Information dynamics: Temporal behavior of uncertainty measures

We carry out a systematic study of uncertainty measures that are generic to dynamical processes of varied origins, provided they induce suitable continuous probability distributions. The major technical tool are the information theory methods and inequalities satisfied by Fisher and Shannon information measures. We focus on a compatibility of these inequalities with the prescribed (deterministic, random or quantum) temporal behavior of pertinent probability densities.Comment: Incorporates cond-mat/0604538, title, abstract changed, text modified, to appear in Cent. Eur. J. Phy

Advances in optimal control of differential systems with the state suprema

This paper deals with a further development of analytic techniques for Optimal Control Problems (OCPs) involving differential systems with the state suprema. Differential equations evolving with state suprema (maxima) provide a useful modelling framework for various real-world applications, namely, in electrical engineering and in biology. The corresponding dynamic models lead to Functional Differential Equations (FDEs) in the presence of state-dependent delays. We study some particular (but important) cases of optimal control processes governed by systems with sup-operator in the right hand sides of the differential equations and obtain constructive characterizations of optimal solutions. The constrained OCPs we examine are formulated assuming the (linear) feedback-type control law. The case study presented in this article constitutes a formal extension of the concept of positive dynamic systems to differential systems with the state suprema. © 2017 IEEE

On the optimal control of systems evolving with state suprema

This paper studies optimal control processes governed by a specific family of systems described by functional differential equations (FDEs) involving the sup-operator. Systems evolving with the state suprema constitute a useful abstraction for various models of technological and biological processes. The specific theoretic framework incorporates state suprema in the right hand side of the initially given differential equation and finally leads to a FDE with the state-dependent delays. We study a class of nonlinear FDE-featured optimal control problems (OCPs) in the presence of some additional control constraints. Our aim is to develop implementable first-order optimality conditions for the retarded OCPs under consideration. We use the celebrated Lagrange approach and prove a variant of the Pontryagin-like Minimum Principle for the given OCPs. Moreover, we discuss a computational approach to the main dynamic optimization problems and also consider a possible application of the developed methodology to the Maximum Power Point Tracking (MPPT) control of solar energy plants. © 2016 IEEE

Delay-independent stability of linear neutral systems A Riccati equation approach

International audienceThis note focuses on the problem of asymptotic stability of a class of linear neutral systems described by differential equations with delayed state. The delay is assumed unknown, but constant. Sufficient conditions for delayindependent asymptotic stability are given in terms of the existence of symmetric and positive definite solutions of a continuous Riccati algebraic matrix equation coupled with a discrete Lyapunov equation. The approach adopted here is based on a Lyapunov-Krasovskii functional technique

On the Optimal Control of Multidimensional Dynamic Systems Evolving with State Suprema

This paper constitutes a further generalization of the numerical solution approaches to Optimal Control Problems (OCPs) of systems evolving with state suprema. We study multidimensional control systems described by differential equations with the sup-operator in the right hand sides. A specific state-observer model and the linear type feedback control design under consideration imply a resulting closed-loop system that can formally be characterized as a multidimensional Functional Differential Equation (FDE) with delays. We study OCPs associated with the obtained FDEs and establish some fundamental solution properties of this class of problems. A particular structure of the resulting dynamic optimization problem makes it possible to consider the originally given sophisticated OCP in the framework of the nonlinear separate programming in some Euclidean spaces. This fact makes it possible to apply effective and relative simple splitting type computational algorithms to the initially given sophisticated OCPs for systems evolving with state suprema. © 2018 IEEE

Stability of linear systems with delayed state A guided tour

International audienceIn this paper, some recent stability results on linear time-delay systems are outlined. The goal is to give an overview of the state of the art of the techniques used in delay system stability analysis. In particular, two specific problems (delay-independent/ delay-dependent) are considered and some references where the reader can find more details and proofs are pointed out. This paper is based on Niculescu et al. (1997). Copyright (C) 1998 IFAC

Stability of linear systems with delayed state A guided tour

International audienceIn this paper, some recent stability results on linear time-delay systems are outlined. The goal is to give an overview of the state of the art of the techniques used in delay system stability analysis. In particular, two specific problems (delay-independent/ delay-dependent) are considered and some references where the reader can find more details and proofs are pointed out. This paper is based on Niculescu et al. (1997). Copyright (C) 1998 IFAC

Robust Optimal Control of Linear-Type Dynamic Systems with Random Delays

Our contribution deals with a class of Optimal Control Problems (OCPs) of dynamic systems with randomly varying time delays. We study the minimax-type OCPs associated with a family of delayed differential equations. The presented minimax dynamic optimization has a natural interpretation as a robustness (in optimization) with respect to the possible delays in control system under consideration. A specific structure of a delayed model makes it possible to reduce the originally given sophisticated OCP to an equivalent convex program in an Euclidean space. This analytic transformation implies a possibility to derive the necessary and sufficient optimality conditions for the original OCP. Moreover, it also allows consideration of the wide range of effective numerical procedures for the constructive treatment of the obtained convex-like OCP. The concrete computational methodology we follow in this paper involves a gradient projected algorithm. We give a rigorous formal analysis of the proposed solution approach and establish the necessary numerical consistence properties of the resulting robust optimization algorithm. © 201