In practical applications, complex dynamic systems are often subject to various constraints. These constraints are critical for ensuring safe system operation. However, traditional control methods typically focus on the asymptotic stability of dynamic systems, often neglecting transient constraints during transitional phases. This oversight can lead to unsafe system states during transitions. Barrier Lyapunov Functions (BLFs) are powerful tools for effectively addressing transient constraints in dynamic systems. However, designing and analyzing BLF-based control becomes technically challenging when the control direction is unknown. The uncertainty in the control direction makes it difficult to achieve stable control while ensuring compliance with transient constraints. To address this issue, this chapter proposes a novel BLF-based design incorporating Nussbaum functions. This approach effectively handles unknown control directions while ensuring that transient constraints are satisfied throughout the entire dynamic process.

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Adaptive Nussbaum Design for Asymptotic Tracking Control with Full-State Constraints

  • Yongliang Yang,
  • Guilong Liu,
  • Qing Li

摘要

In practical applications, complex dynamic systems are often subject to various constraints. These constraints are critical for ensuring safe system operation. However, traditional control methods typically focus on the asymptotic stability of dynamic systems, often neglecting transient constraints during transitional phases. This oversight can lead to unsafe system states during transitions. Barrier Lyapunov Functions (BLFs) are powerful tools for effectively addressing transient constraints in dynamic systems. However, designing and analyzing BLF-based control becomes technically challenging when the control direction is unknown. The uncertainty in the control direction makes it difficult to achieve stable control while ensuring compliance with transient constraints. To address this issue, this chapter proposes a novel BLF-based design incorporating Nussbaum functions. This approach effectively handles unknown control directions while ensuring that transient constraints are satisfied throughout the entire dynamic process.