Decentralized stabilization of state constrained interconnected nonlinear systems based on adaptive dynamic programming

A decentralized stabilization method based on adaptive dynamic programming (ADP) is proposed for a class of interconnected nonlinear systems with constant-value state constraints． A barrier function is introduced so that the original system is converted into an unconstrained system by coordinate transformation． Auxiliary subsystems and improved cost functions enabled transformation of robust decentralized stabilization problem into an optimal regulation problem． The Hamilton-Jacobi-Bellman (HJB) equation is solved by policy iteration after constructing a local critic neural network for each auxiliary subsystem so that an approximate optimal stabilization control law is obtained． According to the Lyapunov stability theory, the proposed method can drive estimation errors of closed-loop interconnected system and local critic neural networks to be ultimately uniformly bounded dynamically． Numerical simulations validate the effectiveness of proposed decentralized stabilization method．