The presence of such digital and wireless communication channels which connect the sensor and the controller or the actuator and the controller brings up many challenges, and makes some traditional control approaches inapplicable or inefficient.One of the earliest papers on the topic is [7], where a weaker stability concept called containability was introduced, and the issue of coding and communication protocol became an integral part of the analysis. The research on stabilization of linear time-invariant systems with limited data rate was addressed. The fundamental problem of finding the lower bound on the data rate for stabilization was solved in [8][9][10]. There has been a lot of new interest in quantized feedback control where the measurements are quantized, coded and transmitted over a digital communication channel. A fundamental problem is how to design a quantization, coding and control scheme in order to achieve some given control performances.The research on quantized feedback control can be categorized depending on whether the quantizer is static or dynamic. Static quantizers were employed in [11][12][13]. In particular, it was shown in [8] that the coarsest quantizer is logarithmic. The results were generalized in [13] to a number of output feedback problems using a sector bound approach. Furthermore, dynamic quantizers were employed in [14][15][16][17][18]. It was shown in [14] that stabilization of a singleinput single-output (SISO) linear time-invariant (LTI) system could be achieved by employing only a finite number of quantization levels. It was shown in [15] that a feedback policy could be designed to bring the closed-loop state arbitrarily close to zero for an arbitrarily long time by employing a quantizer with various sensitivity.We addressed the observer-based, dynamic state feedback stabilization problem for

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Fault Detection of Networked Control Systems

Mahmoud

Xia

2013

Analysis and Synthesis of Fault‐Tolerant Control Systems

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Exponential stabilisability of finite-dimensional linear systems with limited data rates

Cited by 438 publications

References 14 publications

Optimal Infinite Horizon Control Under a Low Data Rate 2

Optimal Infinite Horizon Control Under a Low Data Rate 2

Stabilization of Unmanned Air Vehicles over Wireless Communication Channels

Fault Detection of Networked Control Systems

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