RESEARCH INITIATION AWARD:Analysis and Synthesis of Robust Control Systems Using Integral Quadratic Constraints

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9410531 Megretski The main project objective are: to develop a unified approach to the robustness and performance analysis of control systems in the presence of mixed (real parametric, non-linear, slowly time varying etc. structured uncertainty and non-stochastic correlated exogenous signals; to present a less conservative linear feedback control synthesis procedure based on the analysis; to implement the theoretical results in a set of computer algorithms; and to test the method by applying it in the practical problems of control of highly uncertain dynamics, such as compressor antisurge control and greenhouse climate control. The main method to be employed in the analysis part of the project is based on describing (conservatively) each component of uncertainty and noise by a set of Integral Quadratic Constraints (IQC's). Then the robust stability (or a prescribed level of performance) is achieved if a certain system of Linear Matrix Inequalities (LMI's), defined by the choice of IQC's has a solution. In the synthesis, a Projective Parameterization of the set of admissible controllers will be used to reduce the problem (possibly conservatively) to a system of LMI. Alternatively, an analog of the heuristic D-K Iteration algorithm will be studied. The significance of the proposed research activity is in its potential to enhance the power and extend the field of application of many recently known methods of robust control analysis, including u-synthesis, quadratic stability, positivity theory and Kharitonov-type arguments. ***