Inverted Pendulum Control Based On Approximate Dynamic Programming

The control of inverted pendulum system has long considered an intriguing problem for control theory and its applications. It is well known as test bed for new control theory and techniques. As a highly nonlinear and unstable system, the stabilization control of inverted pendulum system is a primary challenge for researchers in this field because of the difficulty of the problem. Approximate dynamic programming contains the idea of neural network and typical dynamic programming, this method can solve plant modeling problem and avoid "curse of dimensionality". It's a kind of advanced control theory.ADHDP (Action-Dependent Heuristic Dynamic Programming) and ADDHP ( Action-Dependent Dual Heuristic Programming ) of approximate dynamic programming are researched in this paper. Through the analysis of ADHDP, ADDHP and the state variables of inverted pendulum, Critic Network (CN) and Action Network (AN) are designed. The state variables and AN output are put into the input layer of CN, and the output of CN was employed to approximate the cost function in dynamic programming. Through minimizing the error of approximation, the weight of CN is updated. Then the updated CN influences the weight update rule in AN, in order to generate a control action signal which is very close to the optimal control action. The training error functions of CN and AN are based on Bellman optimal principle, and CN includes a model network in fact. So the plant model is not need to be build, and the configuration is simplified. The simulation results for the control of inverted pendulum show that the method has the advantages of fast speed and good stability.So, the controller design and implementation of control algorithms have an important academic and practical significance.