Stabilization with data-rate-limited feedback: tightest attainable bounds

Nair, Girish N.; Evans, Robin J.

doi:10.1016/s0167-6911(00)00037-2

Cited by 292 publications

(172 citation statements)

References 11 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: 79%

“…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: 79%

Section: Introductionmentioning

confidence: 99%

Optimal Infinite Horizon Control Under a Low Data Rate 2

Nair

Huang

Evans

2006

IFAC Proceedings Volumes

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“…The stabilization problem by quantized feedback has been widely studied in the last few years: see [1,2,4,5,7,13,16,18,19] and the reference therein. Quantization can not be avoided in the digital control setting and it is indeed a natural way to insert into the control design complexity constraints of the controller and communication constraints of the channels which connect the controller and the plant.…”

Section: Introductionmentioning

confidence: 99%

Quantized Stabilization of Linear Systems: Complexity Versus Performance

Fagnani

Zampieri

2004

IEEE Trans. Automat. Contr.

100

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Quantized feedback control has been receiving much attention in the control community in the past few years. Quantization is indeed a natural way to take into consideration in the control design the complexity constraints of the controller as well as the communication constraints in the information exchange between the controller and the plant. In this paper we analyze the stabilization problem for discrete time linear systems with multidimensional state and one-dimensional input using quantized feedbacks with a memory structure, focusing on the trade off between complexity and performance. A quantized controller with memory is a dynamical system with a state space, a state updating map and an output map.The quantized controller complexity is modelled by means of three indices. The first index L coincides with the number of the controller states. The second index is the number M of the possible values that the state updating map of the controller can take at each time. The third index is the number N of the possible values that the output map of the controller can take at each time. The index N corresponds also to the number of the possible control values that the controller can choose at each time.In this paper the performance index is chosen to be the time T needed to shrink the state of the plant from a starting set to a target set. Finally, the contraction rate C, namely the ratio between the volumes of the starting and target sets, is introduced. We evaluate the relations between these parameters for various quantized stabilizers, with and without memory, and we make some comparisons. Then we prove a number of results showing the intrinsic limitations of the quantized control. In particular we show that, in order to obtain a control strategy which yields arbitrarily small values of T / ln C (requirement which can be interpreted as a weak form of the pole assignability property), we need to have that LN/ ln C is big enough.

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“…This value should be high enough for stabilizing the closed-loop system (cf. [WB99,NE00]) and make the white noise model a reasonable assumption in a feedback control context (cf. [WKL96,FPW90]).…”

Section: White-noise Quantization Error Modelmentioning

confidence: 99%

Joint Optimization of Wireless Communication and Networked Control Systems

Xiao

Johansson

Hindi

et al. 2005

Switching and Learning in Feedback Systems

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Abstract. We consider a linear system, such as an estimator or a controller, in which several signals are transmitted over wireless communication channels. With the coding and medium access schemes of the communication system fixed, the achievable bit rates are determined by the allocation of communications resources such as transmit powers and bandwidths, to different channels. Assuming conventional uniform quantization and a standard white-noise model for quantization errors, we consider two specific problems. In the first, we assume that the linear system is fixed and address the problem of allocating communication resources to optimize system performance. We observe that this problem is often convex (at least, when we ignore the constraint that individual quantizers have an integral number of bits), hence readily solved. We describe a dual decomposition method for solving these problems that exploits the problem structure. We briefly describe how the integer bit constraints can be handled, and give a bound on how suboptimal these heuristics can be. The second problem we consider is that of jointly allocating communication resources and designing the linear system in order to optimize system performance. This problem is in general not convex. We present an iterative heuristic method based on alternating convex optimization over subsets of variables, which appears to work well in practice.

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Stabilization with data-rate-limited feedback: tightest attainable bounds

Cited by 292 publications

References 11 publications

Optimal Infinite Horizon Control Under a Low Data Rate 2

Optimal Infinite Horizon Control Under a Low Data Rate 2

Quantized Stabilization of Linear Systems: Complexity Versus Performance

Joint Optimization of Wireless Communication and Networked Control Systems

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