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Receding horizon revisited: An easy way to robustly stabilize and LTV system. (English) Zbl 0751.93059

Summary: Stabilization schemes are often based on infinite horizon optimization of a non-singular cost functional. For such schemes to make sense in a time varying context, a fairly good knowledge of the system parameters at all times is a prerequisite. That is a major disadvantage in adaptive implementations. When applicable, the receding horizon approach overcomes this difficulty as, though it relies on general qualitative long-term properties (such as controllability), it requires quantitative knowledge only of (temporally) local parameter values. Work done on receding horizon stabilization during the 1970’s focused on LQ (=‘\(H_ 2\)’) optimization criteria. Looking for a stabilization method which carriers also the robustness properties of infinite horizon \(H_ \infty\) design, we consider here local minimization of the \(L_ 2\)-induced I/O norm (=‘\(H_ \infty\) optimization’) as the design objective. Both state and observation based feedback scheme are derived, and relations to finite and infinite horizon optimization are discussed.

MSC:

93C99 Model systems in control theory
93C35 Multivariable systems, multidimensional control systems

Keywords:

time-dependent
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References:

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