Robust control
Faculteit  Science and Engineering 
Jaar  2020/21 
Vakcode  WMMA02105 
Vaknaam  Robust control 
Niveau(s)  master 
Voertaal  Engels 
Periode  semester II a 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Robust control  
Leerdoelen  At the end of the course, the student is able to: 1. reproduce the geometric characterizations of the systems properties of controllability, stabilizability, observability and detectability. 2. state the problem of stabilization by dynamic output feedback, and reproduce its solution via the notion of separation principle. 3. state the formulation of the Hinfinity suboptimal control problem, both in the timedomain and in transfer function terms. 4. state the formulation of the bounded real lemma, and to reproduce its proof. 5. state the necessary and sufficient conditions for solvability of the Hinfinity control problem in terms of linear matrix inequalities (LMIs). 6. reproduce the formulation of the optimal robust stabilization problem for additive and multiplicative perturbations, and is able to outline the solutions to these problems using the solution of the Hinfinity control problem. 7. state the small gain theorem, and to outline its proof. 8. apply the material presented in the course to formulate and prove extensions of results from the course, and present these results written in a mathematically sound way. 

Omschrijving  This course is an advanced course in 'postmodern' control theory for linear systems. We start with a review of basic concepts from finitedimensional, linear, timeinvariant systems like controllability, observability, stabilizability and detectability, and the problem of internal stabilization by measurement feedback. The next subject is the design of feedback controllers that make the influence of the unknown external disturbance inputs of the system on the to be controlled system outputs as small as possible. This influence can be measured in several ways. One possibility is the H2 norm of the closed loop transfer matrix. This gives rise to the H2 optimal control problem: find a stabilizing feedback controller that minimizes the H2 norm of the closed loop transfer matrix. The solution to this problem uses algebraic Riccati equations. A second possibility to measure the influence of the disturbances on the to be controlled outputs is the Hinfinity norm of the closed loop transfer matrix. The Hinfinity control problem is then to find a dynamic feedback controller that makes the Hinfinity norm of this transfer matrix as small as possible. The solution to this problem uses the linear matrix inequalities (LMI's) in combination with the famous bounded real lemma. Next, the results on the Hinfinity control problem will be applied to the problem of optimal robust stabilization. Using the small gain theorem, we will solve this problem for three classes of uncertainty; additive, coprime factor, and multiplicative uncertainty. Finally we will deal with networked multiagent systems and study the problem of designing distributed controllers (protocols) that achieve state synchronization in the network. It will be shown that this problem is equivalent to a simultaneous stabilization problem. To conclude the course, we take a look at the case that the agent dynamics is uncertain, and study the design of robustly synchronizing distributed controllers.  
Uren per week  
Onderwijsvorm 
Hoorcollege (LC), Opdracht (ASM)
(The course consists of eight weeks of lectures, 4 hours per week. After week 1 and 4, a set of homework assignments is handed out. The students work on these problems individually for three weeks and then hand in the workedout solutions. Each of the two homework assignments is graded.) 

Toetsvorm 
Opdracht (AST), Schriftelijk tentamen (WE)
(The final grade is determined as the weighted average of the two homework assignments (each counts for 30%) and the grade for the written exam (counting for 40%).) 

Vaksoort  master  
Coördinator  prof. dr. H.L. Trentelman  
Docent(en)  prof. dr. H.L. Trentelman  
Verplichte literatuur 


Entreevoorwaarden  The course builds on knowledge of systems and control, obtained in e.g. "Project Systems Theory” (BSc), “Advanced Systems Theory” (BSc), and "Calculus of Variations and Optimal Control" (BSc).  
Opmerkingen  This course was registered last year with course code WIRC09  
Opgenomen in 
