Robust adaptive sliding mode control for discrete singular systems with randomly occurring mixed time-delays under uncertain occurrence probabilities

Abstract

This paper is concerned with the problem of robust adaptive sliding mode control (RASMC) for discrete singular systems subject to randomly occurring mixed time-delays (ROMTDs) under uncertain occurrence probabilities. The mixed time delays are considered, which are comprised of both the discrete interval delays and infinite distributed delays. Meantime, two random variables obeying the Bernoulli distribution are utilised to depict the phenomena of randomly occurring discrete time-varying delay and distributed time-delay, in which the uncertain occurrence probabilities are modelled by the known scalars. An appropriate sliding surface function is firstly presented. Furthermore, some sufficient criteria via the free weighting matrices idea are obtained to ensure the admissibility of the resultant sliding motion by introducing new Lyapunov-Krasovskii functional. Subsequently, an RASMC law is synthesised to ensure the reachability criterion of pre-designed sliding surface, where an adaptive mechanism is introduced to estimate the related unknown bounds. Finally, the feasibility of the new RASMC strategy is illustrated by a numerical simulation.

Fuzzy-Based Super-Twisting Sliding Mode Stabilization Control for Under-Actuated Rotary Inverted Pendulum Systems

“…(13) assures thatθ is asymptotically stable. In other words, if k θ , k α , λ θ , and λ α are selected to satisfy (19), then the linear system given in (17) is asymptotically stable, which leads to the stability of the nonlinear system given by (15) around the equilibrium point [29]. This completes the proof of the theorem.…”

“…It should be pointed out that it is always possible to select the sliding surface gains k θ , k α , λ θ , and λ α such that (19) is satisfied (see Remark 3). The conditions given in (19) ensure that all eigenvalues of A are in the open left-half of the complex plane. Hence, θ , α, andα are asymptotically stable.…”

“…We mention that the SMC approach has been employed successfully for different fully-actuated systems. Interested readers are referred to [19]- [21] for various applications of the (discontinuous/continuous) SMC to fully-actuated nonlinear systems. However, it should be pointed out again that the RotIPS is an under-actuated, open-loop unstable, and highly nonlinear complex dynamic system.…”

Differentiator-Based Output-Feedback Controller for Uncertain Nonautonomous Nonlinear Systems With Unknown Relative Degree

“…and p j s for j = 1, 2, 3 are defined in (16), (17), and (18), respectively. The constant c in (44) is set as 1, and the initial values for the control input filter (44) and HOSD (43) in all the following simulations are all zeros.…”

“…In universal approximator-based adaptive controllers, neural networks or fuzzy logic systems are used to capture and compensate for the unknown dynamic structure. Second, sliding-mode control (SMC) algorithms for continuous and discrete nonlinear systems [10]- [16] are also being actively researched and adopted. In the SMC, some discontinuous switching control action forces the system dynamics to the sliding surface regardless of the unmodelled uncertainties in the controlled system.…”