Hybrid-impulsive second-order sliding mode control: Lyapunov approach

Abstract

Dynamic system of relative degree two controlled by discontinuous-hybrid-impulsive feedback in the presence of bounded perturbations is considered. The state feedback impulsive-twisting control exhibits a uniform exact finite time convergence to the second-order sliding mode with zero convergence time. The output feedback discontinuous control augmented by a simplified hybrid-impulsive functions provides uniform exact convergence with zero convergence time of the system's states to a real second-order sliding mode in the presence of bounded perturbations. Only 'snap' knowledge of the output derivative, that is, the knowledge of the output derivative in isolated time instants, is required. The output feedback hybridimpulsive control with practically implemented impulsive actions asymptotically drives the system's states to the origin. The Lyapunov analysis of the considered hybrid-impulsive-discontinuous system proves the system's stability. The efficacy of the proposed control technique is illustrated via computer simulations.2-SM, second-order sliding mode. 1074Y. SHTESSEL ET AL.assume that T δ,i + 1 = T δ,i , then the gain K is to be selected to meet inequality 1090 Y. SHTESSEL ET AL.

Impulsive second‐order sliding mode control in reduced information environment

“…Corollary 1. In system (6), (8), the variables x 1 , x 2 → 0 in finite time. Furthermore, Consider system driven by twisting control 1…”

“…Note that the conditions (8) and (11) may be very conservative since they are derived based on a Lyapunov function technique, and the coefficients , > 0 can be easily identified by tuning in the simulations.…”

“…The interest in impulsive control as a control solution that allows driving the system's states to the origin in a very short time has increased over the past few years. [4][5][6]8,9 A hybrid-impulsive 2-SMC was studied in the works of Shtessel et al 8 and Glumineau et al 9 to reduce dramatically the convergence time practically to zero, achieving instantaneous (or short time) convergence and uniformity. 10 Reaction control systems for steering and attitude control of aerospace vehicles can serve as a good example of utility of the impulsive control.…”

Impulsive control for attitude stabilization in the presence of unknown bounded external disturbances

“…[7][8][9][10][11][12] For instance, impulsive control has been used for synchronization of networks, population dynamics, ecosystems evolution, and secure encryption systems. [13][14][15][16][17][18][19] More interestingly, impulsive control method can effectively address the difficulty that certain systems cannot be operated under continuous control input. For example, it is known that the price of gasoline is not suitable to change daily; a spacecraft cannot continuously discard corresponding booster that contains limited fuel support; continuous drug intake may lead to antimicrobial resistance problem.…”

Output feedback relay control in the second‐order sliding mode context with application to an electropneumatic system

“…Finally, another second‐order sliding mode output feedback controller (denoted 2SMOFC) using only the sign of the sliding variable and a switching gain strategy has been proposed in , and then completed by . These methods deal with a class of nonlinear systems with relative degree equal to 2, and the controllers have been thought as sampled ones, which is directly connected to real application.…”