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This paper investigates the problem of distributed nonblocking supervisory control for timed discrete-event systems (DESs). The distributed supervisors communicate with each other over networks subject to nondeterministic communication delays and losses. Given that the delays are counted by time, techniques have been developed to model the dynamics of the communication channels. By incorporating the dynamics of the communication channels into the system model, we construct a communication automaton to model the interaction process between the supervisors. Based on the communication automaton, we define the observation mappings for the supervisors, which consider delays and losses occurring in the communication channels. Then, we derive the necessary and sufficient conditions for the existence of a set of supervisors for distributed nonblocking supervisory control. These conditions are expressed as network controllability, network joint observability, and system language closure. Finally, an example of intelligent manufacturing is provided to show the application of the proposed framework.

In the context of networked discrete-event systems (DESs), communication delays and losses exist between the plant and the supervisor for observation and between the supervisor and the actuator for control. In this paper, we first introduce a new framework for supervisory control of networked DESs. Under the introduced framework, we address the state estimation problem for supervisor synthesis of networked DESs with both communication delays and losses. The estimation algorithm considers the effect of the controls imposed on the system. Additionally, the estimation algorithm is based on the control decisions available up to the moment, and all the future control decisions are assumed to be unknowable. Two notions, called "observation channel configuration" for tracking observation delays and losses and "control channel configuration" for tracking control delays and losses, are defined. Then, we introduce an online approach for state estimation of the controlled system. Compared with the existing approach, the proposed approach under the introduced framework can estimate the state of the controlled system more accurately. As an application of the proposed approach, we finally show that the existing methods can be easily applied to synthesize maximally permissible and safe networked supervisors.

In decentralized networked supervisory control of discrete-event systems (DESs), the local supervisors observe event occurrences subject to observation delays to make correct control decisions. Delay coobservability describes whether these local supervisors can make sufficient observations. In this paper, we provide an efficient way to verify delay coobservability. For each controllable event, we partition the specification language into a finite number of sets such that strings in different sets have different lengths. For each of the sets, we construct a verifier to check if delay coobservability holds for the controllable event. The computational complexity of the proposed approach is polynomial with respect to the number of states, the number of events, and the upper bounds on observation delays and only exponential with respect to the number of local supervisors. It has lower complexity order than the existing approaches. In addition, we investigate the relationship between the decentralized supervisory control of networked DESs and the decentralized fault diagnosis of networked DESs and show that delay $K$-codiagnosability is transformable to delay coobservability. Thus, techniques for the verification of delay coobservability can be leveraged to verify delay $K$-codiagnosability.

Correctly formulated continuum models for lipid-bilayer membranes present a significant challenge to computational mechanics. In particular, the mid-surface behavior is that of a 2-dimensional fluid, while the membrane resists bending much like an elastic shell. Here we consider a well-known Helfrich-Cahn-Hilliard model for two-phase lipid-bilayer vesicles, incorporating mid-surface fluidity, curvature elasticity and a phase field. We present a systematic approach to the direct computation of vesical configurations possessing icosahedral symmetry, which have been observed in experiment and whose mathematical existence has recently been established. We first introduce a radial-graph formulation to overcome the difficulties associated with fluidity within a conventional Lagrangian description. We use the so-called subdivision surface finite element method combined with an icosahedral-symmetric mesh. The resulting discrete equations are well-conditioned and inherit equivariance properties under a representation of the icosahedral group. We use group-theoretic methods to obtain a reduced problem that captures all icosahedral-symmetric solutions of the full problem. Finally we explore the behavior of our reduced model, varying numerous physical parameters present in the mathematical model.

We determine stability boundaries for the wrinkling of highly uni-directionally stretched, finely thin, rectangular elastic sheets. For a given fine thickness and length, a stability boundary here is a curve in the parameter plane, aspect ratio vs. the macroscopic strain; the values on one side of the boundary are associated with a flat, unwrinkled state, while wrinkled configurations correspond to all values on the other. In our recent work we demonstrated the importance of finite elasticity in the membrane part of such a model in order to capture the correct phenomena. Here we present and compare results for four distinct models:(i) the popular F\"oppl-von K\'arm\'an plate model (FvK), (ii) a correction of the latter, used in our earlier work, in which the approximate 2D F\"oppl strain tensor is replaced by the exact Green strain tensor, (iii) and (iv): effective 2D finite-elasticity membrane models based on 3D incompressible neo-Hookean and Mooney-Rivlin materials, respectively. In particular, (iii) and (iv) are superior models for elastomers. The 2D nonlinear, hyperelastic models (ii)-(iv) all incorporate the same quadratic bending energy used in FvK. Our results illuminate serious shortcomings of the latter in this problem, while also pointing to inaccuracies of model (ii), in spite of yielding the correct qualitative phenomena in our earlier work. In each of these, the shortcoming is a due to a deficiency of the membrane part of the model.