Biblio

This note studies self-triggered tracking control of underactuated surface vessels considering both unknown model dynamics and stochastic noise, where the measured states in the sensors are intermittently transmitted to the controller decided by the triggering condition. While the multi-layer neural network (NN) serves to approximate the unknown model dynamics, a self-triggered adaptive neural model is fabricated to direct the design of control laws. This setup successfully solves the ``jumps of virtual control laws'' problem, which occurs when combining the event-triggered control (ETC) with the backstepping method, seeing [1]–[4]. Moreover, the adaptive model can act as the filter of states, such that the complicated analysis and control design to eliminate the detrimental influence of stochastic noise is no longer needed. Released from the continuous monitoring of the controller, the devised triggering condition is located in the sensors and designed to meet the requirement of stability. All the estimation errors and the tracking errors are proved to be exponentially mean-square (EMS) bounded. Finally, a numerical experiment is conducted to corroborate the proposed strategy.

We study coding schemes for multiparty interactive communication over synchronous networks that suffer from stochastic noise, where each bit is independently flipped with probability ε. We analyze the minimal overhead that must be added by the coding scheme in order to succeed in performing the computation despite the noise. Our main result is a lower bound on the communication of any noise-resilient protocol over a synchronous star network with n-parties (where all parties communicate in every round). Specifically, we show a task that can be solved by communicating T bits over the noise-free network, but for which any protocol with success probability of 1-o(1) must communicate at least Ω(T log n / log log n) bits when the channels are noisy. By a 1994 result of Rajagopalan and Schulman, the slowdown we prove is the highest one can obtain on any topology, up to a log log n factor. We complete our lower bound with a matching coding scheme that achieves the same overhead; thus, the capacity of (synchronous) star networks is Θ(log log n / log n). Our bounds prove that, despite several previous coding schemes with rate Ω(1) for certain topologies, no coding scheme with constant rate Ω(1) exists for arbitrary n-party noisy networks.