Related papers: Bounds on set exit times of affine systems, using …
The problem of motion planning for affine control systems consists of designing control inputs that drive a system from a well-defined initial to final states in a desired amount of time. For control systems with drift, however,…
We consider the problem of developing automated techniques for solving recurrence relations to aid the expected-runtime analysis of programs. Several classical textbook algorithms have quite efficient expected-runtime complexity, whereas…
In this paper we introduce a general framework for casting fully dynamic transitive closure into the problem of reevaluating polynomials over matrices. With this technique, we improve the best known bounds for fully dynamic transitive…
Linear max-plus systems describe the behavior of a large variety of complex systems. It is known that these systems show a periodic behavior after an initial transient phase. Assessment of the length of this transient phase provides…
The fitness level method is a popular tool for analyzing the hitting time of elitist evolutionary algorithms. Its idea is to divide the search space into multiple fitness levels and estimate lower and upper bounds on the hitting time using…
In this paper we provide a thorough, rigorous theoretical framework to assess optimality guarantees of sampling-based algorithms for drift control systems: systems that, loosely speaking, can not stop instantaneously due to momentum. We…
We present a new method for proving lower bounds on the expected running time of evolutionary algorithms. It is based on fitness-level partitions and an additional condition on transition probabilities between fitness levels. The method is…
In the context of studying periodic processes, this paper investigates first under which conditions switching affine systems in the plane generate stable limit cycles. Based on these conditions, a design methodology is proposed by which the…
Switching time optimization arises in finite-horizon optimal control for switched systems where, given a sequence of continuous dynamics, one minimizes a cost function with respect to the switching times. We propose an efficient method for…
Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…
It is well-known that the Ford-Fulkerson algorithm for finding a maximum flow in a network need not terminate if we allow the arc capacities to take irrational values. Every non-terminating example converges to a limit flow, but this limit…
Hybrid systems play a crucial role in modeling real-world applications where discrete and continuous dynamics interact, including autonomous vehicles, power systems, and traffic networks. Safety verification for these systems requires…
We present an algorithm for evaluating a linear ``intersection transform'' of a function defined on the lattice of subsets of an $n$-element set. In particular, the algorithm constructs an arithmetic circuit for evaluating the transform in…
Firstly, we compute the distribution function for the hitting time of a linear time-dependent boundary $t\mapsto a+bt,\ a\geq 0,\,b\in \R,$ by a reflecting Brownian motion. The main tool hereby is Doob's formula which gives the probability…
We derive novel bounds for the performance of algorithms that estimate the downlink covariance matrix from the uplink covariance matrix in frequency division duplex (FDD) massive multiple-input multiple-output (MIMO) systems. The focus is…
This paper proposes a method to compute finite abstractions that can be used for synthesizing robust hybrid control strategies for nonlinear systems. Most existing methods for computing finite abstractions utilize some global, analytical…
For any quantity of interest in a system governed by ordinary differential equations, it is natural to seek the largest (or smallest) long-time average among solution trajectories, as well as the extremal trajectories themselves. Upper…
We present new tight bounds for averaging differential inclusions, which we apply to multi-frequency inclusions consisting of a sum of time periodic set-valued mappings. For this family of inclusions we establish an a tight estimate of…
We study the problem of counting the total number of affine solutions of a system of n binomials in n variables over an algebraically closed field of characteristic zero. We show that we may decide in polynomial time if that number is…
Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially…