Modular Design of Jointly Optimal Controllers and Forwarding Policies for Wireless Control

Abstract

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...

On Stability Condition of Wireless Networked Control Systems under Joint Design of Control Policy and Network Scheduling Policy

“…wherex i k|k−2 is the predicted state in frame k based on the observation of the state in frame k −1 and the control variable in frame k − 2 (see (8)).…”

A comprehensive overview of cyber-physical systems: from perspective of feedback system

“…Goswami et al [74] proposed a co-design principle for coordinating communication and control in a CPS architecture. Demirel et al [75] consider the joint design of signal transmission and controller design for wireless control systems by utilizing MDP methods. Cao et al [76] proposed a joint optimization framework incorporating the control objective and communication constraints considering the packet losses and physically constrained actuators' action.…”

Minimum-energy packet forwarding policies for guaranteed LQG performance in wireless control systems

“…Proof: The proof relies on a coupling argument on the loss process for the end-to-end transmissions, see [6].…”

“…Let u k = u(kh) be the control signal computed at time kh+τ and applied to the process during the time interval [kh+τ, (k+1)h+τ ) and let x k = x(kh). Then, the continuous-time loss function (1) can be transformed into an equivalent discrete-time loss [6]. The optimal control problem is then to compute the control sequence {u k } that minimizes the discrete-time loss function.…”

“…The co-design framework decomposes the overall design problem into two well-defined control and network subproblems, and the joint optimality can be proved by a similar monotonicity argument as in [2], [6]. In the control subproblem, we develop the optimal controller for fixed sampling interval, transmission delay and end-toend reliability and compute its associated linear-quadratic loss.…”