Optimal control with a worst-case performance criterion and applications (Q1188847)

This monograph deals with differentiable optimal control problems for systems of ordinary differential equations where the cost functionals are products of powers of definite integrals. The text is divided into seven chapters which are more or less unrelated to each other, reflecting individual publications of the author in journals and conference proceedings. Chapter 1 treats general nonlinear control problems with cost functionals in the form of quotients or products of definite integrals. Using the classical theory of Dubivitskii-Milyutin, the author derives the necessary conditions of optimality in terms of the adjoint state variables and the associated variational inequality. Chapter 2 brings a related discussion for the case of linear system dynamics. Chapters 3 and 4 deal with optimal disturbance rejection and performance robustness in linear systems. In Chapter 3 an expression for the worst- case performance with respect to system parameter variations is derived, while Chapter 4 brings the necessary conditions for the control yielding a maximum disturbance rejection. In the Chapters 5 and 6 the finite-interval \(H_{\infty}\)-problem is considered; existence and necessary conditions for optimal controls are derived, as well as an expression for the worst-case performance in terms of system parameter variations. The final Chapter 7 treats the problem of optimal reduction of a high order system to low order. The text is clearly written and an interesting contribution to the existing literature. What is missing is an explicit motivation for the nonstandard cost functionals which are considered; the interested reader would also welcome some further numerical examples in the text.