Optimal sliding-mode controller parameterization using direct single-shooting under input constraints
摘要
This paper presents a systematic framework for tuning sliding-mode controller (SMC) parameters under hard actuator constraints via a constrained finite-horizon optimal control formulation. Classical SMC design relies on heuristic gain selection that often neglects actuator saturation, nonlinear coupling, and the trade-offs between convergence rates, switching gains, and boundary-layer widths. To address these limitations, we formulate an offline optimization problem in which all SMC parameters are collected into a single decision vector and optimized using a direct single-shooting transcription of the closed-loop dynamics. The nonlinear system is integrated forward in time for each candidate parameter set, and analytical state sensitivities are propagated alongside the state to compute exact cost gradients with respect to the SMC parameters. This enables efficient use of gradient-based nonlinear programming (NLP) solvers under hard input constraints. A smooth approximation of the signum function is adopted to ensure differentiability of the closed-loop dynamics while preserving robustness to matched disturbances. The proposed method is validated on a loading-bridge crane and a two-link planar manipulator. Quantitative comparisons with both heuristically tuned SMC and a constrained NMPC benchmark demonstrate that the optimized parameters eliminate actuator constraint violations while maintaining competitive tracking accuracy and improved transient behavior. The results confirm that the proposed framework offers a systematic, offline approach for high-performance SMC design in constrained nonlinear systems.