Control of systems partially unknown: variable structure approach

This paper presents a new control approach for the design of nonlinear systems partially unknown, using the theory of variable structure systems (VSS). All the best features of the VSS such as robustness and Lyapunov stability are preserved. Furthermore, the dynamic of the system and the unexpected disturbances are treated as an unknown function. The control system structure is based only on the estimation of the function representing the effect of the unknown dynamics and the unexpected disturbances. In other words, this control algorithm requires neither explicit system parameters nor an explicit plant model. The estimation of the unknown function is accomplished by Lagrange extrapolation using past information of the state variables.