Retrospective Cost Adaptive Control of Nonlinear Systems Using Ersatz Nonlinear Models

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The goal of this project is to investigate adaptive control techniques for nonlinear systems under minimal modeling information. The basis of this work is retrospective cost adaptive control (RCAC), which is applicable to linear systems under extremely limited modeling information. The goal is to extend this approach to nonlinear systems. A prototypical case is a linear system preceded by an uncertain input nonlinearity, such as a deadzone or saturation. The novel component of this project is the use of ersatz nonlinear models, which capture key features of the otherwise uncertain nonlinearity in order to ensure correct adaptation. For example, the only reliable information about the true nonlinearity may be its monotonicity, that is, intervals within which it is increasing or decreasing. The ersatz nonlinearity then captures this behavior, but may be otherwise incorrect in all other details. The research goal is thus to determine the features of the nonlinearities whose knowledge is essential to RCAC.Control systems that affect humans must be extremely reliable since their failure can endanger lives and property. Unfortunately, control systems are often unable to operate under emergency conditions, which is, ironically, the times when they are often most needed. Humans control vehicles and machines without using computers, but rather by learning from experience as the system operates. Our goal is thus to extend this ability to computers, which lack the intuition about the real world that humans possess. The ability of computers to adaptively control a vehicle or machine will increase the reliability of the control system, which may be crucial in an emergency situation, such as when an automobile brakes on an icy road or an airplane experiences a failure. An additional benefit of this research is the reduced time and cost needed to implement reliable control systems.