Robust control
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Faculteit  Science and Engineering 
Jaar  2022/23 
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 different classes of uncertainty. Finally, we will study the problems of designing feedback controllers and analyzing system properties (like controllability and stabilizability) on the basis of measured time series data. This "datadriven" setting naturally leads to uncertain dynamical systems because real datasets are imperfect, i.e., they contain too few data samples or are contaminated by noise. We will provide robust, datadriven analysis and design techniques that are able to cope with these uncertainties.  
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 on the basis of the grades of the two homework assignments and the written exam: each of the two homework assignment counts for 30%, the written exam counts for 40%.) 

Vaksoort  master  
Coördinator  dr. ir. H.J. van Waarde  
Docent(en)  prof. dr. H.L. Trentelman ,dr. ir. H.J. van Waarde  
Verplichte literatuur 


Entreevoorwaarden  Knowledge assumed: the course builds on knowledge of systems and control, obtained in e.g. "Linear Systems" (BSc), "Project Systems Theory” (BSc), “Advanced Systems Theory” (BSc), and "Calculus of Variations and Optimal Control" (BSc).  
Opmerkingen  
Opgenomen in 
