Adaptive dynamic programming

What is it about?

In this publication, I propose a new method to design an online robust adaptive dynamic programming algorithm (RADPA) for a wheeled mobile robot which is equipped with an omni-directional vision system. To integrate kinematic and dynamic controllers into the unique controller, we transform the strict feedback system dynamics into tracking error dynamics. Then, we propose a control scheme which uses only one neural network rather than three proposed in the actor-critic-based control schemes for the two-player zero-sum game problem. A neural network weight update law is designed for approximating the solution of the Hamilton–Jacobi–Isaacs equation without knowing knowledge of internal system dynamics. To implement the scheme, we propose the online RADPA, in which control and disturbance laws are updated simultaneously in an iterative loop. The convergence and stability of the online RADPA are proven by Lyapunov techniques. Simulations and experiments on a wheeled mobile robot test-bed are carried out to verify the effectiveness of the proposed algorithm.

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Why is it important?

My work is important to readers because it is the first work that uses the robust ADP method to integrate kinematic and dynamic controllers into the unique controller for the WMR without using knowledge of the internal system dynamics. First, we derive tracking error dynamics from the WMR’s nonlinear system in the strict-feedback form, and then we develop the hardware and the software for a WMR test-bed equipped with the omni-directional vision (ODV) system. Second, we propose the control scheme that uses only one NN to reduce the computational complexity and waste of sources. Then, we propose the NN weight update law for approximating the solution of the HJI equation. The online training samples of the NN are collected in just one sampling interval. Third, we design the online RADPA for updating the control law as well as the worst disturbance law simultaneously in only one iterative loop rather than two. Finally, we prove that the tracking errors of the closed-loop system and NN weight errors are Uniformly Ultimately Bounded (UUB) stable and that the value function, the approximated control signals and the approximated worst disturbance signals approach the optimal values with small bounded errors.

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