TY - JOUR
T1 - On vanishing gains in robust adaptation of switched systems
T2 - A new leakage-based result for a class of Euler–Lagrange dynamics
AU - Roy, Spandan
AU - Kosmatopoulos, Elias B.
AU - Baldi, Simone
N1 - Accepted Author Manuscript
PY - 2020
Y1 - 2020
N2 - In the presence of unmodelled dynamics and uncertainties with no a priori constant bounds, conventional robust adaptation strategies for switched systems cannot allow the control gains of inactive subsystems to remain constant during inactive intervals: vanishing gains are typically required in order to prove bounded stability. As a consequence, these strategies, known in literature as leakage-based adaptive methods, might introduce poor transients at each switching instant. Leakage-based adaptive control becomes even more problematic in the switched nonlinear case, where non-conservative state-dependent upper bounds for uncertainties and unmodelled dynamics are required. This work shows that, for a class of switched Euler–Lagrange systems, such difficulties can be mitigated: a novel leakage-based stable mechanism is introduced which allows the gains of inactive subsystems to remain constant. At the same time, unmodelled dynamics and uncertainties with no a priori bounds can be handled by a quadratic state-dependent upper bound structure that reduces conservativeness as compared to state-of-the-art structures. The proposed design is validated analytically and its performance is studied in simulation with a pick-and-place robotic manipulator example.
AB - In the presence of unmodelled dynamics and uncertainties with no a priori constant bounds, conventional robust adaptation strategies for switched systems cannot allow the control gains of inactive subsystems to remain constant during inactive intervals: vanishing gains are typically required in order to prove bounded stability. As a consequence, these strategies, known in literature as leakage-based adaptive methods, might introduce poor transients at each switching instant. Leakage-based adaptive control becomes even more problematic in the switched nonlinear case, where non-conservative state-dependent upper bounds for uncertainties and unmodelled dynamics are required. This work shows that, for a class of switched Euler–Lagrange systems, such difficulties can be mitigated: a novel leakage-based stable mechanism is introduced which allows the gains of inactive subsystems to remain constant. At the same time, unmodelled dynamics and uncertainties with no a priori bounds can be handled by a quadratic state-dependent upper bound structure that reduces conservativeness as compared to state-of-the-art structures. The proposed design is validated analytically and its performance is studied in simulation with a pick-and-place robotic manipulator example.
KW - Euler–Lagrange systems
KW - Robust adaptive control
KW - Switched systems
KW - Vanishing inactive gains
UR - http://www.scopus.com/inward/record.url?scp=85089835344&partnerID=8YFLogxK
U2 - 10.1016/j.sysconle.2020.104773
DO - 10.1016/j.sysconle.2020.104773
M3 - Article
AN - SCOPUS:85089835344
SN - 0167-6911
VL - 144
JO - Systems and Control Letters
JF - Systems and Control Letters
M1 - 104773
ER -