328,197 research outputs found

### Geometric characterization on the solvability of regulator equations

The solvability of the regulator equation for a general nonlinear system is discussed in this paper by using geometric method. The ‘feedback’ part of the regulator equation, that is, the feasible controllers for the regulator equation, is studied thoroughly. The concepts of minimal output zeroing control invariant submanifold and left invertibility are introduced to find all the possible controllers for the regulator equation under the condition of left invertibility. Useful results, such as a necessary condition for the output regulation problem and some properties of friend sets of controlled invariant manifolds, are also obtained

### Timely-Throughput Optimal Scheduling with Prediction

Motivated by the increasing importance of providing delay-guaranteed services
in general computing and communication systems, and the recent wide adoption of
learning and prediction in network control, in this work, we consider a general
stochastic single-server multi-user system and investigate the fundamental
benefit of predictive scheduling in improving timely-throughput, being the rate
of packets that are delivered to destinations before their deadlines. By
adopting an error rate-based prediction model, we first derive a Markov
decision process (MDP) solution to optimize the timely-throughput objective
subject to an average resource consumption constraint. Based on a packet-level
decomposition of the MDP, we explicitly characterize the optimal scheduling
policy and rigorously quantify the timely-throughput improvement due to
predictive-service, which scales as
$\Theta(p\left[C_{1}\frac{(a-a_{\max}q)}{p-q}\rho^{\tau}+C_{2}(1-\frac{1}{p})\right](1-\rho^{D}))$,
where $a, a_{\max}, \rho\in(0, 1), C_1>0, C_2\ge0$ are constants, $p$ is the
true-positive rate in prediction, $q$ is the false-negative rate, $\tau$ is the
packet deadline and $D$ is the prediction window size. We also conduct
extensive simulations to validate our theoretical findings. Our results provide
novel insights into how prediction and system parameters impact performance and
provide useful guidelines for designing predictive low-latency control
algorithms.Comment: 14 pages, 7 figure

### Nonconforming Virtual Element Method for $2m$-th Order Partial Differential Equations in $\mathbb R^n$

A unified construction of the $H^m$-nonconforming virtual elements of any
order $k$ is developed on any shape of polytope in $\mathbb R^n$ with
constraints $m\leq n$ and $k\geq m$. As a vital tool in the construction, a
generalized Green's identity for $H^m$ inner product is derived. The
$H^m$-nonconforming virtual element methods are then used to approximate
solutions of the $m$-harmonic equation. After establishing a bound on the jump
related to the weak continuity, the optimal error estimate of the canonical
interpolation, and the norm equivalence of the stabilization term, the optimal
error estimates are derived for the $H^m$-nonconforming virtual element
methods.Comment: 33page

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