This paper considers the control of a linear plant when plant state information is being transmitted from a sensor to the controller over a wireless fading channel. The power allocated to these transmissions determines the probability of successful packet reception and is allowed to adapt online to both channel conditions and plant state. The goal is to design plant input and transmit power policies that minimize an infinite horizon cost combining power expenses and the conventional linear quadratic regulator control cost. Since plant inputs and transmit powers are in general coupled, a restricted information structure is imposed allowing them to be designed separately. Under this information structure the standard LQR controller becomes the optimal plant input policy, while the optimal communication policy follows a Markov decision process minimizing transmit power at the sensor and state estimation error at the controller. The optimal power adaptation to channel and plant states is examined qualitatively for general forward error correcting codes. In the particular case of capacity achieving codes event-triggered policies are recovered, where the sensor decides whether to transmit or not based on plant and channel conditions. Approximate dynamic programming is employed to derive a family of tractable suboptimal communication policies exhibiting the same qualitative features as the optimal one. The performance of our suboptimal policies is shown in simulations and is contrasted to other simple transmission policies.

Abstract-We consider a wireless control architecture with multiple control loops and a shared wireless medium. A scheduler observes the random channel conditions that each control system experiences over the shared medium and opportunistically selects systems to transmit at a set of non-overlapping frequencies. The transmit power of each system also adapts to channel conditions and determines the probability of successfully transmitting and closing the loop. We formulate the problem of designing optimal channel-aware scheduling and power allocation mechanisms that minimize the total power consumption while meeting control performance requirements for all systems. In particular it is required that for each control system a given Lyapunov function decreases at a specified rate in expectation over the random channel conditions. We develop an offline algorithm to find the optimal communication design, as well as an online protocol which selects scheduling and power variables based on a random observed channel sequence and converges almost surely to the optimal operating point. We illustrate in simulations the power savings of our approach compared to other non-channel-aware schemes.

We consider the problem of allocating radio resources over wireless communication links to control a series of independent wireless control systems. Low-latency transmissions are necessary in enabling time-sensitive control systems to operate over wireless links with high reliability. Achieving fast data rates over wireless links thus comes at the cost of reliability in the form of high packet error rates compared to wired links due to channel noise and interference. However, the effect of the communication link errors on the control system performance depends dynamically on the control system state. We propose a novel control-communication co-design approach to the low-latency resource allocation problem. We incorporate control and channel state information to make scheduling decisions over time on frequency, bandwidth and data rates across the nextgeneration Wi-Fi based wireless communication links that close the control loops. Control systems that are closer to instability or further from a desired range in a given control cycle are given higher packet delivery rate targets to meet. Rather than a simple priority ranking, we derive precise packet error rate targets for each system needed to satisfy stability targets and make scheduling decisions to meet such targets while reducing total transmission time. The resulting Control-Aware Low Latency Scheduling (CALLS) method is tested in numerous simulation experiments that demonstrate its effectiveness in meeting controlbased goals under tight latency constraints relative to controlagnostic scheduling.

We consider a problem where multiple agents participate in solving a quadratic optimization problem subject to linear inequality constraints in a privacy-preserving manner. Several variables of the objective function as well as the constraints are privacy-sensitive and are known to different agents. We propose a privacy-preserving protocol based on partially homomorphic encryption where each agent encrypts its own information before sending it to an untrusted cloud computing infrastructure. To find the optimal solution the cloud applies a gradient descent algorithm on the encrypted data without the ability to decrypt it. The privacy of the proposed protocol against coalitions of colluding agents is analyzed using the cryptography notion of zero knowledge proofs.

In this paper, we focus on applications in machine learning, optimization, and control that call for the resilient selection of a few elements, e.g. features, sensors, or leaders, against a number of adversarial denial-of-service attacks or failures. In general, such resilient optimization problems are hard and cannot be solved exactly in polynomial time, even though they may involve objective functions that are monotone and submodular. In this paper, we provide for the solution of such optimization problems the first scalable approximation algorithm that is valid for any number of attacks or failures and which, for functions with low curvature, guarantees superior approximation performance. Notably, the curvature has been known to tighten approximations for several non-resilient optimization problems, yet its effect on resilient optimization had hitherto been unknown. We complement our theoretical analyses with empirical evaluations.