Prescribed convergence time control of spacecraft attitude dynamics with parametric uncertainty

Unified Sufficient Conditions for Predefined-Time Stability of Non-Linear Systems and Its Standard Controller Design

“…)) are known non-linear functions; w = M −1 (x 1 )F u denotes the disturbances and system uncertainties, which satisfies |w| ≤ b where b is a positive scalar; and u ∈ R is the control input. Through the application of Theorem 1, a standard predefined-time controller design method is presented here based on the sliding mode control technique for system (17). In the control framework, a new predefined-time sliding mode surface is first designed using piecewise function methods, in order to avoid potential singularities.…”

“…Therefore, there is no singularity for the term ΦV q 1 x 1 when an appropriate q is selected. For system (17), the control input u is designed as…”

“…Lyapunov theory-an effective instrument for analyzing the stability of control systemsis often combined with sliding mode control, backstepping control, and adding power integrator techniques to design controllers to ensure asymptotic [9], finite-time [10][11][12], fixed-time [13][14][15], and predefined-time [16,17] stability of the controlled system. In particular, the sliding mode control technique is usually used to design a controller to guarantee the controlled system's finite-time stability [17][18][19][20][21][22].…”

“…Lyapunov theory-an effective instrument for analyzing the stability of control systemsis often combined with sliding mode control, backstepping control, and adding power integrator techniques to design controllers to ensure asymptotic [9], finite-time [10][11][12], fixed-time [13][14][15], and predefined-time [16,17] stability of the controlled system. In particular, the sliding mode control technique is usually used to design a controller to guarantee the controlled system's finite-time stability [17][18][19][20][21][22]. As detailed in [4,23,24], some paradigms of the predefined-time controller were formulated to achieve the control requirements of second-order non-linear systems featuring uncertainties, but challenges related to the singularity of sliding mode control were encountered.…”

“…As detailed in [4,23,24], some paradigms of the predefined-time controller were formulated to achieve the control requirements of second-order non-linear systems featuring uncertainties, but challenges related to the singularity of sliding mode control were encountered. To overcome this drawback, alternative non-singular predefined-time sliding mode controllers were presented in [17,20,25]. The aforementioned predefined-time controllers, designed using different Lyapunov-based predefined-time stability theorems, can be applied to many systems and exhibit predefinedtime stability properties.…”