On globally stable adaptive control providing l₁ tracking performance for linear discrete-time systems

ABSTRACT

Existing adaptive control algorithms at best guarantee that the tracking error is a l ₂ sequence. This paper presents globally stable adaptive control algorithms for linear discrete-time systems providing l ₁ tracking performance. Two algorithms with different degree of complexity are proposed, one for the case of known control directions, and a separate algorithm for the case of unknown control directions. It is demonstrated that in both cases the tracking error is l ₁ sequence, while the input and output signals are uniformly bounded.

KEYWORDS:

• l ₁-adaptive performance
• global stability
• parameter estimates convergence
• unknown control directions

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of M. S. Stanković has been supported by the EU Seventh Framework Programme, Marie Curie CIG [grant number 334098].