Integral sliding mode predictive control with disturbance attenuation for discrete‐time systems

Abstract

In this paper, the output tracking control is addressed for discrete‐time multi‐input‐multi‐output nonlinear systems subjected to external disturbance by a novel output‐based discrete‐time integral sliding mode predictive control scheme. First of all, a control law is proposed based on a new type of discrete‐time integral sliding mode surfaces. To further improve control accuracy, an integral sliding mode predictive control law is obtained in combination with the designed integral sliding mode control and model predictive control. Rigorous analysis is provided to demonstrate that the quasi‐sliding‐mode band width and ultimate bound of output tracking error under the designed discrete‐time integral sliding mode predictive control law are of higher accuracy than those under the designed integral sliding mode control law. Numerical simulations are performed to illustrate that the presented integral sliding mode predictive control law offers better performance than the proposed integral sliding mode control law.

Observer‐based sliding mode H∞$H_\infty$ control for offshore structures with nonlinear energy sink mechanisms

“…In the control law (38), let 𝜂 = 0.4, in the H ∞ performance index (29), set 𝛾 = 0.6, and in Equation ( 43), set 𝛿 = 0.2. By solving inequalities (34), one yields the controller gain matrix K and observer gain matrix L as:…”

“…become one of effective schemes for the synthesis of control system and has been applied in many real applications [13,[27][28][29][30][31]. In this paper, a more general nonlinear dynamic model of the offshore structure with an NES device is presented.…”

“…Note that due to the strong robustness to the system uncertainties and external disturbances, sliding mode control has become one of effective schemes for the synthesis of control system and has been applied in many real applications [13, 27–31]. In this paper, a more general nonlinear dynamic model of the offshore structure with an NES device is presented.…”

A Discrete-Time Integral Sliding Mode Control Law for Systems With Matched and Unmatched Disturbances

“…The same approach was extended to systems with unmatched disturbances in [19]. Finally, the authors of [20] proposed a DT-ISM control law designed using an MPCbased approach.…”

“…In all mentioned works on DT-ISM control, the bounds on the disturbance terms were always given in terms of 2-norms, apart from [18], [20], where the infinity-norm was utilized, and [19], where the disturbances were subject to box constraints. Moreover, if we indicate the value of the sliding variable at the discrete step k as σ k (which in DT-ISM control formulations must be equal to zero from the beginning, i.e., σ 0 = 0), the DT-ISM equivalent control at step k was calculated by posing σ k+1 = 0 in [13]- [16], and, as an alternative approach, by posing σ k+1 − σ k = 0 in [17]- [20].…”