Rate-cost tradeoffs in control

Consider a distributed control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is minimize a quadratic cost function. The most basic special case of that cost function is the mean-square deviation of the system state from the desired state. We study the fundamental tradeoff between the communication rate r bits/sec and the limsup of the expected cost b, and show a lower bound on the rate necessary to attain b. The bound applies as long as the system noise has a probability density function. If target cost b is not too large, that bound can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's belief about the current state and the true state

Rate-Cost Tradeoffs in Control

Consider a control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is to minimize a quadratic cost function in the state variables and control signal, known as the linear quadratic regulator (LQR). We study the fundamental tradeoff between the communication rate r bits/sec and the expected cost b. We obtain a lower bound on a certain rate-cost function, which quantifies the minimum directed mutual information between the channel input and output that is compatible with a target LQR cost. The rate-cost function has operational significance in multiple scenarios of interest: among others, it allows us to lower-bound the minimum communication rate for fixed and variable length quantization, and for control over noisy channels. We derive an explicit lower bound to the rate-cost function, which applies to the vector, non-Gaussian, and partially observed systems, thereby extending and generalizing an earlier explicit expression for the scalar Gaussian system, due to Tatikonda el al. [2]. The bound applies as long as the differential entropy of the system noise is not −∞ . It can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's belief about the current state and the true state. Via a separation principle between control and communication, similar results hold for causal lossy compression of additive noise Markov sources. Apart from standard dynamic programming arguments, our technical approach leverages the Shannon lower bound, develops new estimates for data compression with coding memory, and uses some recent results on high resolution variablelength vector quantization to prove that the new converse bounds are tight

Rate-cost tradeoffs in control

Consider a distributed control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is minimize a quadratic cost function. The most basic special case of that cost function is the mean-square deviation of the system state from the desired state. We study the fundamental tradeoff between the communication rate r bits/sec and the limsup of the expected cost b, and show a lower bound on the rate necessary to attain b. The bound applies as long as the system noise has a probability density function. If target cost b is not too large, that bound can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's belief about the current state and the true state

Quantifying the Resiliency of Fail-Operational Real-Time Networked Control Systems

In time-sensitive, safety-critical systems that must be fail-operational, active replication is commonly used to mitigate transient faults that arise due to electromagnetic interference (EMI). However, designing an effective and well-performing active replication scheme is challenging since replication conflicts with the size, weight, power, and cost constraints of embedded applications. To enable a systematic and rigorous exploration of the resulting tradeoffs, we present an analysis to quantify the resiliency of fail-operational networked control systems against EMI-induced memory corruption, host crashes, and retransmission delays. Since control systems are typically robust to a few failed iterations, e.g., one missed actuation does not crash an inverted pendulum, traditional solutions based on hard real-time assumptions are often too pessimistic. Our analysis reduces this pessimism by modeling a control system\u27s inherent robustness as an (m,k)-firm specification. A case study with an active suspension workload indicates that the analytical bounds closely predict the failure rate estimates obtained through simulation, thereby enabling a meaningful design-space exploration, and also demonstrates the utility of the analysis in identifying non-trivial and non-obvious reliability tradeoffs

Will 5G See its Blind Side? Evolving 5G for Universal Internet Access

Internet has shown itself to be a catalyst for economic growth and social equity but its potency is thwarted by the fact that the Internet is off limits for the vast majority of human beings. Mobile phones---the fastest growing technology in the world that now reaches around 80\% of humanity---can enable universal Internet access if it can resolve coverage problems that have historically plagued previous cellular architectures (2G, 3G, and 4G). These conventional architectures have not been able to sustain universal service provisioning since these architectures depend on having enough users per cell for their economic viability and thus are not well suited to rural areas (which are by definition sparsely populated). The new generation of mobile cellular technology (5G), currently in a formative phase and expected to be finalized around 2020, is aimed at orders of magnitude performance enhancement. 5G offers a clean slate to network designers and can be molded into an architecture also amenable to universal Internet provisioning. Keeping in mind the great social benefits of democratizing Internet and connectivity, we believe that the time is ripe for emphasizing universal Internet provisioning as an important goal on the 5G research agenda. In this paper, we investigate the opportunities and challenges in utilizing 5G for global access to the Internet for all (GAIA). We have also identified the major technical issues involved in a 5G-based GAIA solution and have set up a future research agenda by defining open research problems

Energy-Delay Tradeoffs of Virtual Base Stations With a Computational-Resource-Aware Energy Consumption Model

The next generation (5G) cellular network faces the challenges of efficiency, flexibility, and sustainability to support data traffic in the mobile Internet era. To tackle these challenges, cloud-based cellular architectures have been proposed where virtual base stations (VBSs) play a key role. VBSs bring further energy savings but also demands a new energy consumption model as well as the optimization of computational resources. This paper studies the energy-delay tradeoffs of VBSs with delay tolerant traffic. We propose a computational-resource-aware energy consumption model to capture the total energy consumption of a VBS and reflect the dynamic allocation of computational resources including the number of CPU cores and the CPU speed. Based on the model, we analyze the energy-delay tradeoffs of a VBS considering BS sleeping and state switching cost to minimize the weighted sum of power consumption and average delay. We derive the explicit form of the optimal data transmission rate and find the condition under which the energy optimal rate exists and is unique. Opportunities to reduce the average delay and achieve energy savings simultaneously are observed. We further propose an efficient algorithm to jointly optimize the data rate and the number of CPU cores. Numerical results validate our theoretical analyses and under a typical simulation setting we find more than 60% energy savings can be achieved by VBSs compared with conventional base stations under the EARTH model, which demonstrates the great potential of VBSs in 5G cellular systems.Comment: 5 pages, 3 figures, accepted by ICCS'1