State feedback linearization using block companion similarity transformation

In this research work, a new method is proposed for linearizing a class of nonlinear multivariable system; where the number of inputs divides exactly the number of states. The idea of proposed method consists in representing the original nonlinear system into a state-dependent coefficient form and applying block similarity transformations that allow getting the linearized system in block companion form. Because the linearized system’s eigenstructure can determine system performance and robustness far more directly and explicitly than other indicators, the given class multivariable system is chosen. Examples are used to illustrate the application and show the effectiveness of the given approach.

Application of Natural-Inspired Paradigms on System Identification

In this chapter, the application of nature-inspired paradigms on system identification is discussed. A review of the recent applications of techniques such as genetic algorithms, genetic programming, immuno-inspired algorithms, and particle swarm optimization to the system identification is presented, discussing the application to linear, nonlinear, time invariant, time variant, monovariable, and multivariable cases. Then the application of an immuno-inspired algorithm to solve the linear time variant multivariable system identification problem is detailed with examples and comparisons to other methods. Finally, the future directions of the application of nature-inspired paradigms to the system identification problem are discussed, followed by the chapter conclusions.

MODELING THE DYNAMICS OF THE TUMOR DEVELOPMENT PROCESS

This article discusses the well-known mathematical model of American scientists Rescigno and De Lisi, describing the growth of a tumor of a living organism. The model is a multivariable system of ordinary differential equations with respect to variables characterizing tumor cell and lymphocyte populations. On the basis of the mathematical package of MathCad, a detailed study of various options for the possible development of the tumor is carried out.