Finite-Horizon Optimal Control for Nonlinear Multi-Input Systems With Online Adaptive Integral Reinforcement Learning

In this paper, a novel adaptive integral reinforcement learning (AIRL) is utilized to online handle the finite-horizon optimum control policies of the partially unknown multi-input nonlinear system. Firstly, the concept of Nash equilibrium is introduced to make the multiple cost functions reach the saddle point. Then, dual neural networks (NNs) are applied to approach the performance index functions based on the integral reinforcement signal. Simultaneously, two novel learning algorithms are proposed to update the NN weights, in which the convergence of weights is proved. Then, the optimal strategies can be obtained by using the obtained weights. The designed controllers based on the data-driven AIRL scheme can avoid the internal state of the system and the derivatives of NN activations in the weight learning process. Finally, the stability of the controlled system is analyzed. An F-16 aircraft model and another nonlinear system are utilized to prove the validity and rationality of the algorithm.
Note to Practitioners
—There exist many multi-input systems in practical engineering, which includes multi-engine driven F-16 aircraft, large radar servo system and large artillery systems, etc. The finite-horizon optimal control of these systems is crucial for the better performance of system state. However, an accurate engineering model is difficult to obtain, and the finite-horizon cannot generally be achieved. To address these issues, this paper proposes the finite-horizon optimal control for these systems based on a novel adaptive integral reinforcement learning (AIRL). The AIRL can realize an optimal performance for these multi-input systems in finite-time without internal system dynamics, which is a good development for the multi-input system in practical engineering.