Volume 2, Issue 3 (1991), pp. 414–433
In this paper open-loop three-level Stackelberg strategies in deterministic, sequential decision-making problems for linear continuous-time singular systems and quadratic cost function are studied. Necessary conditions under which the existence of open-loop Stackelberg strategies are derived. The analytical solution of three-level open-loop Stackelberg problem is given by means of the eigenvector method. An example is given to illustrate the proposed method.
Volume 2, Issue 2 (1991), pp. 233–247
This paper is concerned with the derivation of open-loop Stackelberg (OLS) solutions of a class of continuous-time two-player nonzero-sum differential games characterized by quadratic cost functionals and linear singular systems. By applying the calculus of variations, necessary conditions are derived under which the open-loop Stackelberg solution of the leader exists. Under the transformation by which the matrix E has diagonal form, we derive a matrix Riccati differential equation from the necessary conditions. An example is given to illustrate the results of the paper.