A parallel multistate framework for atomistic non-equilibrium reaction dynamics of solutes in strongly interacting organic solvents

We describe a parallel linear-scaling computational framework developed to implement arbitrarily large multi-state empirical valence bond (MS-EVB) calculations within CHARMM. Forces are obtained using the Hellman-Feynmann relationship, giving continuous gradients, and excellent energy conservation. Utilizing multi-dimensional Gaussian coupling elements fit to CCSD(T)-F12 electronic structure theory, we built a 64-state MS-EVB model designed to study the F + CD3CN -> DF + CD2CN reaction in CD3CN solvent. This approach allows us to build a reactive potential energy surface (PES) whose balanced accuracy and efficiency considerably surpass what we could achieve otherwise. We use our PES to run MD simulations, and examine a range of transient observables which follow in the wake of reaction, including transient spectra of the DF vibrational band, time dependent profiles of vibrationally excited DF in CD3CN solvent, and relaxation rates for energy flow from DF into the solvent, all of which agree well with experimental observations. Immediately following deuterium abstraction, the nascent DF is in a non-equilibrium regime in two different respects: (1) it is highly excited, with ~23 kcal mol-1 localized in the stretch; and (2) not yet Hydrogen bonded to the CD3CN solvent, its microsolvation environment is intermediate between the non-interacting gas-phase limit and the solution-phase equilibrium limit. Vibrational relaxation of the nascent DF results in a spectral blue shift, while relaxation of its microsolvation environment results in a red shift. These two competing effects result in a post-reaction relaxation profile distinct from that observed when DF vibration excitation occurs within an equilibrium microsolvation environment. The parallel software framework presented in this paper should be more broadly applicable to a range of complex reactive systems.Comment: 58 pages and 29 Figure

Backstepping controller synthesis and characterizations of incremental stability

Incremental stability is a property of dynamical and control systems, requiring the uniform asymptotic stability of every trajectory, rather than that of an equilibrium point or a particular time-varying trajectory. Similarly to stability, Lyapunov functions and contraction metrics play important roles in the study of incremental stability. In this paper, we provide characterizations and descriptions of incremental stability in terms of existence of coordinate-invariant notions of incremental Lyapunov functions and contraction metrics, respectively. Most design techniques providing controllers rendering control systems incrementally stable have two main drawbacks: they can only be applied to control systems in either parametric-strict-feedback or strict-feedback form, and they require these control systems to be smooth. In this paper, we propose a design technique that is applicable to larger classes of (not necessarily smooth) control systems. Moreover, we propose a recursive way of constructing contraction metrics (for smooth control systems) and incremental Lyapunov functions which have been identified as a key tool enabling the construction of finite abstractions of nonlinear control systems, the approximation of stochastic hybrid systems, source-code model checking for nonlinear dynamical systems and so on. The effectiveness of the proposed results in this paper is illustrated by synthesizing a controller rendering a non-smooth control system incrementally stable as well as constructing its finite abstraction, using the computed incremental Lyapunov function.Comment: 23 pages, 2 figure

Combining Subgoal Graphs with Reinforcement Learning to Build a Rational Pathfinder

In this paper, we present a hierarchical path planning framework called SG-RL (subgoal graphs-reinforcement learning), to plan rational paths for agents maneuvering in continuous and uncertain environments. By "rational", we mean (1) efficient path planning to eliminate first-move lags; (2) collision-free and smooth for agents with kinematic constraints satisfied. SG-RL works in a two-level manner. At the first level, SG-RL uses a geometric path-planning method, i.e., Simple Subgoal Graphs (SSG), to efficiently find optimal abstract paths, also called subgoal sequences. At the second level, SG-RL uses an RL method, i.e., Least-Squares Policy Iteration (LSPI), to learn near-optimal motion-planning policies which can generate kinematically feasible and collision-free trajectories between adjacent subgoals. The first advantage of the proposed method is that SSG can solve the limitations of sparse reward and local minima trap for RL agents; thus, LSPI can be used to generate paths in complex environments. The second advantage is that, when the environment changes slightly (i.e., unexpected obstacles appearing), SG-RL does not need to reconstruct subgoal graphs and replan subgoal sequences using SSG, since LSPI can deal with uncertainties by exploiting its generalization ability to handle changes in environments. Simulation experiments in representative scenarios demonstrate that, compared with existing methods, SG-RL can work well on large-scale maps with relatively low action-switching frequencies and shorter path lengths, and SG-RL can deal with small changes in environments. We further demonstrate that the design of reward functions and the types of training environments are important factors for learning feasible policies.Comment: 20 page