Identification Of State Space Systems With Time-Delays

Mathematical model is the foundation of system control. The state space model can be utilized to describe dynamic systems. Some of the practically controlled objects contain time delay. This thesis mainly focuses on identi?cation of the state space system with time delay, which has important theoretical signi?cance and application prospects. Based on the data ?ltering technique, the hierarchical identi?cation principle and the Moving Horizon Estimation principle, this dissertation studies the parameter identi?cation, and state and time delay estimation of the standard state space model with time delay. The following results are obtained.(1) For the state space model with a unit time delay, the corresponding input–output expression and the identi?cation model are derived by using shift operators. Since the information vector contains unknown variables, we use the measurable information of the system to construct an auxiliary model, and replace the output of the auxiliary model with the unknown variables, this thesis proposes the auxiliary model based least squares identi?cation method for the state space model with a unit time delay. Furthermore, For the input nonlinear state space model with a unit time delay, the identi?cation model is derived, and the unknown state variables in the information vector are replaced by the states of the state observer based on the parameter estimation. This thesis proposes the gradient iterative parameter identi?cation algorithm and the least squares iterative parameter identi?cation algorithm based on the state observer.(2) For the state space model with d-step time delay, the identi?cation model is derived. The main feature of this model is that the information vector contains the unknown state variables of the system, the estimated states are replaced by the unknown states in the information vector. This thesis estimates the parameters by proposing the recursive least squares identi?cation algorithm based on the state estimation, and uses the parameter estimates to calculate the states of the system. For the multivariable state space model with d-step time delay, including signi?cant amount of input–output variables, large number of the parameters, and large calculated amount of the identi?cation algorithm,this thesis improves computational e?ciency by utilizing the hierarchical least squares identi?cation algorithm based on state estimation, which derives from the hierarchical identi?cation theory and Kalman ?ltering.(3) For the multivariable state space model with multi-state delays, this thesis utilizes decomposition techniques to divide the system into two subsystems. Then hierarchical gradient based iterative identi?cation algorithm and hierarchical least squares based iterative identi?cation algorithm are derived from the decomposed subsystems. For the dual-rate state space model with multi-state delays, the auxiliary model based least squares algorithm is derived based on an auxiliary model idea, which replaces the unmeasurable variables and the noise variables with the output of the auxiliary model and the estimated residual error, respectively. In order to improve accuracy, the ?ltering based auxiliary model least square algorithm is derived by utilizing parameters from the system model and the noise model, after taking cross estimation of ?ltering into consideration.(4) For the uncertain state space model with time delay, the time delay is assumed to follow a Markov model, the Moving Horizon Estimation algorithm is derived from the data and the cost function of the Moving Horizon to optimize the objective function. When the time delay follows uniform distribution, the Expectation Maximization algorithm for the multirate uncertain state space model with time delay is derived. This algorithm contains the E step and the M step. The E step calculates the Expectation of the complete data(usually referred as the Q function), and the M step maximizes the Q function. These two steps iterate until the results converge.This thesis veri?es the e?ectiveness of the algorithms by performing simulations in regards to the proposed parameter estimation algorithms.