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Robust Suboptimal Control of Nonlinear Systems

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Open access
Authors
Loxton, Ryan
Teo, Kok Lay
Rehbock, Volker
Date
2011
Type
Journal Article

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Loxton, Ryan and Teo, Kok Lay and Rehbock, Volker. 2011. Robust Suboptimal Control of Nonlinear Systems. Applied Mathematics and Computations. 217 (14): pp. 6566-6576.
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Applied Mathematics and Computations
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Department of Mathematics and Statistics
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NOTICE: this is the author’s version of a work that was accepted for publication in Applied Mathematics and Computations. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Mathematics and Computations, 217, 14, 2011. DOI: 10.1016/j.amc.2011.01.039

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Abstract

In this paper, we consider a nonlinear dynamic system with uncertain parameters. Our goal is to choose a control function for this system that balances two competing objectives: (i) the system should operate efficiently; and (ii) the system's performance should be robust with respect to changes in the uncertain parameters. With this in mind, we introduce an optimal control problem with a cost function penalizing both the system cost (a function of the final state reached by the system) and the system sensitivity (the derivative of the system cost with respect to the uncertain parameters). We then show that the system sensitivity can be computed by solving an auxiliary initial value problem. This result allows one to convert the optimal control problem into a standard Mayer problem, which can be solved directly using conventional techniques. We illustrate this approach by solving two example problems using the software MISER3.