This paper proposes a data-driven optimal tracking control scheme for unknown general nonlinear systems using neural networks. First, a new neural networks structure is established to reconstruct the unknown system dynamics of the form ˙ x(t) = f (x(t))+g(x(t))u(t). Two networks in parallel are designed to approximate the functions
f (x) and g(x). Then the obtained data-driven models are used to build the optimal tracking control. The developed control consists of two parts, the feed-forward control and the optimal feedback control. The optimal feedback control is developed by approximating the solution of the Hamilton-Jacobi-Bellman equation with neural networks. Unlike other studies, the Hamilton-Jacobi-Bellman solution is found by estimating the value function
derivative using neural networks. Finally, the proposed control scheme is tested on a delta robot. Two trajectory tracking examples are provided to verify the effectiveness of the proposed optimal control approach.
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Robust Neural Network Approach to System Identification in the High-Noise Regime
We present a new algorithm for learning unknown gov- erning equations from trajectory data, using a family of neural net- works. Given samples of solutions x(t) to an unknown dynamical system x ̇ (t) = f (t, x(t)), we approximate the function f using a family of neural networks. We express the equation in integral form and use Euler method to predict the solution at every successive time step using at each iter- ation a different neural network as a prior for f. This procedure yields M-1 time-independent networks, where M is the number of time steps at which x(t) is observed. Finally, we obtain a single function f(t,x(t)) by neural network interpolation. Unlike our earlier work, where we numer- ically computed the derivatives of data, and used them as target in a Lipschitz regularized neural network to approximate f, our new method avoids numerical differentiations, which are unstable in presence of noise. We test the new algorithm on multiple examples in a high-noise setting. We empirically show that generalization and recovery of the governing equation improve by adding a Lipschitz regularization term in our loss function and that this method improves our previous one especially in the high-noise regime, when numerical differentiation provides low qual- ity target data. Finally, we compare our results with other state of the art methods for system identification.
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- Award ID(s):
- 2141297
- PAR ID:
- 10519877
- Publisher / Repository:
- Springer Verlag
- Date Published:
- ISSN:
- 0302-9743
- ISBN:
- 978-3-031-44505-7
- Format(s):
- Medium: X
- Location:
- Nice, France
- Sponsoring Org:
- National Science Foundation
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