Modeling, Approximation, and Control for a Class of Nonlinear Systems
This work investigates modeling, approximation, estimation, and control for classes of nonlinear systems whose state evolves in space
The second topic delves into estimation and control of history dependent differential equations. This study is motivated by the increasing interest in estimation and control techniques for robotic systems whose governing equations include history dependent nonlinearities. The governing dynamics are modeled using a specific form of functional differential equations. The class of history dependent differential equations in this work is constructed using integral operators that depend on distributed parameters. Consequently, the resulting estimation and control equations define a distributed parameter system whose state, and distributed parameters evolve in finite and infinite dimensional spaces, respectively. The well-posedness of the governing equations is established by deriving sufficient conditions for existence, uniqueness and stability for the class of functional differential equations. The error estimates for multiwavelet approximation of such history dependent operators are derived. These estimates help determine the rate of convergence of finite dimensional approximations of the online estimation equations to the infinite dimensional solution of distributed parameter system. At last, we present the adaptive sliding mode control strategy developed for the history dependent functional differential equations and numerically validate the results on a simplified pitch-plunge wing model.