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Partial differential equations with discrete (concentrated) state-dependent delays in the space of continuous functions are investigated. In general, the corresponding initial value problem is not well posed, so we find an additional…
The main contributions of this paper are three fold. First, our primary concern is to investigate a class of stochastic recursive delayed control problems which arise naturally with sound backgrounds but have not been well-studied yet. For…
Two types of errors can occur when discriminating pairs of quantum states. Asymmetric state discrimination involves minimizing the probability of one type of error, subject to a constraint on the other. We give explicit expressions bounding…
Due to unbounded input operators in partial differential equations (PDEs) with boundary inputs, there has been a long-held intuition that input-to-state stability (ISS) properties and finite gains cannot be established with respect to…
Linear models with additive unknown-but-bounded input disturbances are extensively used to model uncertainty in robust control systems design. Typically, the disturbance set is either assumed to be known a priori or estimated from data…
In this article we are interested in the boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space. We extend the so called "backstepping method" by introducing…
In this article we consider a class of state-dependent delay differential equations which is modelling the dynamics of the number of adult trees in forests. We prove the boundedness of solutions for a single species model as well as a…
We consider a general stochastic differential delay equation (SDDE) with state-dependent colored noises and derive its limit as the time delays and the correlation times of the noises go to zero. The work is motivated by an experiment…
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…
Given a mixture of states, finding a way to optimally discriminate its elements is a prominent problem in quantum communication theory. In this paper, we will address mixtures of density operators that are unitarily equivalent via elements…
We propose upper and lower bounds on the maximum success probability for discriminating given quantum states. The proposed upper bound is obtained from a suboptimal solution to the dual problem of the corresponding optimal state…
This paper proposes a stabilizing state-feedback control law for vector-valued state systems with a scalar control input, governed by a general class of integral difference equations that incorporate both pointwise and distributed input…
We propose a methodology to address two analysis problems concerning complex systems, namely bounding state functionals of stochastic differential equations (SDEs) and verifying set avoidance of systems described by partial differential…
The differential equations with piecewise constant argument (DEPCAs, for short) is a class of hybrid dynamical systems (combining continuous and discrete). In this paper, under the assumption that the nonlinear term is partially unbounded,…
In this paper, we first propose a method that can efficiently compute the maximal robust controlled invariant set for discrete-time linear systems with pure delay in input. The key to this method is to construct an auxiliary linear system…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
One method to determine whether or not a system of partial differential equations is consistent is to attempt to construct a solution using merely the "algebraic data" associated to the system. In technical terms, this translates to the…
Recently, adaptive control systems with relaxed persistent excitation (PE) conditions have been proposed to guarantee true parameter convergence and improve the transient response. However, in some cases, sufficient control performance and…
We study a control problem where the state equation is a nonlinear partial differential equation of the calculus of variation in a bounded domain, perturbed by noise. We allow the control to act on the boundary and set stochastic boundary…
Controlling the growth of material damage is an important engineering task with plenty of real world applications. In this paper we approach this topic from the mathematical point of view by investigating an optimal boundary control problem…