Data-driven sliding mode control for partially unknown nonlinear systems

TL;DR

This work tackles stabilization of discrete-time nonlinear multi-input systems with partially unknown dynamics and bounded disturbances by designing a data-driven sliding mode control (SMC) architecture. A nominal controller gain $K$ is obtained from a data-driven semidefinite program, while a robust component enforces reachability to a sliding surface $s(k)=N x(k)$ using $H_ fty$-based criteria. The approach extends SMC to MIMO settings, providing global stabilization with provable robustness and improved SDP feasibility over prior data-ANC methods. Simulation on an inverted pendulum and a cart–spring example demonstrates enhanced disturbance tolerance and faster stabilization from finite data.

Abstract

This paper presents a new data-driven control for multi-input, multi-output nonlinear systems with partially unknown dynamics and bounded disturbances. Since exact nonlinearity cancellation is not feasible with unknown disturbances, we adapt sliding mode control (SMC) for system stability and robustness. The SMC features a data-driven robust controller to reach the sliding surface and a data-driven nominal controller from a semidefinite program (SDP) to ensure stability. Simulations show the proposed method outperforms existing data-driven approaches with approximate nonlinearity cancellation.

Figures (3)

• Figure 1: Performance comparison for $\delta = 0.01$: Example 1.
• Figure 2: Performance comparison for $\delta = 0.1$: Example 1.
• Figure 3: Performance comparison: Example 2.

Theorems & Definitions (7)

• Lemma 3.1
• Theorem 3.1
• Proof 1
• Theorem 3.2
• Proof 2
• Proposition 3.1
• Proof 3