Sparsity Promoting Fixed-Order ℋ2-Conic Control

While passivity-based control has found wide utility in robust control for large-scale systems, more general input-output methods designed to tackle passivity violations have suffered from relatively poor scalability to date. Sparsity promoting ℋ
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-conic design rectifies this problem by using the Conic Sector Theorem for nonlinear stability while minimizing communication costs and the closed-loop ℋ
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-norm for nominal performance. A fixed-order framework admits any controller structures while improving performance with iterative convex overbounding (ICO). A framework to reconcile sparsity promotion and ICO is proposed. Two prevailing techniques for sparsity promotion are explored and implemented – direct weighted-ℓ
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minimization and the alternating direction method of multipliers (ADMM). Numerical experiments show the surprising result that the simpler direct method performs better.