Inverse optimal control and inverse noncooperative dynamic game theory. A minimum-principle approach (Q2077749)

This monograph discusses inverse problems in optimal control and noncooperative dynamic game theory. It is a mixture between a journey through theoretical aspects and algorithmic explorations. In particular, it presents the theoretical background for discrete- and continuous-time inverse optimal control and generalizations thereof as well as its applications. The first chapter provides motivation for the topics discussed in the book. The second chapter visits forward problems arising in and the background of optimization, optimal control, and noncooperative game theory. It surveys general concepts in optimization and introduces the notion of \textit{discrete}- and \textit{continuous}-time inverse optimal control along with the associated minimum principles. The second chapter concludes with a brief overview of noncooperative dynamic and differential game theory. The third chapter surveys \emph{discrete-time} inverse optimal control problems for discrete-time dynamical systems governed by difference equations. The first part of this chapter lays the foundation by presenting the required background material: the problem formulation and the associated minimum principles. Subsequently, the considered discrete-time optimal control problems are defined and different classes of methods for obtaining exact and approximate solutions to these problems are presented; in particular, bilevel methods as well as (discrete-time versions of) minimum principle methods. The last, and major part of this chapter ``seek[s] to develop results for characterizing the existence and uniqueness of solutions to the minimum principle methods'' in an attempt to address the limitation that the optimality conditions are typically necessary but not sufficient for the optimality of the state and control sequences. Aside from exposing the reader to the theoretical background, the book also lays out several algorithms by presenting their pseudocode. The last section is dedicated to inverse linear-quadratic optimal control in discrete time. The fourth chapter explores analog principles for \textit{continuous-time} dynamical systems governed by ordinary differential equations (bilevel methods, minimum principle methods, as well as method reformulations to address their limitations). Pseudocode is included to enlighten the reader about implementation aspects. The fifth chapter extends chapter two by generalizing discrete-time inverse optimal control via a discussion of inverse noncooperative dynamic games. It starts by discussing foundational aspects followed by an exposition of bilevel methods in the context of solving inverse noncooperative dynamic games. Similar to prior sections, the next topics surveyed are (open loop) minimum-principle methods as well as their reformulation and analysis (and more). Again, pseudocode is provided to expose the reader to implementation aspects. Chapter six on inverse noncooperative differential games provides a similar extension, now for continuous-time inverse optimal control. The book concludes with simulation examples and an experimental case study to illustrate the application of the theory developed in previous chapters.