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Robust filtering for discrete-time systems with bounded noise and parametric uncertainty

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2 Author(s)
El Ghaoui, L. ; Dept. of Electr. Eng. & Comput. Sci., California Univ., Berkeley, CA, USA ; Calafiore, G.

This note presents a new approach to finite-horizon guaranteed state prediction for discrete-time systems affected by bounded noise and unknown-but-bounded parameter uncertainty. Our framework handles possibly nonlinear dependence of the state-space matrices on the uncertain parameters. The main result is that a minimal confidence ellipsoid for the state, consistent with the measured output and the uncertainty description, may be recursively computed in polynomial time, using interior-point methods for convex optimization. With n states, l uncertain parameters appearing linearly in the state-space matrices, with rank-one matrix coefficients, the worst-case complexity grows as O(l(n + l)3.5) With unstructured uncertainty in all system matrices, the worst-case complexity reduces to O(n3.5)

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Automatic Control, IEEE Transactions on  (Volume:46 ,  Issue: 7 )