ε-Optimal Control For Nonlinear Systems With State Delay Based On Finite Horizon ADP Algorithm

Time delay, control constraints often occur in actual industrial system. The system information can not be able to transfer in time with delay, while the controller designed without consideration of constraints will not reach the control requirements and may even lead to system instability. On the other hand, actual system usually needs to be controlled into stable within finite time and minimize the control cost at the same time. Therefore, it is important to study the finite horizon optimal control problems with delay and control constraints.Finite horizon ADP algorithm is an effective way to deal with finite-time optimal control of nonlinear systems. One could obtain approximate optimal control and optimal performance index function in finite iteration step by introducing an error bond ε. In this paper, finite horizon ADP algorithm is used to study on optimal control problems of nonlinear systems with state delay and control constraints. The main results are as follows:1. In order to deal with a class of nonlinear systems with state delay, finite horizon ADP algorithm is introduced to solve discrete time HJB equation with state delay, the convergence of the iterative process is proved and BP neural networks are used to implement our algorithm and ε-optimal control is obtained. The simulation examples show that the controller we proposed works well;2. In order to deal with a class of nonlinear systems with state delay and bounded control constraints, a new performance index function is defined for control constraints, the iterative solution of corresponding HJB equation is got by finite horizon ADP algorithm, we prove that the iterative cost function converges to the optimal performance index function, moreover, the ε-optimal control is obtained, comparing simulation results show the effectiveness of the algorithm;3. In order to deal with the common time-invariant tracking control problems in actual industrial systems, the original system optimal tracking control problem is transformed into optimal regulator problem of a new system by mathematical method, the state variables of the new system is the tracking error. The ε-optimal tracking control of a class of discrete time nonlinear systems with state delay is obtained. Simulation results show that the controller designed in this article can track any state to the target and makes the performance index function converges to optimal.