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Real-time interpolation of streaming data

Dębski Roman

Computer Science

2020

T. 21 (4)

513–532

One of the key elements of the real-time C 1 -continuous cubic spline interpolation of streaming data is an estimator of the first derivative of the interpolated function that is more accurate than those based on finite difference schemas. Two such greedy look-ahead heuristic estimators, based on the calculus of variations (denoted as MinBE and MinAJ2), are formally defined (in closed form), along with the corresponding cubic splines that they generate. They are then comparatively evaluated in a series of numerical experiments involving different types of performance measures. The presented results show that the cubic Hermite splines generated by heuristic MinAJ2 significantly outperformed those that were based on finite difference schemas in terms of all of the tested performance measures (including convergence). The proposed approach is quite general. It can be directly applied to streams of univariate functional data like time-series. Multi-dimensional curves that are defined parametrically (after splitting) can be handled as well. The streaming character of the algorithm means that it can also be useful in processing data sets that are too large to fit in the memory (e.g., edge computing devices, embedded time-series databases).

Online learning algorithm for zero-sum games with integral reinforcement learning

Vamvoudakis K. G., Vrabie D., Lewis F. L.

Journal of Artificial Intelligence and Soft Computing Research

2011

Vol. 1, No. 4

315--332

In this paper we introduce an online algorithm that uses integral reinforcement knowledge for learning the continuous-time zero sum game solution for nonlinear systems with infinite horizon costs and partial knowledge of the system dynamics. This algorithm is a data based approach to the solution of the Hamilton-Jacobi-Isaacs equation and it does not require explicit knowledge on the system’s drift dynamics. A novel adaptive control algorithm is given that is based on policy iteration and implemented using an actor/ disturbance/critic structure having three adaptive approximator structures. All three approximation networks are adapted simultaneously. A persistence of excitation condition is required to guarantee convergence of the critic to the actual optimal value function. Novel adaptive control tuning algorithms are given for critic, disturbance and actor networks. The convergence to the Nash solution of the game is proven, and stability of the system is also guaranteed. Simulation examples support the theoretical result.