The paper studies the problem of mixed H2/H∞ control in the infinite-horizon setting for discrete-time linear time-invariant (LTI) systems. The key insights are:
The optimal causal controller that minimizes the H2-cost of the closed-loop system subject to an H∞ constraint is non-rational, as shown by previous work. However, the paper provides the first exact closed-form solution to this problem in the frequency domain.
While the optimal controller is non-rational, the paper shows that it can be parameterized using a finite-dimensional parameter. This allows the authors to introduce an efficient iterative algorithm to find the optimal causal controller in the frequency domain.
The algorithm is proven to converge when the system is scalar, and numerical evidence suggests exponential convergence for larger systems.
The paper also shows how to find the best (in H∞ norm) fixed-order rational approximations of the optimal mixed H2/H∞ controller, and studies its performance.
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by Vikrant Mali... at arxiv.org 10-01-2024
https://arxiv.org/pdf/2409.20020.pdfDeeper Inquiries