Semidefinite Programming Techniques for Reduced Order Systems with Guaranteed Stability Margins
Computational Optimization and Applications
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The MinMax controller results from a differential game approach to solving the H∞ control problem. As such, the MinMax controller involves a design parameter, which gives a measure of robustness for the controller. There exists no explicit formula for determining the design parameter, and the optimal value must be determined experimentally. Instead of choosing the parameter value experimentally and suffering the computational expense, it would be more efficient if the design parameter could be determined by a prescribed formula based on a mathematically rigorous criterion. In this paper, the author employs continuous sensitivity equation methods to examine the sensitivity of the controlled state with respect to variation of the MinMax control parameter, with the goal being to explore the possibility of determining an efficient assignment of the parameter that is mathematically justified. Numerical simulations are performed on a one-dimensional nonlinear cable-mass system, and the results are presented.