Redundancy-Aware Physics Informed Neural Networks (R-PINNs) Based Learning of Nonlinear Algebraic Systems with Non-Measurable States

The paper presents Redundancy-Aware Physics Informed Neural Networks (R-PINNs) for learning of unknown model parameters of nonlinear algebraic systems in continuous time with non-measurable state variables. R-PINNs accomplish the learning task in presence of non-measurable states of the system by incorporating input-output representation of the a priori available physics based laws, generally in form of nonlinear differential (partial) equations within the NN based learning procedure, leading to learning of a set of optimal parameters that determine the optimal mapping between input-output data while adhering to the known physics. Analytical Redundancy Relationships (ARRs) are able to express input-output representation of system using solely the measured/known variables by exploring the redundancy within the analytical structure of the system. The paper proposes a methodology that includes ARR derivation and suitable integration within PINNs framework to develop R-PINNs. Mathematically rigorous novel proofs on uniform and ultimate boundedness (UUB) of the output and parametric estimation errors in Lyapunov sense is provided. Finally a DC motor enabled friction drive system based simulation study is presented to demonstrate the effectiveness of the approach.