Decentralized stabilization of state constrained interconnected nonlinear systems based on adaptive dynamic programming
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摘要: 针对一类含有常数型状态约束的互联非线性系统，提出一种基于自适应动态规划(adaptive dynamic programming，ADP)的分散镇定方法．引入边界函数对原系统进行坐标变换，将状态约束系统转化为无约束系统．对转化后的系统构造独立子系统和改进的代价函数，将鲁棒分散镇定问题转化为最优调节问题．构建局部评判神经网络并采用策略迭代算法求解哈密顿-雅可比-贝尔曼(Hamilton-Jacobi-Bellman，HJB)方程，进而得到近似最优镇定律．通过李雅普诺夫稳定性理论证明了本文所提方法可使闭环互联系统和局部评判神经网络估计误差动态最终一致有界．数值仿真结果验证了所提出分散镇定方法的有效性．Abstract: 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．
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