Optimal Synchronization Controller Design For Complex Dynamical Networks With Unknown System Dynamics

In this thesis,the major investigated problem is the optimal synchronization controller design for the complex dynamical systems with the unknown internal dynamics.In the beginning,for the complex dynamical networks with linear state couplings,a necessary and sufficient condition of a fact that an acceptable control is the optimal one is given by defining a new quadratic performance index based on the optimal control theory.The optimal state-synchronized controller is composed of the feedback part and the compensated feedforward part,where the feedback gain remains the solution to the well-known Algebraic Riccati Equation(ARE).Moreover,in the case of unknown internal dynamics,to find the feedback control gain of the optimal controller,a novel model-free online iterative algorithm is proposed using the information of system states and inputs to solve ARE.In addition,for the complex dynamical networks with nonlinear state couplings,the optimal output-synchronized controller is provided by defining a new discounted quadratic performance index based on the Bellman optimality principle.Meanwhile,it is shown that the proposed nonlinear optimal control law can solve the output regulator equation implicitly.The above controller consists of the feedback part and the compensated feedforward part,where the feedback can be obtained by solving the well-known Hamilton-Jacobi-Bellman(HJB)quation.Especially,considering the unknown dynamics,a novel online iterative algorithm is provided to solve the HJB equation by using the information of nodes' states and inputs.And,the artificial neural network is applied to implement this algorithm where the critic neural network is used to approximate the performance index and the actor neural network is used to approximate the control law.The least-squared method respect to the approximation errors of neural networks is employed to find the optimal value of the network weights.Finally,the responding theoretical proof of all above proposed results is given,and some simulation examples are provided to show the effectiveness of the controller design scheme.