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Sum-of-squares based observer design for polynomial systems with a known fixed time delay

Branislav Rehák — 2015

Kybernetika

An observer for a system with polynomial nonlinearities is designed. The system is assumed to exhibit a time delay whose value is supposed to be constant and known. The design is carried out using the sum-of-squares method. The key point is defining a suitable Lyapunov-Krasovskii functional. The resulting observer is in form of a polynomial in the observable variables. The results are illustrated by two examples.

Finite element-based observer design for nonlinear systems with delayed measurements

Branislav Rehák — 2019

Kybernetika

This paper presents a computational procedure for the design of an observer of a nonlinear system. Outputs can be delayed, however, this delay must be known and constant. The characteristic feature of the design procedure is computation of a solution of a partial differential equation. This equation is solved using the finite element method. Conditions under which existence of a solution is guaranteed are derived. These are formulated by means of theory of partial differential equations in L 2 -space....

Consensus of a multi-agent systems with heterogeneous delays

Branislav RehákVolodymyr Lynnyk — 2020

Kybernetika

The paper presents an algorithm for the solution of the consensus problem of a linear multi-agent system composed of identical agents. The control of the agents is delayed, however, these delays are, in general, not equal in all agents. The control algorithm design is based on the H -control, the results are formulated by means of linear matrix inequalities. The dimension of the resulting convex optimization problem is proportional to the dimension of one agent only but does not depend on the number...

Biochemical network of drug-induced enzyme production: Parameter estimation based on the periodic dosing response measurement

The well-known bottleneck of systems pharmacology, i. e., systems biology applied to pharmacology, refers to the model parameters determination from experimentally measured datasets. This paper represents the development of our earlier studies devoted to inverse (ill-posed) problems of model parameters identification. The key feature of this research is the introduction of control (or periodic forcing by an input signal being a drug intake) of the nonlinear model of drug-induced enzyme production...

A numerical method for the solution of the nonlinear observer problem

Rehák, Branislav — 2021

Programs and Algorithms of Numerical Mathematics

The central part in the process of solving the observer problem for nonlinear systems is to find a solution of a partial differential equation of first order. The original method proposed to solve this equation used expansions into Taylor polynomials, however, it suffers from rather restrictive assumptions while the approach proposed here allows to generalize these requirements. Its characteristic feature is that it is based on the application of the Finite Element Method. An illustrating example...

A comparison of two FEM-based methods for the solution of the nonlinear output regulation problem

The regulator equation is the fundamental equation whose solution must be found in order to solve the output regulation problem. It is a system of first-order partial differential equations (PDE) combined with an algebraic equation. The classical approach to its solution is to use the Taylor series with undetermined coefficients. In this contribution, another path is followed: the equation is solved using the finite-element method which is, nevertheless, suitable to solve PDE part only. This paper...

Regulatory network of drug-induced enzyme production: parameter estimation based on the periodic dosing response measurement

Papáček, ŠtěpánLynnyk, VolodymyrRehák, Branislav — 2021

Programs and Algorithms of Numerical Mathematics

The common goal of systems pharmacology, i.e. systems biology applied to the field of pharmacology, is to rely less on trial and error in designing an input-output systems, e.g. therapeutic schedules. In this paper we present, on the paradigmatic example of a regulatory network of drug-induced enzyme production, the further development of the study published by Duintjer Tebbens . (2019) in the Applications of Mathematics. Here, the key feature is that the nonlinear model in form of an ODE system...

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