Variable Structure Neural Control

Variable structure control with sliding modes was first proposed in the early 1950s (Utkin, 1964; Ernelyanov, 1967; Itkis, 1976) and has subsequently been used in the design of a wide spectrum of system types including linear and nonlinear systems, large-scale and infinite-dimensional systems, and stochastic systems. It has also been applied to a wide variety of engineering systems. The most distinguished feature of variable structure control based on sliding modes is the ability to improve the robustness of systems which are subject to uncertainty. If, however, the uncertainty exceeds the values allowed for the design, the sliding mode cannot be attained and this results in an undesirable response (Utkin, 1964). In the continuous-time case this problem was solved by combining variable structure and adaptive control (Slotine and Li, 1991), but this requires that all the system variables are available and can be measured. This case has also been discussed for linear discrete systems using input output plant models (Furuta, 1990, 1993; Hung et al., 1993; Pan and Furuta, 1995) and for nonlinear discrete systems where the input output model is unknown (Liu et al., 1997b. 1999b).