Abstract
In this chapter, we investigate inverse optimal control problems for discrete-time dynamical systems. We pose two discrete-time inverse optimal control problems involving the computation of the parameters of discrete-time optimal control cost functions from data. The problems differ in whether the available data consists of whole or truncated state and control sequences. We present and discuss methods for solving these problems based on bilevel optimization and discrete-time versions of the minimum principle. We specifically show that minimum-principle methods reduce to solving systems of linear equations or quadratic programs under a linear parameterization of the class of cost functions, and admit conditions under which they are guaranteed to provide unique cost-function parameters. Finally, we develop a bespoke technique for solving discrete-time inverse optimal control problems with linear dynamical systems and infinite-horizon quadratic cost functions.
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