Information Length Analysis of Linear Autonomous Stochastic Processes

When studying the behaviour of complex dynamical systems, a statistical formulation can provide useful insights. In particular, information geometry is a promising tool for this purpose. In this paper, we investigate the information length for n-dimensional linear autonomous stochastic processes, providing a basic theoretical framework that can be applied to a large set of problems in engineering and physics. A specific application is made to a harmonically bound particle system with the natural oscillation frequency ω, subject to a damping γ and a Gaussian white-noise. We explore how the information length depends on ω and γ, elucidating the role of critical damping γ=2ω in information geometry. Furthermore, in the long time limit, we show that the information length reflects the linear geometry associated with the Gaussian statistics in a linear stochastic process

Causal Information Rate

Information processing is common in complex systems, and information geometric theory provides a useful tool to elucidate the characteristics of non-equilibrium processes, such as rare, extreme events, from the perspective of geometry. In particular, their time-evolutions can be viewed by the rate (information rate) at which new information is revealed (a new statistical state is accessed). In this paper, we extend this concept and develop a new information-geometric measure of causality by calculating the effect of one variable on the information rate of the other variable. We apply the proposed causal information rate to the Kramers equation and compare it with the entropy-based causality measure (information flow). Overall, the causal information rate is a sensitive method for identifying causal relations

Fractional‐order controllers for irrational systems

Abstract In this contribution, fractional‐order controllers of the type PDμ and PIλ are applied to a class of irrational transfer function models that appear in large‐scale systems, such as networks of mechanical/electrical elements and distributed parameter systems. More precisely, by considering the fractional‐order controller kp+kηsα in the Laplace domain with −1≤α≤1, a stability analysis in the parameter‐space (kp,kη,α) is presented. Furthermore, as a way to measure the controller robustness, the controller's fragility analysis using the parameter‐space (kp,kη,α) is derived. Finally, several applications that demonstrate the utility of our results are included