Equalization Control of Nonlinear Systems by Discrete Models of the Volterra Operators

The Associated linear equations (ALEs) are parametric models of the Volterra operators. With them, a Volterra inverse is constructed to be used as open loop control of continuous nonlinear systems. However, most of the actual control systems are of discrete nature, this work introduces the novel discrete version of the ALEs. This discrete version is a series of ARX models of the Volterra operators for both the direct and the inverse series. These discrete models of the ALEs are used for an equalization strategy to create an open loop control on a reported simulated Duffing Oscillator and a physical Duffing system constructed by analog circuits.