Intelligent Constrained Optimal Control of Aerospace Vehicles with Model Uncertainties
Jie Ding, Sivasubramanya Nadar Balakrishnan · Journal of Guidance Control and Dynamics · 2012
Approximate dynamic programming formulation implemented with an “adaptive critic-based” neural network structure has been shown to be a powerful technique to solve theHamilton–Jacobi–Bellman equations. As interest in this technique grows, it is important to consider the enabling factors for their possible implementations. A typical adaptive critic structure consists of two interacting neural networks; in this paper, a new architecture, called the “cost function-based single network adaptive critic” is presented that eliminates one of the networks. This approach is applicable to a wide class of nonlinear systems in engineering where the optimal control equation can be explicitly expressed in terms of the state and cost-related variables. After the “training,” the output of the neural network represents the optimal cost. Optimal control is obtained by finding the derivatives of the output of the network with respect to its input and using it in the expression for optimal control. In practical applications, there usually exist uncertainties in modeling and in system parameters. Furthermore, the controllers have operational limits. The first concern is taken care of through an “approximated system” that contains an estimate of the uncertainties from an online neural network andhelps calculate the optimal control for the changed plant. Regarding the second concern, a nonquadratic term that incorporates the control constraints is used in the performance index. Necessary conditions for optimal control are derived and an algorithm to solve the constrained-control problem with cost function-based single network adaptive critic is developed. Two aerospace systems are used to illustrate the working of the proposed technique.