Adaptive control of a hyperbolic Partial Differential Equation system with uncertain parameters

The main contribution of this paper is the stability analysis and adaptive control design of a hyperbolic Partial Differential Equation (PDE) system model for crowd dynamics. The feedback control of crowd dynamics has become an important area of research and has been under investigation in recent years. The control of such systems is difficult to achieve as the dynamics are governed by hyperbolic PDEs. This paper presents the design of a nonlinear adaptive controller for a hyperbolic partial differential equation model representing crowd dynamics. Most of the adaptive control in literature is studied for parabolic PDEs. In this paper, adaptive control is studied for hyperbolic PDEs. The feedback control is designed in the presence of uncertainties due to unknown parameters. The controller is designed using the Lyapunov method. The controller designed is shown to achieve uniform boundedness.