Interplay Between Transmission Delay, Average Data Rate, and Performance in Output Feedback Control over Digital Communication Channels

The performance of a noisy linear time-invariant (LTI) plant, controlled over a noiseless digital channel with transmission delay, is investigated in this paper. The rate-limited channel connects the single measurement output of the plant to its single control input through a causal, but otherwise arbitrary, coder-controller pair. An infomation-theoretic approach is utilized to analyze the minimal average data rate required to attain the quadratic performance when the channel imposes a known constant delay on the transmitted data. This infimum average data rate is shown to be lower bounded by minimizing the directed information rate across a set of LTI filters and an additive white Gaussian noise (AWGN) channel. It is demonstrated that the presence of time delay in the channel increases the data rate needed to achieve a certain level of performance. The applicability of the results is verified through a numerical example. In particular, we show by simulations that when the optimal filters are used but the AWGN channel (used in the lower bound) is replaced by a simple scalar uniform quantizer, the resulting operational data rates are at most around 0.3 bits above the lower bounds.Comment: A less-detailed version of this paper has been accepted for publication in the proceedings of ACC 201

On the Minimal Average Data-Rate that Guarantees a Given Closed Loop Performance Level

This paper deals with control system design subject to average data-rate constraints. By focusing on SISO LTI plants, and a class of source coding schemes, we establish lower and upper bounds on the minimal average data-rate needed to achieve a prescribed performance level. We also provide a specific source coding scheme, within the proposed class, that is guaranteed to achieve the desired performance level at average data-rates below our upper bound. Our results are based upon a recently proposed framework to address control problems subject to average data-rate constraints.

Energy-Aware Competitive Power Allocation for Heterogeneous Networks Under QoS Constraints

This work proposes a distributed power allocation scheme for maximizing energy efficiency in the uplink of orthogonal frequency-division multiple access (OFDMA)-based heterogeneous networks (HetNets). The user equipment (UEs) in the network are modeled as rational agents that engage in a non-cooperative game where each UE allocates its available transmit power over the set of assigned subcarriers so as to maximize its individual utility (defined as the user's throughput per Watt of transmit power) subject to minimum-rate constraints. In this framework, the relevant solution concept is that of Debreu equilibrium, a generalization of Nash equilibrium which accounts for the case where an agent's set of possible actions depends on the actions of its opponents. Since the problem at hand might not be feasible, Debreu equilibria do not always exist. However, using techniques from fractional programming, we provide a characterization of equilibrial power allocation profiles when they do exist. In particular, Debreu equilibria are found to be the fixed points of a water-filling best response operator whose water level is a function of minimum rate constraints and circuit power. Moreover, we also describe a set of sufficient conditions for the existence and uniqueness of Debreu equilibria exploiting the contraction properties of the best response operator. This analysis provides the necessary tools to derive a power allocation scheme that steers the network to equilibrium in an iterative and distributed manner without the need for any centralized processing. Numerical simulations are then used to validate the analysis and assess the performance of the proposed algorithm as a function of the system parameters.Comment: 37 pages, 12 figures, to appear IEEE Trans. Wireless Commu

On Resilient Control of Nonlinear Systems under Denial-of-Service

We analyze and design a control strategy for nonlinear systems under Denial-of-Service attacks. Based on an ISS-Lyapunov function analysis, we provide a characterization of the maximal percentage of time during which feedback information can be lost without resulting in the instability of the system. Motivated by the presence of a digital channel we consider event-based controllers for which a minimal inter-sampling time is explicitly characterized.Comment: 7 pages, 1 figur