Traditionally, traces are the sequences of labels associated with paths in transition systems X → P(A×X). Here we describe traces more generally, for coalgebras of the form X → P(F (X)), where F is a polynomial functor. The main result states that F ’s final coalgebra Z ∼= −→ F (Z) gives rise to a weakly final coalgebra with state space P(Z), in a suitable category of coalgebras. Weak finality ...

We investigate the asymptotic properties as t → ∞ of the following differential equation in the Hilbert space H (S) ẍ(t) + a(t)ẋ(t) +∇G(x(t)) = 0, t ≥ 0, where the map a : R+ → R+ is non increasing and the potential G : H → R is of class C1. If the coefficient a(t) is constant and positive, we recover the so-called “Heavy Ball with Friction” system. On the other hand, when a(t) = 1/(t + 1) we o...

We introduce a novel framework of reservoir computing. Cellular automaton is used as the reservoir of dynamical systems. Input is randomly projected onto the initial conditions of automaton cells and nonlinear computation is performed on the input via application of a rule in the automaton for a period of time. The evolution of the automaton creates a space-time volume of the automaton state sp...

In this paper, we consider the problem of finding the stability region in state space for uncertain linear systems with input saturation. For stability analysis, two Lyapunov functions are chosen. One is for the linear region and the other is for the saturated region. Piecewise Lyapunov functions are obtained by solving successive linear matrix inequalities(LMIs) relaxations. A sufficient condi...

Positive systems are important class of dynamic systems with impressive properties. The response of such systems to positive initial conditions and positive inputs remain in the nonnegative orthant of the state space. Although positive observers have been designed for positive systems, they are unable to estimate the states when unknown inputs or disturbances are present in the systems. This pa...

In this paper we concerned with study existence and uniqueness of solutions for a class of inverse problems of degenerate differential equations.The main tool perturbation theory for linear operators. consider the inverse problems for degenerate differential equations of the form dBu(t) dt = Au(t) +Bγ(t)f(t), with the initial condition u(0) = u0 and the overdetermination condition (u(t), v) = w...

In this study, the numerical solution of Fredholm integro–differential equation is discussed in a reproducing kernel Hilbert space. A reproducing kernel Hilbert space is constructed, in which the initial condition of the problem is satisfied. The exact solution u x ð Þ is represented in the form of series in the space W 2 2 ½a; bŠ. In the mean time, the n-term approxima te solution u n ðxÞ is o...

The purpose of this article is to present a novel learning paradigm that extracts reward-related low-dimensional state space by combining correlation-based learning like Input Correlation Learning (ICO learning) and reward-based learning like Reinforcement Learning (RL). Since ICO learning can quickly find a correlation between a state and an unwanted condition (e.g., failure), we use it to ext...

The paper presents a new method of sliding mode control for cable suspended load with acceleration constraint. The method employs a time-varying switching line which moves with a decreasing velocity and a constant angle of inclination to the origin of the error state space. Then, it stops moving and it remains fixed. Since at the initial time the line consists of these points in the error state...

| For many chaotic systems there appears to be a single asymptotic distribution describing the frequency with which almost all trajectories visit diierent regions of state space. Such a distribution is commonly called the \physical" invariant measure or \natural" invariant measure of the system. Consider the evolution of a cluster of initial conditions under the action of the system. This clust...