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A linear constraint loop is specified by a system of linear inequalities that define the relation between the values of the program variables before and after a single execution of the loop body. In this paper we consider the problem of…
In this paper, an anti-eavesdropping estimation problem is investigated. A linear encryption scheme is utilized, which first linearly transforms innovation via an encryption matrix and then encrypts some components of the transformed…
In this note we construct a solution of a matrix interval linear equation of the form X=AX+B (the discrete stationary Bellman equation) over partially ordered semirings, including the semiring of nonnegative real numbers and all idempotent…
From a theoretical point of view, finding the solution set of a system of inequalities in only two variables is easy. However, if we want to get rigorous bounds on this set with floating point arithmetic, in all possible cases, then things…
The formalizations of periods of time inside a linear model of Time are usually based on the notion of intervals, that may contain or may not their endpoints. This is not enought when the periods are written in terms of coarse granularities…
We first develop systematic and comprehensive interval observer designs for linear time-invariant (LTI) systems, under standard assumptions of observability and interval bounds on the initial condition and uncertainties. Traditionally, such…
In this book we use only special types of intervals and introduce the notion of different types of interval linear algebras and interval vector spaces using the intervals of the form [0, a] where the intervals are from Zn or Z+ \cup {0} or…
In this paper we present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any cases. This approach allows to give a notion of divisibility…
This paper presents a program analysis method that generates program summaries involving polynomial arithmetic. Our approach builds on prior techniques that use solvable polynomial maps for summarizing loops. These techniques are able to…
We consider extension of a closure system on a finite set S as a closure system on the same set S containing the given one as a sublattice. A closure system can be represented in different ways, e.g. by an implicational base or by the set…
This article presents an identification methodology to capture general relationships, with application to piecewise nonlinear approximations of model predictive control for constrained (non)linear systems. The mathematical formulation…
In real world applications, uncertain parameters are the rule rather than the exception. We present a reachability algorithm for linear systems with uncertain parameters and inputs using set propagation of polynomial zonotopes. In contrast…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
A class of two-dimensional systems of second-order ordinary differential equations is identified in which a system requires fewer Lie point symmetries than required to solve it. The procedure distinguishes among those which are…
Interval systems of linear algebraic equations (ISLAE) are considered in the context of constructing of linear models according to data with interval uncertainty. Sufficient conditions for boundedness and convexity of an admissible domain…
This is a survey on the computational complexity of nonlinear mixed-integer optimization. It highlights a selection of important topics, ranging from incomputability results that arise from number theory and logic, to recently obtained…
Counting integer solutions of linear constraints has found interesting applications in various fields. It is equivalent to the problem of counting lattice points inside a polytope. However, state-of-the-art algorithms for this problem…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…
For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of…