LMIs in Control/Applications/Hinf optimal Model Reduction

Given a full order model and an initial estimate of a reduced order model it is possible to obtain a reduced order model optimal in sense. This methods uses LMI techniques iteratively to obtain the result. The System Given a state-space representation of a system and an initial estimate of reduced order model . Where and . Where are full order, reduced order, number of inputs and number of outputs respectively. The Data The full order state matrices and the reduced model order . The Optimization Problem The objective of the optimization is to reduce the norm distance of the two systems. Minimizing with respect to . The LMI: The Lyapunov Inequality Objective: . Subject to:: It can be seen from the above LMI that the second matrix inequality is not linear in . By making constant it is linear in . And if are constant it is linear in . Hence the following iterative algorithm can be used. (a) Start with initial estimate obtained from techniques like Hankel-norm reduction/Balanced truncation. (b) Fix and optimize with respect to . (c) Fix and optimize with respect to . (d) Repeat steps (b) and (c) until the solution converges. Conclusion: The LMI techniques results in model reduction close to the theoretical limits set by the largest removed hankel singular value. The improvements are often not significant to that of Hankel-norm reduction. Due to high computational load it is recommended to only use this algorithm if optimal performance becomes a necessity. External Links A list of references documenting and validating the LMI. Return to Main Page: