For systems with a "strict-feedback" form, backstepping offers a recursive design procedure. By treating state variables as virtual controls, the designer constructs a Lyapunov function step-by-step. This technique is particularly powerful for robust design because it allows for the integration of nonlinear damping terms—additions to the control law that specifically counteract the effects of bounded uncertainties.
Robust nonlinear control design has a wide range of applications, including: Robust nonlinear control design has a wide range
This creates a "sliding surface" in the state space. The controller uses high-frequency switching to force the system state onto this surface and keep it there, making it incredibly robust against modeling errors. For systems with a "strict-feedback" form
This report provides an overview of the technical content and practical applications discussed in the book Robust nonlinear control design has a wide range
Here, (\mathbfx \in \mathbbR^n) is the state vector (position, velocity, pressure, flux, etc.), (\mathbfu \in \mathbbR^m) is the control input, and (\mathbfy \in \mathbbR^p) is the output. The functions (\mathbff) and (\mathbfh) are generally nonlinear and potentially time-varying.
Simplified mathematical representations of real hardware.