Sliding mode control in indefinite-dimensional systems

Delay-independent sliding mode control for a class of quasi-linear parabolic distributed parameter systems with time-varying delay

“…Up to now, there have been some reports about the SMC of distributed parameter systems. To deal with the control problems of distributed parameter systems using sliding mode methodology, there are two major approaches: infinite-dimensional version [22][23][24][25] and finite-dimensional version [26,27].…”

Lyapunov approach to the boundary stabilisation of a beam equation with boundary disturbance

“…In Guo et al (2011) and Guo and Guo (2013), the stabilisations of one-dimensional wave equation with harmonic uncertainty suffered from input and output are considered. Based on semigroup theory, the sliding mode control method is used to deal with a class of abstract infinite-dimensional systems in Orlov and Utkin (1987), where the control operator and disturbance operator are all assumed to be bounded, which represents mainly the distributed control strategy. The boundary stabilisation for a one-dimensional heat equation with boundary disturbance is studied in Drakunov, Barbieri, and Silver (1996) by sliding mode control, where an integral transformation is used to transform the heat equation that is the second or-926 B.-Z.…”

Robust Control of Infinite-Dimensional Systems via Sliding Modes

“…The boundedness of the interval preceding the sliding motion follows from the inequality resulting from (18), (19):…”

“…The discontinuous control law results from the Lyapunov min-max approach, the origins of which may be found in [7,8]. An extension of this approach to infinite-dimensional systems can be found in [15,18]. Based on the extension, the control is synthesized to guarantee that the time-derivative of a Lyapunov function, selected for a nominal, exponentially stable system, is negative on the trajectories of the system with perturbations caused by uncertainties of a plant operator and environment conditions.…”