We consider a stochastic system where the communication between the controller and the actuator is triggered by a threshold-based rule. The communication is performed across an unreliable link that stochastically erases transmitted packets. To decrease the communication burden, and as a partial protection against dropped packets, the controller sends a sequence of control commands to the actuator in each packet. These commands are stored in a buffer and applied sequentially until the next control packet arrives. In this context, we study dead-beat control laws and compute the expected linear-quadratic loss of the closed-loop system for any given event-threshold. Furthermore, we provide analytical expressions that quantify the trade-off between the communication cost and the control performance of event-triggered control systems. Numerical examples demonstrate the effectiveness of the proposed framework. DRAFT. 2 choice is that there exists a well-developed theory that allows to analyze the stability of closedloop systems, to evaluate their control performance, and to design optimal controllers. Despite all these advantages, periodic implementations might lead to an inefficient use of the communication medium. For instance, transmitting the same actuator value repeatedly when the system is at rest at the desired state is undoubtedly a waste of communication resources. In contrast, eventtriggered implementations of feedback control laws adapt the use of the communication channel to the needs of the physical system. Since event-triggered implementations of control laws are often able to achieve a satisfactory performance using significantly reduced communication rates (see e.g., the tutorial paper [4] and the references therein) they have emerged as an attractive alternative approach to the traditional periodic implementations. A reduced communication rate decreases the energy consumption at the transmitter side and reduces the network congestion when the communication takes place over a shared medium. For all these reasons, eventtriggered implementations have been receiving an increasing attention in many applications including, e.g., control over communication networks [5][6][7][8][9], multi-agent systems [10], distributed optimization [11], and embedded control systems [12]. A. Related WorkA number of different event-triggering mechanisms have been proposed in the literature. These can be broadly categorized as Lyapunov-based [11][12][13][14][15], model-based [16][17][18], or thresholdbased [19][20][21]. It is widely recognized that event-triggered implementations can decrease the communication load in a networked control system compared to periodic ones while still guaranteeing closed-loop stability and performance [22][23][24]. However, quantifying the expected transmission rate of such implementations for specified performance in closed-loop is challenging. A notable work in quantifying such a relation is that of Åström and Bernhardsson [23] who focused on the threshold-based event-triggered implementatio...

We consider networked control systems consisting of multiple independent controlled subsystems, operating over a shared communication network. Such systems are ubiquitous in cyber-physical systems, Internet of Things, and large-scale industrial systems. In many large-scale settings, the size of the communication network is smaller than the size of the system. In consequence, scheduling issues arise. The main contribution of this paper is to develop a deep reinforcement learning-based control-aware scheduling (DEEPCAS) algorithm to tackle these issues. We use the following (optimal) design strategy: First, we synthesize an optimal controller for each subsystem; next, we design a learning algorithm that adapts to the chosen subsystems (plants) and controllers. As a consequence of this adaptation, our algorithm finds a schedule that minimizes the control loss. We present empirical results to show that DEEPCAS finds schedules with better performance than periodic ones.

We consider the joint design of packet forwarding policies and controllers for wireless control loops where sensor measurements are sent to the controller over an unreliable and energy-constrained multi-hop wireless network. For fixed sampling rate of the sensor, the co-design problem separates into two well-defined and independent subproblems: transmission scheduling for maximizing the deadlineconstrained reliability and optimal control under packet loss. We develop optimal and implementable solutions for these subproblems and show that the optimally co-designed system can be efficiently found.Numerical examples highlight the many trade-offs involved and demonstrate the power of our approach. Index Terms Optimal control; Wireless sensor networks; Markov decision process * ACCESS Linnaeus Centre, KTH Royal Institute of Technology, Osquldas vag 10, SE-100 44 Stockholm, Sweden. ‡ Huawei Technologies Sweden AB, Skalhogatan 9-11 box 54, SE-164 94, Kista, Sweden. † Corresponding author. E-mail: burak.demirel@ee.kth.se. A preliminary version of parts of this work was presented at several conferences; see [1]-[3]. November 2, 2018 DRAFT arXiv:1204.3100v3 [math.OC] 1 Jul 2014 DRAFT. 2 on the one hand, and control, on the other. It is then often possible to make the communication and computation appear reliable and predictable at the time scale of the control loop. When communication, computation and control do interact, the burden of ensuring reliable systemlevel performance is typically put on the control system. Using high-level abstractions of the deficiencies introduced by unreliable communication and resource-constrained hardware, controlalgorithms are synthesized to be robust to these uncertainties. However, robustification of control laws can come at a high performance price, and it is sometimes simply not possible to compensate for networking shortcomings in control software.We argue that efficient CPS systems must be based on the joint design of communication, computation, and control. At the same time, it is essential that such a joint design is modular, with well-defined interfaces between control algorithms and networking and computation primitives.Modularity allows for specialized development and innovation within each component without affecting the logical correctness of the overall system, and has been a key to massive proliferation in computing and communications. To this end, this paper explores modular co-design of networked control systems with certain optimality properties of the overall system.Networked control has been an active area of research for more than a decade, and the literature is by now rather extensive, see e.g., [6], [7] and the references therein. The research has mainly focused on control design methods that rely on high-level abstractions of the communication network in terms of its latency or loss. State-of-the-art control design techniques are extremely powerful when the control system is able to cope with the network deficiencies. However, when the resulting closed-loop performan...

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Abstract-We consider a finite-horizon linear-quadratic optimal control problem where only a limited number of control messages are allowed for sending from the controller to the actuator. To restrict the number of control actions computed and transmitted by the controller, we employ a threshold-based event-triggering mechanism that decides whether or not a control message needs to be calculated and delivered. Due to the nature of threshold-based event-triggering algorithms, finding the optimal control sequence requires minimizing a quadratic cost function over a non-convex domain. In this paper, we firstly provide an exact solution to the non-convex problem mentioned above by solving an exponential number of quadratic programs. To reduce computational complexity, we, then, propose two efficient heuristic algorithms based on greedy search and the Alternating Direction Method of Multipliers (ADMM) method. Later, we consider a receding horizon control strategy for linear systems controlled by event-triggered controllers, and we also provide a complete stability analysis of receding horizon control that uses finite horizon optimization in the proposed class. Numerical examples testify to the viability of the presented design technique.