Design and Validation of Zeroing Neural Network to Solve Time-Varying Algebraic Riccati Equation

Many control problems require solving the algebraic Riccati equation (ARE). Previous studies have focused more on solving the time-invariant ARE than on solving the time-varying ARE (TVARE). This paper proposes a typical recurrent neural network called zeroing neural network (ZNN) to determine the solution of TVARE. Specifically, the ZNN model, which is formulated as an implicit dynamic equation, is developed by defining an indefinite error function and using an exponential decay formula. Then, such a model is theoretically analyzed and proven to be effective in solving the TVARE. Computer simulation results with two examples also validate the efficacy of the proposed ZNN model.