Recurrent learning algorithms for designing optimal controllers of continuous systems

Abstract

This paper proposes the recurrent learning algorithm for designing thr controllers of continuous dynamical systems in the optimal control problems. The designed controllers are in the form of unfolded recurrent neural networks embedded with physical laws coming from the classical control techniques. The proposed learning algorithm is characterized by its double-forward-recurrent-loops structure for solving both the temporal recurrent and the structure recurrent problems. The first problem is resulted from the nature of general optimal control problems, where the objective functions are often related to (evaluated at) some specific (instead of all) time steps or system states only, causing missing Learning signals at some time steps or system states. The second problem is due to the high-order discretization of the continuous systems bg the Runge-Kutta method that we perform to increase the control accuracy. This discretization transforms the system into several identical subnetworks interconnected together, like a recurrent neural network expanded in the time axis. Two recurrent learning algorithms with different convergence properties are derived; the first- and second-order learning algorithms. The computations of both algorithms are local and performed efficiently as network signal propagation. We also propose two new nonlinear controller structures for two specific control problems:1) two-dimensional (2-D) guidance problem and 2) optimal PI control problem. Under the training of the proposed recurrent learning algorithms, these two controllers can be easily tuned to be suboptimal for given objective functions. Extensive computer simulations have shown the optimization and generalization abilities of the controllers designed bg the proposed learning scheme.