Design of an adaptive terminal sliding‐function controller for nonlinear multivariable systems

Abstract

SUMMARYThis paper presents an adaptive terminal sliding-function controller approach for controlling a class of nonlinear multivariable systems with uncertainty. An appropriate terminal sliding function (TSF) is designed and then applied to the control law. Based on the Lyapunov stability theory, the adaptive terminal sliding-function controller for nonlinear multivariable systems guarantees that the TSF is asymptotically convergent. Different from classical terminal sliding mode control, which uses a discontinuous switching control law, the TSF control uses a continuous TSF and thus avoids the chattering problem. The simulation results demonstrate that the proposed method achieves satisfactory stability.

Adaptive Observer‐Based Global Sliding Mode Control for Uncertain Discrete‐Time Nonlinear Systems with Time‐Delays and Input Nonlinearity

“…Next, applying the concept and technique used in, [30] the reaching condition of sliding manifolds (6) and (10) can be satisfied and the results are expressed in Lemma 1 and Lemma 2, respectively. Lemma 1.…”

“…Theorem 2. The overall closed-loop uncertain discrete time-delay nonlinear system with input nonlinearity (3) and the state observer (4) is stable if the sliding manifolds (6) and (10), the control law (11), and the auxiliary control (14) are employed, and there exist a matrix W ∈ R m × n and positive-definite symmetric matrices X ∈ R n × n and M ∈ R n × n such that the LMI condition 7 is satisfied.…”

“…Hence, the problem of robust stabilization and tracking control for uncertain nonlinear systems has been widely investigated. Over the past decades, a range of research has been undertaken in this field . However, these studies assumed that all system states are known.…”

“…It is well known that SMC is an effective robust control scheme and has been extensively used to improve the stability, performance, and robustness of uncertain linear and nonlinear systems. Many studies on adaptive SMC have been presented in the literature . However, none of the above methods can deal with the robustness against parameter uncertainties, time‐delays, and input nonlinearity by using partial known state information in discrete‐time domain.…”

“…Over the past decades, a range of research has been undertaken in this field. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] However, these studies assumed that all system states are known. From a practical point of view, the system states may not be available and only the system outputs can be measured in many systems.…”