The Input-Mapping-Based Online Learning Sliding Mode Control Strategy With Low Computational Complexity

The data-driven sliding mode control (SMC) method proves to be highly effective in addressing uncertainties and enhancing system performance. In our previous work, we implemented a co-design approach based on an input-mapping data-driven technique, which effectively improves the convergence rate through historical data compensation. However, this approach increases computational complexity in multi-input and multi-output (MIMO) systems due to the dependency of the number of online optimization variables on system dimensions. To improve applicability, this paper introduces a novel input-mapping-based online learning SMC strategy with low computational complexity. First, a new sliding mode surface is established through online convex combination of pre-designed offline surfaces. Then, an input-mapping-based online learning sliding mode control (IML-SMC) strategy is designed, utilizing a reaching law with adaptively adjusted convergence and switching coefficients to minimize chattering. The input-mapping technique employs the mapping relationship between historical input and output data for predicting future system dynamics. Accordingly, an optimization problem is formulated to learn from the past dynamics of the uncertain system online, thereby enhancing system performance. The optimization problem in this paper features fewer variables and is independent of system dimension. Additionally, the stability of the proposed method is theoretically validated, and the advantages are demonstrated through a MIMO system. Note to Practitioners—The design of control strategies that reduce the impact of mismatches between practical systems and models on system performance, while also ensuring applicability, is crucial. To address this issue, this paper proposes a low-complexity IML-SMC strategy. This strategy uses historical real input-output information and the mapping relationship with future dynamics to compensate for the impact of unknown dynamics and improve the system’s convergence rate. Notably, the control strategy introduced in this paper significantly reduces online computational complexity, ensuring applicability, and stability is proven. When there is a deviation between the model and the actual system, practitioners can implement the low-complexity IMC-SMC strategy proposed in this paper to more quickly achieve the control objectives in the actual system.