TY - JOUR
T1 - A unifying framework for global regulation via nonlinear output feedback
T2 - From ISS to iISS
AU - Jiang, Z. P.
AU - Mareels, Iven
AU - Hill, David J.
AU - Huang, Jie
N1 - Funding Information:
Manuscript received November 1, 2002; revised July 23, 2003. Recommended by Associate Editor R. Freeman. This work was supported in part by the Othmer Institute for Interdisciplinary Studies of Polytechnic University, the National Science Foundation under Grant ECS-0093176 and Grant INT-9987317, the Hong Kong Research Grant Council under Grant CUHK4168/03E, and the National Natural Science Foundation of China under Grant 60374038.
PY - 2004/4
Y1 - 2004/4
N2 - This paper presents a unifying framework for the problem of robust global regulation via output feedback for nonlinear systems with integral input-to-state stable inverse dynamics, subject to possibly unknown control direction. The contribution of the paper is two-fold. Firstly, we consider the problem of global regulation, instead of global asymptotic stabilization (GAS), for systems with generalized dynamic uncertainties. It is shown by an elementary example that GAS is not solvable using conventional smooth output feedback. Secondly, we reduce the stability requirements for the disturbance and demand relaxed assumptions for the system. Using our framework, most of the known classes of output feedback form systems are broadened in several directions: unmeasured states and unknown parameters can appear nonlinearly, restrictive matching and growth assumptions are removed, the dynamic uncertainty satisfies the weaker condition of Sontag's integral input-to-state stability, and the sign of high-frequency gain may be unknown. A constructive strategy is proposed to design a dynamic output feedback control law, that drives the state to the origin while keeping all other closed-loop signals bounded.
AB - This paper presents a unifying framework for the problem of robust global regulation via output feedback for nonlinear systems with integral input-to-state stable inverse dynamics, subject to possibly unknown control direction. The contribution of the paper is two-fold. Firstly, we consider the problem of global regulation, instead of global asymptotic stabilization (GAS), for systems with generalized dynamic uncertainties. It is shown by an elementary example that GAS is not solvable using conventional smooth output feedback. Secondly, we reduce the stability requirements for the disturbance and demand relaxed assumptions for the system. Using our framework, most of the known classes of output feedback form systems are broadened in several directions: unmeasured states and unknown parameters can appear nonlinearly, restrictive matching and growth assumptions are removed, the dynamic uncertainty satisfies the weaker condition of Sontag's integral input-to-state stability, and the sign of high-frequency gain may be unknown. A constructive strategy is proposed to design a dynamic output feedback control law, that drives the state to the origin while keeping all other closed-loop signals bounded.
KW - Input-to-state stability (ISS)
KW - Integral ISS (iISS)
KW - Nonlinear systems
KW - Output feedback
KW - Small-gain
KW - Universal adaptive control
KW - Unknown control direction
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U2 - 10.1109/TAC.2004.825663
DO - 10.1109/TAC.2004.825663
M3 - Article
AN - SCOPUS:2442664176
SN - 0018-9286
VL - 49
SP - 549
EP - 562
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 4
ER -