Instructor: Professor Marc Bodson

Office: MEB 3268, Tel.: 581-8590

E-mail: bodson@ece.utah.edu

Class: TTh, 9:10AM-10:30AM, MEB 2325

The concept of adaptation in control is appealing and many applications have been studied. In aerospace, adaptive control has been proposed to account for changes in the dynamics of flight vehicles, due to variations in altitude and velocity. In process control, it has been used to compensate for deviations due to aging and varying set points. In robotics, adaptation is helpful to control manipulators with unknown loads or changing configurations. Much progress has been achieved over the years, both in the theory and in the applications of adaptive control algorithms. At the same time, many research problems remain open, which makes adaptive control an exciting and dynamic area of research.

The course has two main objectives:

• to provide a knowledge of existing algorithms for adaptive control, with a basic understanding of their stability properties and of how to implement them;
• to provide the theoretical foundations of the field and to introduce the student to research in adaptive control.

 The theory of adaptive control systems is challenging, due to their nonlinear, time-varying nature. However, it is the basis for understanding the dynamic properties of adaptive systems. The two objectives are therefore complementary, and we will keep a balance between methodologies for adaptive control (algorithms), and analytic methods and results.

Introduction: Basic approaches to adaptive control. Applications of adaptive control.

Identification: Error formulations linear in the parameters. Gradient and normalized gradient algorithms. Convergence properties. Least-squares and modified least-squares algorithms. Identification of linear time-invariant systems. Adaptive observers.

Indirect adaptive control: Pole placement control. Model reference control. Predictive control. Indirect adaptation. Singularity regions.

Direct adaptive control: Linear error equations with dynamics. Gradient and pseudo-gradient algorithms. Strictly positive real transfer functions. Kalman-Yacubovitch-Popov lemma. Passivity theory. Direct model reference adaptive control. Stability proofs.

Parameter convergence: Persistency of excitation conditions. Generalized harmonic analysis and sufficient richness conditions. Averaging methods of approximation and analysis.

Robustness: Mechanisms of instability. Methods to improve robustness. Averaging analysis and tuned values.

Disturbance rejection (if time permits): Adaptive internal model principle. Integral control and adaptive bias cancellation. Periodic disturbances.

ECE 3510: Introduction to Feedback Systems. A course on state-space control methods (such as ME 5210 or 6210) is also recommended.

S. Sastry and M. Bodson, Adaptive Control: Stability, Convergence, and Robustness, Prentice-Hall, 1989. The book is available (for free) in PDF form through the web page: http://www.ece.utah.edu/~bodson/acscr.

K.J. Astrom and B. Wittenmark, Adaptive Control, Addison-Wesley, 2^nd edition, 1995.

G.C. Goodwin and K.S. Sin, Adaptive Filtering, Prediction, and Control, Prentice-Hall, 1984. P.A. Ioannou & J. Sun, Robust Adaptive Control, Prentice Hall, Upper Saddle River, NJ, 1996.

I.D. Landau, R. Lozano, and M. M'Saad, Adaptive Control, Springer Verlag, London, 1998.

K.S. Narendra and A.M. Annaswamy, Stable Adaptive Systems, Prentice-Hall, 1989.

P.E. Wellstead & M.B. Zarrop, Self-Tuning Systems: Control and Signal Processing, J. Wiley & Sons, Chichester, England, 1991.

There will be no final exam. Grades will be determined based on homeworks and a final project report (50/50). A grade B will correspond to a satisfactory completion of the homeworks and of the final project. Students who perform particularly well in both categories will receive a grade A. Grades of C or less will be given in cases when homeworks or reports are not turned in, or the quality of the work is below standards.

Homeworks will consist both in exercises and in computer simulations. The simulations will illustrate the properties derived analytically and will help to gain insight into the dynamic behavior of adaptive systems.

Completion of a project is required for the class. A project may consist in a survey of papers from the literature, or in an independent investigation of a topic related to the course. Students are responsible for the selection of the topic of their project and are encouraged to discuss topics early on with the instructor, especially in the case of an independent investigation. The timetable is as follows:

The criteria for the grading of the reports will be:

(a) originality and critical thinking

(b) technical accuracy

(c) scope of the work

(d) quality of presentation (logical organization, clarity and neatness of the report).

In the case of a survey project, at least 5 papers from the research literature, organized around a common topic, should be reviewed. Findings should be summarized in the report, with copies of the papers attached in appendix. Examples of journals with contributions in the field of adaptive control are: the IEEE Trans. on Automatic Control, Automatica, the IEEE Trans. on Control Systems Technology, the International Journal of Control, and the International Journal of Adaptive Control and Signal Processing. Journals in specific application areas are also valuable sources.

For the report, copying from the papers (or simply paraphrasing) will not be considered a valid contribution. Students are expected to write the report in their own words and to demonstrate that they have read the papers, understood them, and thought about them in a critical and investigative manner. Examples of contributions include: critical evaluation of the significance of the results, comparison of different approaches, independent verification of the results (e.g., through simulations), simplified or expanded analysis of the results. A project focussing on an independent investigation of a specific topic should include a list of references, but does not need to study their contributions to the same extent as a survey project.

Examples of topics for projects include:

• identification and adaptive control with uncertainty estimates;
• extremum-seeking algorithms;
• self-tuning systems;
• iterative learning control;
• reconfigurable and fault tolerant control;
• active noise and vibration control;
• applications (motion control, biomedical, automotive,…).