On dynamical input reconstruction in a distributed second order equation

A second order nonlinear differential equation is considered. An algorithm for reconstructing an input from inaccurate measurements of the solution at discrete times is designed. The algorithm based on the constructions of feedback control theory and theory of ill-posed problems is stable with respect to informational noises and computational errors.

Policy iteration for Hamilton–Jacobi–Bellman equations with control constraints

Policy iteration is a widely used technique to solve the Hamilton Jacobi Bellman (HJB) equation, which arises from nonlinear optimal feedback control theory. Its convergence analysis has attracted much attention in the unconstrained case. Here we analyze the case with control constraints both for the HJB equations which arise in deterministic and in stochastic control cases. The linear equations in each iteration step are solved by an implicit upwind scheme. Numerical examples are conducted to solve the HJB equation with control constraints and comparisons are shown with the unconstrained cases.

Implications of Optimal Feedback Control Theory for Sport Coaching and Motor Learning: A Systematic Review

Best practice in skill acquisition has been informed by motor control theories. The main aim of this study is to screen existing literature on a relatively novel theory, Optimal Feedback Control Theory (OFCT), and to assess how OFCT concepts can be applied in sports and motor learning research. Based on 51 included studies with on average a high methodological quality, we found that different types of training seem to appeal to different control processes within OFCT. The minimum intervention principle (founded in OFCT) was used in many of the reviewed studies, and further investigation might lead to further improvements in sport skill acquisition. However, considering the homogenous nature of the tasks included in the reviewed studies, these ideas and their generalizability should be tested in future studies.

A Proposed Postural Control Theory Synthesizing Optimal Feedback Control Theory, Postural Motor Learning, and Cerebellar Supervision Learning

Multiple theories regarding motor learning and postural control development aim to explain how the central nervous system (CNS) acquires, adjusts, and learns postural behaviors. However, few theories of postural motor development and learning propose possible neurophysiologic correlates to support their assumptions. Evidence from behavioral and computational models support the cerebellum’s role in supervising motor learning through the production of forward internal models, corrected by sensory prediction errors. Optimal Feedback Control Theory (OFCT) states that the CNS learns new behaviors by minimizing the cost of multi-joint movements that attain a task goal. By synthesizing principles of the OFCT, postural sway characteristics, and cerebellar anatomy and its internal models, we propose an integrated learning model in which cerebellar supervision of postural control is governed by movement cost functions.