In this paper, we introduce a new finite element method for solving the Stokes equations in primary velocity-pressure formulation using H(div) elements to approximate velocity. Like other methods with velocity discretized by conforming elements, our has advantages of an exact divergence-free field and pressure-robustness. However, most require stabilizers enforce weak continuity tangential dire...

Abstract A new family of hybrid/mixed finite elements optimized for numerical stability is introduced. It comprises a linear hexahedral and quadratic tetrahedral elements. The element formulation derived from consistent linearization well-known three-field functional related to Simo–Taylor–Pister () For the we derive (static reduced) discontinuous hybrid elements, as well continuous mixed with ...

We present a new model of incomplete information games without private information in which the players use a distributionally robust optimization approach to cope with the payoff uncertainty. With some specific restrictions, we show that our “Distributionally Robust Game” constitutes a true generalization of three popular finite games. These are the Complete Information Games, Bayesian Games a...

We consider the problem of fixed-interval smoothing of a continuous-time partially observed nonlinear stochastic dynamical system. Existing results for such smoothers require the use of two-sided stochastic calculus. The main contribution of this paper is to present a robust formulation of the smoothing equations. Under this robust formulation, the smoothing equations are nonstochastic paraboli...

In this paper, the robust adaptive finite-time synchronization problem for nonlinear resource management system with uncertain parameters is discussed. By incorporating the finite-time stability theory and adaptive control approach, a novel and more general adaptive finite-time synchronization control scheme is proposed. The developed result depends on the terminal attractors, which can not onl...

Optimal solutions to Markov decision problems may be very sensitive with respect to the state transition probabilities. In many practical problems, the estimation of these probabilities is far from accurate. Hence, estimation errors are limiting factors in applying Markov decision processes to real-world problems. We consider a robust control problem for a finite-state, finite-action Markov dec...

We consider the problem of approximating plants with discrete sensors and actuators (termed ‘systems over finite alphabets’) by deterministic finite memory systems for the purpose of certified-by-design controller synthesis. We propose a new, control-oriented notion of input/output approximation for these systems, that builds on ideas from robust control theory and behavioral systems theory. We...

Optimal solutions to Markov decision problems may be very sensitive with respect to the state transition probabilities. In many practical problems, the estimation of these probabilities is far from accurate. Hence, estimation errors are limiting factors in applying Markov decision processes to real-world problems. We consider a robust control problem for a finite-state, finite-action Markov dec...

We define robust estimators for the parameters of the Cauchy distribution based on the probability integral method. The proposed estimators have bounded influence functions and high breakdown points. These estimators are simple, robust and consistent, but asymptotically less efficient than the maximum likelihood estimators which are not robust. A simulation study for finite sample size shows th...