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Efficient analysis and synthesis tools for robust and scheduled controller design against time-varying and dynamic uncertainties

Project members:  prof. C.W. Scherer, S.G. Dietz, H. Koroglu
 
Keywords:  Optimization-based control, Old - project will be removed
 
Sponsored by:  STW
 
In recent years optimization based robust controller analysis and synthesis techniques have emerged as powerful tools in numerous practical control applications. Despite impressive progress, the state of the art algorithms are unable to deal with large scale problems as they exist in industry. In particular, there is a strong demand to better understand how mixtures of dynamic time-invariant and rate-bounded time-varying uncertainties can systematically be included in controller analysis and synthesis algorithms. This project aims at developing a framework that allows for these general uncertainty models, as they occur in practice, to be included in the design. To break the complexity barrier, it is essential to exploit the specific problem-structure and to employ relaxation schemes by which the conservatism of the computations can be reduced. Moreover, numerical reliability of the algorithms must be improved. This fundamentally novel strategy leads to the second goal: development of the corresponding robust and scheduled controller synthesis techniques, with the demonstration of their applicability for regulating systems whose dynamics vary with time or nonlinearly. These schemes will involve a partition of uncertainty value sets such that robust or scheduled controller design will be intimately related to the design of multi-objective and switched controllers for a large number of models.

Problems Currently under Investigation

  • Robust Stability Analysis for Slowly Time-Varying Systems: We consider time-varying uncertainties and investigate the ways to reduce conservatism in stability analysis. Taking into account the bound on the rate of variation of the uncertainty/uncertain parameters, we study this problem in generalized plant framework in two directions by employing LMI methods as efficient numerical tools:
    1. Develop robust stability tests using the well-known frequency domain methods for robust stability analysis (mu-analysis, D-scaling, IQC multipliers).
    2. Construct parameter-dependent Lyapunov functions in a systematic way such that we can more precisely answer the question of robust stability of an LPV system.
  • LPV Design for Slowly Time-Varying Parameters: In order to reduce conservatism, we intend to employ in LPV design the robust stability tests that we develop for slowly time-varying uncertainties within the study of the above problem.

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