Advanced Systems Theory

Uitgebreide vaknaam	Advanced Systems Theory
Leerdoelen	1. The student is able to reproduce the geometric characterizations of the systems properties of controllability, stabilizability, observability and detectability and is able to reproduce the Hautus tests for verifying the above system properties, and apply these tests to given linear input-output systems. 2. The student is able to reproduce the formulation of the pole placement problem and its solution, is able to reproduce the proof of the pole placement problem, and is able to compute a suitable feedback controller in the single input/single output case. 3. The student can reproduce the problem of stabilization by dynamic output feedback, and can reproduce its solution via the notion of separation principle. 4. The student is able to compute observers and dynamic stabilizing controllers for simple examples of concrete linear systems. 5. The student is able to reproduce the formulations of the disturbance decoupling problems by state feedback and dynamic output feedback, respectively, and is able to reproduce their solutions in geometric terms. The student is also able to modify the theory to solve extensions of the disturbance decoupling problems. 6. The student is able to reproduce the formulation of the problem of tracking and regulation, and can reproduce its solution in terms of solvability of certain linear matrix equations. For simple examples the student is able to compute a regulator. 7. The student is able to reproduce the problem of designing static and dynamic protocols for linear networked multi-agent systems, and is able to reproduce the necessary and sufficient conditions for the existence of these protocols. 8. The student is able to apply these conditions to single integrator and double integrator linear multi-agent systems.
Omschrijving	This course deals with linear input-output systems in state space form. The course starts with a review of the most important concepts on linear systems that were already taught in the first year course Linear Systems. We review the notions of internal and external stability, controllability and observability with special emphasis on their geometric characterizations. We also review the notions of stabilizability and detectability and discuss their relevance in the design of stabilizing controllers and observer design. We then shift to systems with disturbance inputs, and formulate the design problems of disturbance decoupling by state feedback, both with and without the requirement of internal stability. We give necessary and sufficient conditions for solvability of these problems in terms of controlled invariant subspaces and stabilizability subspaces. Next, we consider the more general formulations of these problems where only part of the state is available for feedback. In this case we are forced to apply dynamic output feedback, and the solution of the decoupling problems in addition uses the concepts of conditioned invariant and detectability subspaces. We also discuss the classical problem of tracking and regulation that requires the design of dynamic controllers such that the output of the controlled system asymptotically follows a given time signal, despite the fact that the systems is affected by external disturbances. This problem is studied by means of solvability of linear matrix equations. As a final subject, we consider linear networked multi-agent systems, which deals with controlling (possibly large numbers of) interconnected linear input-output systems. The interconnection structure of such networks are described by graphs, representing the communication between the agents. We discuss the notions of consensus and synchronization for such systems, and study under what conditions controllers exist that achieve consensus.
Uren per week
Onderwijsvorm	Hoorcollege (LC), Opdracht (ASM), Werkcollege (T)
Toetsvorm	Opdracht (AST), Schriftelijk tentamen (WE) (The final grade is determined on the basis of the grades of the two homework assignments and the written exam: each of the two homework assignment counts for 25%, the written exam counts for 50%.)
Vaksoort	bachelor
Coördinator	Prof. Dr. M.K. Camlibel
Docent(en)	Prof. Dr. M.K. Camlibel
Verplichte literatuur	Titel Auteur ISBN Prijs Additional lecture notes will be handed out during the course. "Control Theory for Linear Systems”, Springer, 2001 (The pdf file can be downloaded from http://www.math.rug.nl/~harry/ under “publications”) H.L. Trentelman, M.L.J. Hautus, and A.A. Stoorvogel
Entreevoorwaarden	Prerequisites are the courses Linear Algebra 1, Linear Algebra 2 and Linear Systems
Opmerkingen	This course was registered last year with course code WBMA14002
Opgenomen in	Opleiding Jaar Periode Type BSc Courses for Exchange Students: AI - Computing Science - Mathematics - semester I a BSc Mathematics: General Mathematics  (Electives and Minor General Mathematics) 3 semester I a keuze BSc Mathematics: Probability and Statistics 3 semester I a keuze BSc Technische Wiskunde 3 semester I a verplicht