Dynamic Optimal Linearization of Nonlinear Systems

Dynamic optimal linearization determines a linear model that best approximates the response of a given nonlinear-system for specified inputs. Conventionally, a nonlinear system is linearized about an equilibrium point by the linear term in a Taylor series expansion of the nonlinear system. Unlike the conventional method, dynamic optimal linearization does not require the nonlinear function to be continuously differentiable. With the control input specified in advance, the problem is formulated as parameter optimal control. The solution is obtained for two such formulations. An example is used to demonstrate the special case when dynamic optimal lineariztion reduces to the conventional method. Various properties of the proposed technique are discussed.