Fast Non-Parametric Learning to Accelerate Mixed-Integer Programming for Online Hybrid Model Predictive Control

Today's fast linear algebra and numerical optimization tools have pushed the frontier of model predictive control (MPC) forward, to the efficient control of highly nonlinear and hybrid systems. The field of hybrid MPC has demonstrated that exact optimal control law can be computed, e.g., by mixed-integer programming (MIP) under piecewise-affine (PWA) system models. Despite the elegant theory, online solving hybrid MPC is still out of reach for many applications. We aim to speed up MIP by combining geometric insights from hybrid MPC, a simple-yet-effective learning algorithm, and MIP warm start techniques. Following a line of work in approximate explicit MPC, the proposed learning-control algorithm, LNMS, gains computational advantage over MIP at little cost and is straightforward for practitioners to implement

Machine learning plasma-surface interface for coupling sputtering and gas-phase transport simulations

Thin film processing by means of sputter deposition inherently depends on the interaction of energetic particles with a target surface and the subsequent particle transport. The length and time scales of the underlying physical phenomena span orders of magnitudes. A theoretical description which bridges all time and length scales is not practically possible. Advantage can be taken particularly from the well-separated time scales of the fundamental surface and plasma processes. Initially, surface properties may be calculated from a surface model and stored for a number of representative cases. Subsequently, the surface data may be provided to gas-phase transport simulations via appropriate model interfaces (e.g., analytic expressions or look-up tables) and utilized to define insertion boundary conditions. During run-time evaluation, however, the maintained surface data may prove to be not sufficient. In this case, missing data may be obtained by interpolation (common), extrapolation (inaccurate), or be supplied on-demand by the surface model (computationally inefficient). In this work, a potential alternative is established based on machine learning techniques using artificial neural networks. As a proof of concept, a multilayer perceptron network is trained and verified with sputtered particle distributions obtained from transport of ions in matter based simulations for Ar projectiles bombarding a Ti-Al composite. It is demonstrated that the trained network is able to predict the sputtered particle distributions for unknown, arbitrarily shaped incident ion energy distributions. It is consequently argued that the trained network may be readily used as a machine learning based model interface (e.g., by quasi-continuously sampling the desired sputtered particle distributions from the network), which is sufficiently accurate also in scenarios which have not been previously trained

Online-Computation Approach to Optimal Control of Noise-Affected Nonlinear Systems with Continuous State and Control Spaces

© 2007 EUCA.A novel online-computation approach to optimal control of nonlinear, noise-affected systems with continuous state and control spaces is presented. In the proposed algorithm, system noise is explicitly incorporated into the control decision. This leads to superior results compared to state-of-the-art nonlinear controllers that neglect this influence. The solution of an optimal nonlinear controller for a corresponding deterministic system is employed to find a meaningful state space restriction. This restriction is obtained by means of approximate state prediction using the noisy system equation. Within this constrained state space, an optimal closed-loop solution for a finite decision-making horizon (prediction horizon) is determined within an adaptively restricted optimization space. Interleaving stochastic dynamic programming and value function approximation yields a solution to the considered optimal control problem. The enhanced performance of the proposed discrete-time controller is illustrated by means of a scalar example system. Nonlinear model predictive control is applied to address approximate treatment of infinite-horizon problems by the finite-horizon controller

Identification of nonlinear time-varying systems using an online sliding-window and common model structure selection (CMSS) approach with applications to EEG

The identification of nonlinear time-varying systems using linear-in-the-parameter models is investigated. A new efficient Common Model Structure Selection (CMSS) algorithm is proposed to select a common model structure. The main idea and key procedure is: First, generate K 1 data sets (the first K data sets are used for training, and theK 1 th one is used for testing) using an online sliding window method; then detect significant model terms to form a common model structure which fits over all the K training data sets using the new proposed CMSS approach. Finally, estimate and refine the time-varying parameters for the identified common-structured model using a Recursive Least Squares (RLS) parameter estimation method. The new method can effectively detect and adaptively track the transient variation of nonstationary signals. Two examples are presented to illustrate the effectiveness of the new approach including an application to an EEG data set