University of Pannonia, Faculty of Information Technology
Department of Electrical Engineering and Information Systems

Advanced Nonlinear Control Methods: Theory and applications (PhD Course)

Date:  August 30 -  September 3, 2021

The aim of this condensed 5-day PhD course is to introduce basic notions in nonlinear systems and control to interested students. The studied topics will cover the classical theory of input-affine systems (analysis of basic properties such as reachability, observability, stability; linearization-based controller design), passivity, Hamiltonian system representation, model based predictive control,  as well as the control of multi-agent systems. For each day, 4x45 mins of theoretical lectures and tutorials are planned.

The course includes the following topics:

  • Introduction: mathematical models of dynamical systems, linear and nonlinear models, control goals and constraints, summary of LTI systems
  • Mathematical tools: Vector fields, diffeomorphisms, tangent vectors, Lie derivative, Lie product, distributions, co-distributions
  • Most important special nonlinear system classes: positive systems, polynomial systems, QP-systems, CRNs, Hamiltonian systems. 
  • The underlying physical picture behind these classes
  • Summary of the theory of nonlinear autonomous systems: continuity, existence and unicity of solutions, equilibrium points, stability
  • Nonlinear control systems in ODE-form, steady states, linearization around steady states/solutions
  • Analysis of input-affine systems: reachability and controllability
  • Classical control of input-affine systems: exact linearization, zero dynamics, input-output linearization (SISO and MIMO cases)
  • Dissipative and passive systems: storage functions, dissipativity, passivity, Lq-gain. Control Lyapunov functions, passivation, feedback equivalence, minimum-phase nonlinear systems.
  • Hamiltonian systems: system interconnections and Hamiltonian functions, control by feedback and interconnection, generalized Hamiltonian systems
  • Model-based predictive controllers and their application for traffic systems.
  • Analysis and control of multi-agent systems.

Application for the course

Program

August 30

Time Room Topic Lecturer Notes
9:00-10:30 I122 Nonlinear state space models (lecture)
Review of LTI state space and input-output models; Input-affine state space models; Local linearization		 Katalin Hangos presentation
11:00-12:30 I122 Basic tools (computer tutorial)
Review of MATLAB and its important toolboxes 		Péter Polcz materials
13:30-14:30 I122 Model transformations and properties (lecture, blackboard tutorial)
Review of LTI state transformations, canonical model forms; Lie derivative, Lie brackets, relative degree; Nonlinear state transformations		 Katalin Hangos presentation
14:45-15:45 I122 Model transformations II. (lecture, blackboard tut.)
Nonlinear feedback form for general and input affine systems, the notion of feedback equivalence to ensure a required property; the notion of relative degree; normal form of SISO nonlinear systems; the zero dynamics; exact linearization and I/O linearization via feedback linearization in the MIMO case		 Gábor Szederkényi presentation

August 31

Time Room Topic Lecturer Notes
9:00-10:30 I122 Distributions and co-distributions; Reachability analysis, local and global reachability, controllability distribution; Observability analysis, local and global observability, observability co-distribution; Minimal realizations Gábor Szederkényi presentation
11:00-12:30 I122 Stability (Lecture and tutorial)
 BIBO and asymptotic stability of LTI systems, Lyapunov stability, Lq stability for nonlinear systems, Lq-gain		 Attila Magyar presentation
13:30-14:30 I122 Stabilizing controller design (Lecture and tutorial)
LTI state feedback controllers (pole placement and LQ),Control Lyapunov functions; Passivity, passivity by feedback		 Attila Magyar presentation
14:45-15:45 I122 Model analysis and control (computer and blackboard tutorial) basic and advanced Attila Magyar  

September 1

Time Room Topic Lecturer Notes
9:00-9:45 I122 Basics of system identification, Gaussian Processes, GP-based identification, theory part 1 Roland Tóth materials
10:00-10:45 I122 Basics of system identification, Gaussian Processes, GP-based identification, theory part 2 Roland Tóth  
11:00-11:45 I122 Basics of system identification, Gaussian Processes, GP-based identification, theory part 3 Roland Tóth  
13:00-14:30 I122 Basics of system identification, Gaussian Processes, GP-based identification, tutorial Roland Tóth  

September 2

Time Room Topic Lecturer Notes
9:00-10:30 I122 Analysis and control of Multi-Agent Systems
Multi-Agent Systems: Basic notions. Consensus over undirected graphs. Weak formation control 		 Lőrinc Márton presentation
11:00-12:30 I122 Consensus over directed graphs. Strong formation control. Synchronization of nonlinear passive systems. Application example: Lotka-Volterra networks. Lőrinc Márton materials
13:30-14:30 I122 MATLAB Tutorial: The consensus protocol Áron Fehér  
14:45-15:45 I122 MATLAB Tutorial: Formation control Áron Fehér  

September 3

Time Room Topic Lecturer Notes
9:00-10:30 I122 Special nonlinear model classes: QP and CRN models (lecture, blackboard)
Positive polynomial system classes; Special nonlinear transformations of QP and CRN models
Stability analysis, structural (robust) stability		 Katalin Hangos presentation
11:00-12:30 I122 Stabilyzing controller design for QP and CRN models (lecture)
LQ controllers for LV systems; (Robust) stabilyzing controllers based on CRN models		 Gábor Szederkényi