Distributed Learning Model Predictive Control for Linear Systems

This paper presents a distributed learning model predictive control (DLMPC) scheme for distributed linear time invariant systems with coupled dynamics and state constraints. The proposed solution method is based on an online distributed optimization scheme with nearest-neighbor communication. If the control task is iterative and data from previous feasible iterations are available, local data are exploited by the subsystems in order to construct the local terminal set and terminal cost, which guarantee recursive feasibility and asymptotic stability, as well as performance improvement over iterations. In case a first feasible trajectory is difficult to obtain, or the task is non-iterative, we further propose an algorithm that efficiently explores the state-space and generates the data required for the construction of the terminal cost and terminal constraint in the MPC problem in a safe and distributed way. In contrast to other distributed MPC schemes which use structured positive invariant sets, the proposed approach involves a control invariant set as the terminal set, on which we do not impose any distributed structure. The proposed iterative scheme converges to the global optimal solution of the underlying infinite horizon optimal control problem under mild conditions. Numerical experiments demonstrate the effectiveness of the proposed DLMPC scheme

Bayesian model predictive control: Efficient model exploration and regret bounds using posterior sampling

Tight performance specifications in combination with operational constraints make model predictive control (MPC) the method of choice in various industries. As the performance of an MPC controller depends on a sufficiently accurate objective and prediction model of the process, a significant effort in the MPC design procedure is dedicated to modeling and identification. Driven by the increasing amount of available system data and advances in the field of machine learning, data-driven MPC techniques have been developed to facilitate the MPC controller design. While these methods are able to leverage available data, they typically do not provide principled mechanisms to automatically trade off exploitation of available data and exploration to improve and update the objective and prediction model. To this end, we present a learning-based MPC formulation using posterior sampling techniques, which provides finite-time regret bounds on the learning performance while being simple to implement using off-the-shelf MPC software and algorithms. The performance analysis of the method is based on posterior sampling theory and its practical efficiency is illustrated using a numerical example of a highly nonlinear dynamical car-trailer system

Remembering Forward: Neural Correlates of Memory and Prediction in Human Motor Adaptation

We used functional MR imaging (FMRI), a robotic manipulandum and systems identification techniques to examine neural correlates of predictive compensation for spring-like loads during goal-directed wrist movements in neurologically-intact humans. Although load changed unpredictably from one trial to the next, subjects nevertheless used sensorimotor memories from recent movements to predict and compensate upcoming loads. Prediction enabled subjects to adapt performance so that the task was accomplished with minimum effort. Population analyses of functional images revealed a distributed, bilateral network of cortical and subcortical activity supporting predictive load compensation during visual target capture. Cortical regions – including prefrontal, parietal and hippocampal cortices – exhibited trial-by-trial fluctuations in BOLD signal consistent with the storage and recall of sensorimotor memories or “states” important for spatial working memory. Bilateral activations in associative regions of the striatum demonstrated temporal correlation with the magnitude of kinematic performance error (a signal that could drive reward-optimizing reinforcement learning and the prospective scaling of previously learned motor programs). BOLD signal correlations with load prediction were observed in the cerebellar cortex and red nuclei (consistent with the idea that these structures generate adaptive fusimotor signals facilitating cancelation of expected proprioceptive feedback, as required for conditional feedback adjustments to ongoing motor commands and feedback error learning). Analysis of single subject images revealed that predictive activity was at least as likely to be observed in more than one of these neural systems as in just one. We conclude therefore that motor adaptation is mediated by predictive compensations supported by multiple, distributed, cortical and subcortical structures