Neural Lyapunov Control

We propose new methods for learning control policies and neural network Lyapunov functions for nonlinear control problems, with provable guarantee of stability. The framework consists of a learner that attempts to find the control and Lyapunov functions, and a falsifier that finds counterexamples to quickly guide the learner towards solutions. The procedure terminates when no counterexample is found by the falsifier, in which case the controlled nonlinear system is provably stable. The approach significantly simplifies the process of Lyapunov control design, provides end-to-end correctness guarantee, and can obtain much larger regions of attraction than existing methods such as LQR and SOS/SDP. We show experiments on how the new methods obtain high-quality solutions for challenging control problems.Comment: NeurIPS 201

Neural MRAC based on modified state observer

A new model reference adaptive control design method with guaranteed transient performance using neural networks is proposed in this thesis. With this method, stable tracking of a desired trajectory is realized for nonlinear system with uncertainty, and modified state observer structure is designed to enable desired transient performance with large adaptive gain and at the same time avoid high frequency oscillation. The neural network adaption rule is derived using Lyapunov theory, which guarantees stability of error dynamics and boundedness of neural network weights, and a soft switching sliding mode modification is added in order to adjust tracking error. The proposed method is tested by different theoretical application problems simulations, and also Caterpillar Electro-Hydraulic Test Bench experiments. Satisfying results show the potential of this approach --Abstract, page iv

doi:10.1155/2008/868425 Research Article Neural Network Adaptive Control for Discrete-Time Nonlinear Nonnegative Dynamical Systems

Nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative. These models are widespread in engineering and life sciences, and they typically involve the exchange of nonnegative quantities between subsystems or compartments, wherein each compartment is assumed to be kinetically homogeneous. In this paper, we develop a neuroadaptive control framework for adaptive set-point regulation of discrete-time nonlinear uncertain nonnegative and compartmental systems. The proposed framework is Lyapunov-based and guarantees ultimate boundedness of the error signals corresponding to the physical system states and the neural network weighting gains. In addition, the neuroadaptive controller guarantees that the physical system states remain in the nonnegative orthant of the state space for nonnegative initial conditions. Copyright q 2008 Wassim M. Haddad et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1