Recent successes in the field of machine learning, as well as the availability of increased sensing and computational capabilities in modern control systems, have led to a growing interest in learning and data-driven control techniques. Model predictive control (MPC), as the prime methodology for constrained control, offers a significant opportunity to exploit the abundance of data in a reliable manner, particularly while taking safety constraints into account. This review aims at summarizing and categorizing previous research on learning-based MPC, i.e., the integration or combination of MPC with learning methods, for which we consider three main categories. Most of the research addresses learning for automatic improvement of the prediction model from recorded data. There is, however, also an increasing interest in techniques to infer the parameterization of the MPC controller, i.e., the cost and constraints, that lead to the best closed-loop performance. Finally, we discuss concepts that leverage MPC to augment learning-based controllers with constraint satisfaction properties.
This paper presents an inverse optimal control methodology and its application to training a predictive model of human motor control from a manipulation task. It introduces a convex formulation for learning both objective function and constraints of an infinite-horizon constrained optimal control problem with nonlinear system dynamics. The inverse approach utilizes Bellman's principle of optimality to formulate the infinitehorizon optimal control problem as a shortest path problem and Lagrange multipliers to identify constraints. We highlight the key benefit of using the shortest path formulation, i.e., the possibility of training the predictive model with short and selected trajectory segments. The method is applied to training a predictive model of movements of a human subject from a manipulation task. The study indicates that individual human movements can be predicted with low error using an infinite-horizon optimal control problem with constraints on shoulder movement.
This paper presents convex formulations for inverse optimal control problems for linear systems to infer cost function matrices of a quadratic cost from both optimal and non-optimal closed-loop gains. It introduces an optimality measure which enables a formulation of the problem as a convex semidefinite program for the general case and a linear program for several special cases. We derive an explicit algebraic expression for general objective function matrices as well as conditions under which the solution to the inverse optimal control problem is unique. The result is derived by means of a vectorization and parametrization of the algebraic Riccati equation. A simulation example highlights the robust performance in the presence of noise on the measured closed-loop gain and the computational efficiency of the proposed problem formulations.
Normal pressure hydrocephalus (NPH) is a chronic and progressive disease that affects predominantly elderly subjects. The most prevalent symptoms are gait disorders, generally determined by visual observation or measurements taken in complex laboratory environments. However, controlled testing environments can have a significant influence on the way subjects walk and hinder the identification of natural walking characteristics. The study aimed to investigate the differences in walking patterns between a controlled environment (10 m walking test) and real-world environment (72 h recording) based on measurements taken via a wearable gait assessment device. We tested whether real-world environment measurements can be beneficial for the identification of gait disorders by performing a comparison of patients’ gait parameters with an aged-matched control group in both environments. Subsequently, we implemented four machine learning classifiers to inspect the individual strides’ profiles. Our results on twenty young subjects, twenty elderly subjects and twelve NPH patients indicate that patients exhibited a considerable difference between the two environments, in particular gait speed (p-value p=0.0073), stride length (p-value p=0.0073), foot clearance (p-value p=0.0117) and swing/stance ratio (p-value p=0.0098). Importantly, measurements taken in real-world environments yield a better discrimination of NPH patients compared to the controlled setting. Finally, the use of stride classifiers provides promise in the identification of strides affected by motion disorders.
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