ABSTRACT
In this chapter we show that the structurally simple and computationally
inexpensive PID control, popular with SISO linear time-invariant systems, can be
generalized and extended to control nonlinear MIMO systems with nonparametric
uncertainties and actuation failures. By utilizing the Nussbaum-type function and
the matrix decomposition technique, non-square systems with unknown control
direction are also considered. Furthermore, with the proposed analytic algorithms
for adaptively tuning PID gains, the resultant PID control can be made robust,
adaptive and fault-tolerant, and applicable to nonlinear systems with non-vanishing
uncertainties and unexpected actuation faults.
