We study the effectiveness of iterated elimination strictly-dominated actions in random games. show that dominance solvability games is vanishingly small as number at least one player's grows. Furthermore, conditional on solvability, iterations required to converge Nash equilibrium grows rapidly action sets grow. Nonetheless, when are highly imbalanced, simplifies game substantially by ruling o...

For higher order systems of differential equations solvability and correctness conditions of periodic type boundary value problems are established.

In this paper, we consider the discrete-time mixed H2/H∞ filtering problem for affine nonlinear systems. Sufficient conditions for the solvability of this problem with a finite-dimensional filter are given in terms of a pair of coupled discrete-time Hamilton-Jacobi-Isaac’s equations (DHJIE) with some side conditions. Both the finite-horizon and infinitehorizon problems are discussed for the cas...

For a general class of dynamical systems, this paper presents a necessary and sufficient characterization of invariance of transient responses to symmetries in inputs. A particular example of this property, scale-invariance or “fold-change detection” (FCD), has been shown to be exhibited in biological sensory systems ranging from bacterial chemotaxis pathways to signal transduction mechanisms i...

Abstract. In this paper, the solvability of a class of forward-backward stochastic di erential equations (SDEs for short) over an arbitrarily prescribed time duration is studied. We design a stochastic relaxed control problem, with both drift and di usion all being controlled, so that the solvability problem is converted to a problem of nding the nodal set of the viscosity solution to a certain...

The problem of Finite Settling Time Stabilisation (FSTS) for multivariable, discrete-time systems is discussed in this paper. The approach is algebraic and the problem reduces to the solution of a polynomial Diophantine equation; many of the solvability conditions are expressed as standard linear algebra tests. A Kučera-YoulaBonjiorno type parametrisation of the family of the FSTS controllers i...