Discrete‐time extended state observer‐based model‐free adaptive sliding mode control with prescribed performance

Abstract

To tackle the trajectory tracking problem and achieve high control accuracy in many actual nonlinear systems with unknown disturbance, a novel discrete-time extended state observer-(DESO) based model-free adaptive sliding mode control strategy with prescribed tracking performance is studied, which only relies on the input/output data of the system rather than explicit model information. Firstly, a compact-form dynamic linearization method is used to reconstruct the discrete-time nonlinear process, where the time-varying parameter linearly connected with the control input is obtained by an adaptive method and the unknown nonlinear term is estimated by a DESO. Then, by considering the prescribed performance and using an unconstrained vector transformed from the constrained tracking error, one model-free sliding mode controller is designed. In addition, a rigorous stability analysis is presented to show the boundedness of the sliding mode function and the prescribed transient-state and steady-state performance of the output tracking error. Finally, the simulations with comparing results verify the effectiveness and superiority of the developed control scheme. K E Y W O R D Sdiscrete-time extended state observer, discrete-time system, model-free adaptive control, prescribed performance, sliding mode control INTRODUCTIONWith the continuous development of engineering technologies, the complexity of the practical system is intensively increasing, which leads to accurate system modeling becoming one of the most difficult tasks. 1 Thus, the control strategies based on mathematical models are not suitable for such complicated systems. To overcome this problem, data-driven control is proposed where only the input and output data are used. Data-driven methods have been applied in many practical scenes, for instance, quadrotor vehicles, 2 automated vehicles, 3 continuum robots, 4 and other industrial process systems. 5,6 Among these data-driven methods, model-free adaptive control (MFAC) approach has aroused a lot of attention because only the input and output data are used without employing explicit or implicit knowledge of the mathematic

Event‐triggered model‐free adaptive fractional order sliding mode I/O constrained control for a class of nonlinear systems

“…Thus, the actual tracking can be refined as −𝜎𝜚(k r )𝜁(k r ) < e(k r ) < 𝜎𝜚(k r )𝜁(k r ) where 𝜎 < 1 and 𝜎 → 1 − . Besides, the triggering condition (17)…”

“…Among the controller parameters, the ultimate convergence bound 𝜁 k f and event-triggered coefficient 𝜎 exert an enormous function on the balance between tracking precision and computation cost. On one hand, the tracking precision would be improved with the decrease of 𝜁 k f on account of the principle of PPC, which leads to the increase of computation cost according to the triggering condition (17) and vice versa. On the other hand, the computation cost would be reduced with the decrease of triggered times by diminishing 𝜎 and thereby indirectly reduces the tracking precision.…”

“…In contrast, PPC is widely applied and intensively studied with MFAC recently. [15][16][17] The demand of tracking precision is considered as the output constraint problem with a prescribed range, and can be converted into an unconstrained form via a transformed function according to the principle of PPC. 18 Liu et al 15 explores the model-free adaptive sliding mode control (MFASMC) method with PPC for nonlinear systems with unknown dynamics.…”

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

“…In [3], an improved discrete-time fast terminal sliding mode surface was presented for the discrete linear single-input single-output model, and a fast terminal sliding mode control law capable of providing higher accuracy was designed based on equivalent control method. For the discrete-time nonlinear system subject to disturbance, a model-free sliding mode control law based on an extended state observer was proposed in [4] to achieve trajectory tracking with higher accuracy. In [5], an adaptive discrete-time fractional-order sliding mode tracking control method was designed for the discrete-time model of a linear motor containing nonlinear friction and uncertain-ties.…”

Model-Free Adaptive State Feedback Control for a Class of Nonlinear Systems

“…Note that stability analysis of a MFAC based on full form dynamic linearization was proposed in [20], but this does not consider the unmeasurable state of the system. An extended state observer has been used in some MFAC approaches, such as [35] and [36], but these methods were used to observe the modeling error and disturbance rather than the system internal states. A state feedback model-free control was proposed in [37], but this requires that the system state is measured, that is, the system output equals the system state, which cannot be achieved in many real cases.…”