Approximate dynamic programming based control of hyperbolic PDE systems using reduced-order models from method of characteristics

Approximate dynamic programming (ADP) is a model based control technique suitable for nonlinear systems. Application of ADP to distributed parameter systems (DPS) which are described by partial differential equations is a computationally intensive task. This problem is addressed in literature by the use of reduced order models which capture the essential dynamics of the system. Order reduction of DPS described by hyperbolic PDEs is a difficult task as such systems exhibit modes of nearly equal energy. The focus of this contribution is ADP based control of systems described by hyperbolic PDEs using reduced order models. Method of characteristics (MOC) is used to obtain reduced order models. This reduced order model is then used in ADP based control for solving the set-point tracking problem. Two case studies involving single and double characteristics are studied. Open loop simulations demonstrate the effectiveness of MOC in reducing the order and the closed loop simulations with ADP based controller indicate the advantage of using these reduced order models.