# B. (Bayu) Jayawardhana, Prof

Professor in Mechatronics and Control of Nonlinear Systems
Telephone:
Tel (+31503637156)
E-mail:
b.jayawardhana rug.nl

﻿This graduate course (organized by the Dutch Institute for Systems and Control, an accredited Dutch national graduate school) aims at introducing basic properties of nonlinear systems, fundamental stability notions in nonlinear systems and a set of self-contained results on the control design of nonlinear systems.

Lecture 1 (Introduction to nonlinear systems).
During this lecture, the students will be given examples on nonlinear systems, and several fundamental properties and stability notions of nonlinear systems will be introduced.

Lecture 2 (Lyapunov stability).
The students will learn Lyapunov converse theorem and characterization of input-to-state stability notion.

Lecture 3 (Feedback linearization).
In this lecture, the students will be introduced to the concept of relative-degree and normal forms. The application of these notions to feedback linearization and for control design will be given.

Lecture 4 (Nonlinear control design).
During this lecture, the students will learn the backstepping and forwarding control design approach.

A signal is nothing but a function of time, for instance the voltage across a resistor or the outdoor temperature. During the course, we will be mainly interested in linear finite-dimensional time-invariant systems. After reviewing fundamental issues and properties (such as impulse response, stability, step and frequency response) for such systems, we will study the Fourier series for periodic signals, Fourier transformation, and Laplace transformation. This will be followed by the treatment of the relations between these transformations and linear constant coefficient differential equations. Towards the end of the course, we will have a glimpse of basic filtering theory.

Upon the completion of the course, the students are expected to know the theory and algorithm of numerical methods with respect to:

1. Signals: continuous-time and discrete-time signals, periodic systems, non-periodic systems, energy and power;
2. Periodic signals and their line spectra: Complex and real Fourier series, the fundamental theorem of Fourier series, convolution and Parseval’s theorem;
3. Non-periodic signals and their continuous spectra: the Fourier integral theorem, Fourier transform properties, convolution and correlation, amplitude modulation;
4. Generalized functions and Fourier transforms: the delta function and its properties, introduction to generalized functions, generalized derivatives, generalized Fourier transforms;
5. Linear time-invariant (LTI) systems: LTI systems in time-domain and in frequency domain, ideal filters;
6. The Laplace transform: Laplace transforms of piecewise smooth signals, signals with delta components, properties of Laplace transform. Systems described by ordinary linear differential equations: state variables and state equations, solution of input-state-output equations, initially at rest signals and systems, bounded-input-bounded-output-stable systems, steady-state behavior.

Dynamical modeling has played an important role for the analysis, optimization and control design of systems, including, electro-mechanical systems, chemical processes, operations, biomedical systems and biological systems. The models are generally constructed based on physical laws or phenomenological behavior. These models contain parameters which need to be identified in order to capture the essential systems dynamical behavior. In this course, the students will learn methodologies for estimating the parameters in the models using the available data. The topics that are covered in the class include:

1. Introduction to difference equations
2. Auto-correlation and cross-correlation functions
3. Wiener filter
4. Least-mean square filter
5. Recursive Kalman filter and recursive least-square filter
6. Maximum-likelihood filter
7. Particle filter and extended Kalman filter
8. Bayesian filter

This course aims at providing background and mathematical tools for fitting parameters in a dynamical model to available data. It complements courses on the modeling of (complex) systems. At the end of the course, students will be able: i) to construct an ARMAX or IIR or discrete-time state-space model from input-output signals; ii) to estimate/to identify the unknown parameters in a dynamical model, which fit with the available data, using various computational tools; iii) to refine/to adapt the parameters recursively based on newly acquired data. This course is also suitable for anyone who will be involved in the analysis, optimization and control design of dynamical systems, including, electro-mechanical systems, chemical processes, operations, biomedical systems and biological systems.

Mechatronics

In this graduate course, the students will learn various advanced topics in mathematical modeling of electro-mechanical systems, control systems and the integration of mechatronic systems.

The following materials will be given in the course:

• Introduction to Mechatronic systems
• Advanced mathematical modeling of mechanical systems
• Simulation of dynamical systems
• Electrical, thermal and fluid systems