Co-design of safe and efficient networked control systems in factory automation with state-dependent wireless fading channels

Abstract

In factory automation, heterogeneous manufacturing processes need to be coordinated over wireless networks to achieve safety and efficiency. These wireless networks, however, are inherently unreliable due to shadow fading induced by the physical motion of the machinery. To assure both safety and efficiency, this paper proposes a state-dependent channel model that captures the interaction between the physical and communication systems. By adopting this channel model, sufficient conditions on the maximum allowable transmission interval are then derived to ensure stochastic safety for a nonlinear physical system controlled over a state-dependent wireless fading channel. Under these sufficient conditions, the safety and efficiency co-design problem is formulated as a constrained cooperative game, whose equilibria represent optimal control and transmission power policies that minimize a discounted joint-cost in an infinite horizon. This paper shows that the equilibria of the constrained game are solutions to a non-convex generalized geometric program, which are approximated by solving two convex programs. The optimality gap is quantified as a function of the size of the approximation region in convex programs, and asymptotically converges to zero by adopting a branch-bound algorithm. Simulation results of a networked robotic arm and a forklift truck are presented to verify the proposed co-design method.

Optimal codesign of industrial networked control systems with state‐dependent correlated fading channels

“…The codesign problem in NCS is often reduced to a joint stabilization and optimization formulation under the constraints of limited channel capacity and control resource. This joint stabilization/optimization problem can be classified into several categories according to communication resource/channel characteristics (eg, transmission power, [11][12][13][14] data rate, 15,16 bandwidth, 17,18 or network topology 19 ) and imperfections (eg, delay and packet dropout 11,12,16 ). In terms of guaranteeing the energy efficiency in NCS, prior work 12 has shown that optimal codesign of both transmission power and control policies for linear dynamical system over wireless fading channel can be decoupled by placing restrict assumptions on the information structure.…”

“…Under newly defined mild assumptions, the derived conditions are convex (ie, have linear or quadratic structures) and are thus different from nonconvex condition that were developed in prior works. 11 As a result, the newly proposed conditions can be examined computationally in a more efficient manner. • The second contribution of this paper is the formulation of more computationally efficient methods for solving the codesign problem of NCS.…”

“…The proposed computational methods essentially distinguish this paper from prior works. 11 The remainder of this paper is organized as follows. The description and modeling framework of the considered industrial NCS are presented in Section 2.…”

“…In particular, define Ω s = {x ∈ ℝ n ||x| ≤ Δ} to be the target region toward which the system states x are driven. Then, the probability of exiting Ω s as defined in (11) satisfies…”

“…Specifically, based on newly derived sufficient conditions for safety, this paper shows that the codesign problem can be formulated and solved using either linear programming (LP) (for the weak notion of safety in expectation ) or quadratic programming (QP) (for the strong notion of almost sure asymptotic safety ). The proposed computational methods essentially distinguish this paper from prior works …”