Global H ∞ control for a class of interconnected nonlinear systems

Abstract

Abstract This paper is concerned with a global H ∞ control problem for a class of interconnected nonlinear systems. We first consider a fairly general class of large-scale nonlinear systems with strong nonlinear interconnections. It is shown that the decentralized H ∞ control problem for the system can be converted into centralized H ∞ control problems associated with a set of auxiliary systems whose solutions are related to the Hamilton Jacobi Isaacs (HJI) inequalities. Realizing that finding a global solution of the HJI inequality is usually impossible, we then concentrate on a globally inverse H ∞ , control problem for a class of interconnected nonlinear systems which are transformable to interconnected systems with lower triangular structure. We show that the decentralized control laws and the weights can be constructed explicitly using a two-way (backward and forward) recursive design technique extended from (Isidori and Lin, 1998).