A near-optimal decentralized control approach for polynomial nonlinear interconnected systems

This article tackles the decentralized near-optimal control problem for the class of nonlinear polynomial interconnected system based on a shifted Legendre polynomials direct approach. The proposed method converts the interconnected optimal control problems into a nonlinear programming one with multiple constraints. In light of the formulated NLP optimization, state and control coefficients are used to design a nonlinear decentralized state feedback controller. Overall closed-loop system stability sufficient conditions are investigated with the help of Gronwall lemma. The triple inverted pendulum case is considered for simulation. Satisfactory results are obtained in both open-loop and closed-loop schemes with comparison to collocation and state-dependent Riccati equation techniques.