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

summary: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. Three examples demonstrate viability of this approach and provide a comparison with the solution method based on expansions into Taylor polynomials

Design of a Predictive Hierarchical Controller Using FEMLAB

A hierarchical controller with two levels is proposed. One level is based on dynamic optimization while the second is responsible for tracking the optimal trajectory and rejecting disturbances. Its implementation using the FEMLAB system is described. Some simulations are presented at the end of the paper, together with an evaluation of the performance.

Consensus of multi-agent systems and stabilization of large-scale systems with time delays and nonlinearities - a comparison of both problems

summary:The problem of stabilization of large-scale systems and the consensus problem of multi-agent systems are related, similar tools for their solution are used. Therefore, they are occasionally confused. Although both problems show similar features, one can also observe important differences. A comparison of both problems is presented in this paper. In both cases, attention is paid to the explanation of the effects of the time delays. The most important fact is that, if the time delays are heterogeneous, full synchronization of the multi-agent systems cannot be achieved; however, stabilization of the large-scale network is reachable. In the case of nonlinear systems, we show that the stabilization of a large-scale nonlinear system is possible under more restrictive assumptions compared to the synchronization of a nonlinear multi-agent system

A process of making a coffee table

Bakalárska práca sa zaoberá návrhom a opisom jednotlivých procesov výroby konferenčného stolíka. Obsahuje zhrnutie dnešných trendov výroby stolíkov, návrh vlastného originálneho dizajnu a vhodných konštrukčných spojov. Ďalej je práca zameraná na výber vhodných výrobných technológií, použitých strojov a nástrojov pre výrobu navrhnutého výrobku. Súčasťou práce je potrebná výkresová dokumentácia, výrobný postup zvolenej súčiastky a fotografie zo samotnej výroby.The bachelor's thesis deals with the design and description of individual production processes of a coffee table. It contains a summary of today's trends in the production of tables, and making its own original design and suitable structural joints. Furthermore, the work focuses on the selection of suitable production technologies, used machines and tools for the production of the proposed product. Part of the work is necessary drawing documentation, production process of the selected part and photographs from the production itself.

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

summary: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 \textit{et al}. (2019) in the Applications of Mathematics. Here, the key feature is that the nonlinear model in form of an ODE system is controlled (or periodically forced) by an input signal being a drug intake. Our aim is to test the model features under both periodic and nonrecurring dosing, and eventually to provide an innovative method for a parameter estimation based on the periodic dosing response measurement

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

summary: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 in the form of a system of ordinary differential equations. First, we tested the model features under periodic dosing, and subsequently, we provided an innovative method for a parameter estimation based on the periodic dosing response measurement. A numerical example approved the satisfactory behavior of the proposed algorithm