Robust Nonlinear Control Design State Space And Lyapunov Techniques Systems Control Foundations Applications

infu𝜕V𝜕xf(x)+𝜕V𝜕xg(x)u

Robust Nonlinear Control Design: Leveraging State Space and Lyapunov Techniques

Suppose we have a nominal nonlinear system (\dot\mathbfx = \mathbff(\mathbfx) + \mathbfg(\mathbfx)\mathbfu) with a known CLF and a stabilizing control (\mathbfu_\textnom(\mathbfx)). Now add a bounded disturbance (\mathbfd(t)) and parametric uncertainty (\Delta(\mathbfx)):

penalizes state deviations. Finding explicit solutions to the HJI inequality is analytically challenging, often requiring numerical approximations or tensor-based solvers. 6. Synthesis and Comparative Analysis