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Direct Adaptive Dynamic Compensation for Minimum Phase Systems With Unknown Relative Degree

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2 Author(s)
Hoagg, J.B. ; Dept. of Aerosp. Eng., Michigan Univ., Ann Arbor, MI ; Bernstein, D.S.

We consider parameter-monotonic direct adaptive control for single-input-single-output minimum-phase linear time-invariant systems with knowledge of the sign of the high-frequency gain (first nonzero Markov parameter) and an upper bound on the magnitude of the high-frequency gain. The first part of the paper is devoted to fixed-gain analysis of single-parameter high-gain-stabilizing controllers. Two novel fixed-gain dynamic compensators are presented for stabilizing minimum-phase systems. One compensator stabilizes systems with arbitrary-but-known relative degree, while the other utilizes a Fibonacci series construction to stabilize systems with unknown-but-bounded relative degree. Next, we provide a general treatment of parameter-monotonic adaptive control, including a result that guarantees state convergence to zero. This result is then combined with the high-gain-stabilizing controllers to yield parameter-monotonic direct adaptive dynamic compensation for minimum-phase systems with either arbitrary-but-known or unknown-but-bounded relative degree

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Automatic Control, IEEE Transactions on  (Volume:52 ,  Issue: 4 )