Date: August 28 - September 1, 2023
The aim of this condensed 4-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 compartmental 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 compartmental systems.
Preliminary program
August 28
| Time | Room | Topic | Lecturer | Notes |
| 9:00-10:30 | I416 | 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 | I416 | Basic tools (computer tutorial) Review of MATLAB and its important toolboxes |
Wijaya Kurniawan |
|
| 13:30-14:30 | I416 | 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 | I416 | 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 29
| Time | Room | Topic | Lecturer | Notes |
| 9:00-10:30 | I416 | 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 | I416 | 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 | I416 | 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 | I416 | Model analysis and control (computer and blackboard tutorial) basic and advanced | Attila Magyar |
August 30
| Time | Room | Topic | Lecturer | Notes |
| 9:00-10:30 | I416 | Control of nonlinear systems – the flatness-based approach: Lie-Backlund equivalence, Cartan fields, differential and orbital flatness, connection to exact linearization, trajectrory design, tracking control and disturbance rejection. Time-scaling and robustness of exact linearization. | Bálint Kiss | presentation |
| 11:00-12:30 | I416 | Nonlinear control applications: underactuaed and nonholonomic mechanical systems – tutorial with Matlab and Simulink | Bálint Kiss | |
| 13:30-14:30 | I416 | Basics notions of compartmental systems | Katalin Hangos | presentation |
| 14:45-15:45 | I416 | Dynamic analysis, control and applications of compartmental systems | Gábor Szederkényi | presentation |
August 31
| Time | Room | Topic | Lecturer | Notes |
| 9:00-10:30 | online | 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 | online | Consensus over directed graphs. Strong formation control. Synchronization of nonlinear passive systems. Application example: Lotka-Volterra networks. | Lőrinc Márton | materials |
| 13:30-14:30 | I416 | MATLAB Tutorial: The consensus protocol | Wijaya Kurniawan | |
| 14:45-15:45 | I416 | MATLAB Tutorial: Formation control | Wijaya Kurniawan | homework |
September 1
| Time | Room | Topic | Lecturer | Notes |
| Consultation | online |