Stability (learning theory)

Discrete mathematics

Electrical engineering

Mathematics

Adaptive control

Epistemology

Machine learning

Engineering

Counterexample

Mathematical analysis

Philosophy

Control system

Artificial intelligence

Control (management)

Programming language

Constant (computer programming)

Computer science

A priori and a posteriori

Robust control

Bounded function

Control theory (sociology)

Upper and lower bounds

Time constant

IEEE Transactions on Control Systems Technology

This brief proposes a new adaptive-robust formulation for time-delay control (TDC) under a less-restrictive stability condition. TDC relies on estimating the unknown system dynamics via the artificial introduction of a time delay, often referred to as time-delay estimation (TDE). In conventional TDC, the estimation error, called TDE error, is taken to be upper bounded by a constant under the assumption of small time delay and, most importantly, of a priori bounded states. We highlight the issues of such a conventional methodology via an unstable counterexample. Consequently, a new less-restrictive structure for the upper bound of the TDE error is formulated, which has an explicit dependence on system states and is valid for any chosen time delay. This insight leads to a new TDC design, namely, time-delayed adaptive-robust control (TDARC). The effectiveness of TDARC is substantiated via a multiple-degrees-of-freedom robot.

A New Adaptive-Robust Design for Time Delay Control Under State-Dependent Stability Condition