Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems
Top Cited Papers
- 15 April 2003
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 48 (4), 590-606
- https://doi.org/10.1109/tac.2003.809820
Abstract
A new method to design asymptotically stabilizing and adaptive control laws for nonlinear systems is presented. The method relies upon the notions of system immersion and manifold invariance and, in principle, does not require the knowledge of a (control) Lyapunov function. The construction of the stabilizing control laws resembles the procedure used in nonlinear regulator theory to derive the (invariant) output zeroing manifold and its friend. The method is well suited in situations where we know a stabilizing controller of a nominal reduced order model, which we would like to robustify with respect to higher order dynamics. This is achieved by designing a control law that asymptotically immerses the full system dynamics into the reduced order one. We also show that in adaptive control problems the method yields stabilizing schemes that counter the effect of the uncertain parameters adopting a robustness perspective. Our construction does not invoke certainty equivalence, nor requires a linear parameterization, furthermore, viewed from a Lyapunov perspective, it provides a procedure to add cross terms between the parameter estimates and the plant states. Finally, it is shown that the proposed approach is directly applicable to systems in feedback and feedforward form, yielding new stabilizing control laws. We illustrate the method with several academic and practical examples, including a mechanical system with flexibility modes, an electromechanical system with parasitic actuator dynamics and an adaptive nonlinearly parameterized visual servoing application.Keywords
This publication has 38 references indexed in Scilit:
- Overcoming the detectability obstacle in certainty equivalence adaptive controlAutomatica, 2002
- A robustly stable output feedback saturated controller for the boost DC-to-DC converterSystems & Control Letters, 2000
- A tutorial on visual servo controlIEEE Transactions on Robotics and Automation, 1996
- On characterizations of the input-to-state stability propertySystems & Control Letters, 1995
- Adaptive regulation: Lyapunov design with a growth conditionInternational Journal of Adaptive Control and Signal Processing, 1992
- Stabilizability of the angular velocity of a rigid body revisitedSystems & Control Letters, 1992
- Robustness of adaptive controllers—A surveyAutomatica, 1989
- Adaptive control of linearizable systemsIEEE Transactions on Automatic Control, 1989
- An integral manifold approach to the feedback control of flexible joint robotsIEEE Journal on Robotics and Automation, 1987
- Integral manifolds of slow adaptationIEEE Transactions on Automatic Control, 1986