Determining Human Control Intent Using Inverse LQR Solutions

2013 ◽  
Author(s):  
M. Cody Priess ◽  
Jongeun Choi ◽  
Clark Radcliffe
Keyword(s):  
Human Subjects ◽  
Optimal Solution ◽  
Linear Matrix ◽  
Minimization Method ◽  
Human Control ◽  
Balance Task ◽  
Lqr Problem ◽  
Seated Balance ◽  
Gradient Based ◽  
Time Invariant

In this paper, we have developed a method for determining the control intention in human subjects during a prescribed motion task. Our method is based on the solution to the inverse LQR problem, which can be stated as: does a given controller K describe the solution to a time-invariant LQR problem, and if so, what weights Q and R produce K as the optimal solution? We describe an efficient Linear Matrix Inequality (LMI) method for determining a solution to the general case of this inverse LQR problem when both the weighting matrices Q and R are unknown. Additionally, we propose a gradient-based, least-squares minimization method that can be applied to approximate a solution in cases when the LMIs are infeasible. We develop a model for an upright seated-balance task which will be suitable for identification of human control intent once experimental data is available.

scholarly journals The optimal convergence factor of the gradient based iterative algorithm for linear matrix equations

Filomat ◽  
2012 ◽  
Vol 26 (3) ◽  
pp. 607-613 ◽  
Author(s):  
Xiang Wang ◽  
Dan Liao
Keyword(s):  
Iterative Algorithm ◽  
Numerical Experiments ◽  
Linear Matrix ◽  
Matrix Equations ◽  
Convergence Factor ◽  
Gradient Based ◽  
Gradient Type ◽  
And Mathematics ◽  
Computers And Mathematics ◽  
Linear Matrix Equations

A hierarchical gradient based iterative algorithm of [L. Xie et al., Computers and Mathematics with Applications 58 (2009) 1441-1448] has been presented for finding the numerical solution for general linear matrix equations, and the convergent factor has been discussed by numerical experiments. However, they pointed out that how to choose a best convergence factor is still a project to be studied. In this paper, we discussed the optimal convergent factor for the gradient based iterative algorithm and obtained the optimal convergent factor. Moreover, the theoretical results of this paper can be extended to other methods of gradient-type based. Results of numerical experiments are consistent with the theoretical findings.

Intelligent fuzzy algorithm for nonlinear discrete-time systems

2019 ◽  
Vol 42 (7) ◽  
pp. 1358-1374
Author(s):  
Tim Chen ◽  
CYJ Chen
Keyword(s):  
Large Scale ◽  
Optimal Solution ◽  
Bat Algorithm ◽  
Linear Matrix ◽  
Neural Network Modeling ◽  
Rule Base ◽  
Large Scale System ◽  
Model Based ◽  
Linear Differential ◽  
The Stability

This paper is concerned with the stability analysis and the synthesis of model-based fuzzy controllers for a nonlinear large-scale system. In evolved fuzzy NN (neural network) modeling, the NN model and LDI (linear differential inclusion) representation are established for the arbitrary nonlinear dynamics. The evolved bat algorithm (EBA) is first incorporated in the controlled algorithm of stability conditions, which could rapidly find the optimal solution and raise the control performance. This representation is constructed by taking advantage of sector nonlinearity that converts the nonlinear model to a multiple rule base linear model. A new sufficient condition guaranteeing asymptotic stability is implemented via the Lyapunov function in terms of linear matrix inequalities. Subsequently, based on this criterion and the decentralized control scheme, an evolved model-based fuzzy H infinity set is synthesized to stabilize the nonlinear large-scale system. Finally, a numerical example and simulation is given to illustrate the results.

Experimentally Confirmed Mathematical Model for Human Control of a Non-Rigid Object

2004 ◽  
Vol 91 (3) ◽  
pp. 1158-1170 ◽  
Author(s):  
Jonathan B. Dingwell ◽  
Christopher D. Mah ◽  
Ferdinando A. Mussa-Ivaldi
Keyword(s):  
Mathematical Model ◽  
Human Subjects ◽  
Movement Planning ◽  
Relative Speed ◽  
Rigid Object ◽  
Hand Motion ◽  
Human Control ◽  
Rigid Objects ◽  
Minimum Jerk ◽  
Neuroscience Research

Determining the principles used to plan and execute movements is a fundamental question in neuroscience research. When humans reach to a target with their hand, they exhibit stereotypical movements that closely follow an optimally smooth trajectory. Even when faced with various perceptual or mechanical perturbations, subjects readily adapt their motor output to preserve this stereotypical trajectory. When humans manipulate non-rigid objects, however, they must control the movements of the object as well as the hand. Such tasks impose a fundamentally different control problem than that of moving one's arm alone. Here, we developed a mathematical model for transporting a mass-on-a-spring to a target in an optimally smooth way. We demonstrate that the well-known “minimum-jerk” model for smooth reaching movements cannot accomplish this task. Our model extends the concept of smoothness to allow for the control of non-rigid objects. Although our model makes some predictions that are similar to minimum jerk, it predicts distinctly different optimal trajectories in several specific cases. In particular, when the relative speed of the movement becomes fast enough or when the object stiffness becomes small enough, the model predicts that subjects will transition from a uni-phasic hand motion to a bi-phasic hand motion. We directly tested these predictions in human subjects. Our subjects adopted trajectories that were well-predicted by our model, including all of the predicted transitions between uni- and bi-phasic hand motions. These findings suggest that smoothness of motion is a general principle of movement planning that extends beyond the control of hand trajectories.

scholarly journals Trunk muscle coactivation is tuned to changes in task dynamics to improve responsiveness in a seated balance task

2015 ◽  
Vol 25 (5) ◽  
pp. 765-772 ◽  
Author(s):  
Nathalie M.C.W. Oomen ◽  
N. Peter Reeves ◽  
M. Cody Priess ◽  
Jaap H. van Dieën
Keyword(s):  
Trunk Muscle ◽  
Balance Task ◽  
Seated Balance

A New Approach to Delay-Dependent H∞ Control of Linear State-Delayed Systems

2004 ◽  
Vol 126 (1) ◽  
pp. 201-205 ◽  
Author(s):  
De-Jin Wang
Keyword(s):  
Controller Design ◽  
Linear Matrix ◽  
State Delay ◽  
Delayed Systems ◽  
Cross Term ◽  
Closed Loop Systems ◽  
Linear State ◽  
Delay Dependent ◽  
Time Invariant ◽  
Control Criterion

An alternative delay-dependent H∞ controller design is proposed for linear, continuous, time-invariant systems with unknown state delay. The resulting delay-dependent H∞ control criterion is obtained in terms of Park’s inequality for bounding cross term. The H∞ controller determined by a convex optimization algorithm with linear matrix inequality (LMI) constraints, guarantees the asymptotic stability of the closed-loop systems and reduces the effect of the disturbance input on the controlled output to within a prescribed level. A numerical example illustrates the effectiveness of our method.

Design Optimization by Integration of Evolutionary Search and Cumulative Approximation

2005 ◽  
Author(s):  
Kikuo Fujita ◽  
Tomoki Ushiro ◽  
Noriyasu Hirokawa
Keyword(s):  
Design Optimization ◽  
Computational Cost ◽  
Optimal Solution ◽  
Response Surfaces ◽  
Evolutionary Search ◽  
Design Problems ◽  
Real Coded Genetic Algorithm ◽  
Cumulative Function ◽  
Gradient Based ◽  
New Framework

This paper proposes a new design optimization framework by integrating evolutionary search and cumulative function approximation. While evolutionary algorithms are robust even under multi-peaks, rugged natures, etc., their computational cost is inferior to ordinary schemes such as gradient-based methods. While response surface techniques such as quadratic approximation can save computational cost for complicated design problems, the fidelity of solution is affected by density of samples. The new framework simultaneously performs evolutionary search and constructs response surfaces. That is, in its early phase the search is performed over roughly but globally approximated surfaces with the relatively small number of samples, and in its later phase the search is performed intensively around promising regions, which are revealed in the preceded phases, over response surfaces enhanced with additional samples. This framework is expected to be able to robustly find the optimal solution with less sampling. An optimization algorithm is implemented by combining a real-coded genetic algorithm and a Voronoi diagram based cumulative approximation, and it is applied to some numerical examples for discussing its potential and promises.

Closing the Loops Without Human Subjects: A Survey of Control Approaches in Simulation of Human-Artifact Interaction

2010 ◽  
Author(s):  
Wilhelm “Wilfred” F. van der Vegte ◽  
Imre Horva´th
Keyword(s):  
Closed Loop ◽  
Human Subjects ◽  
Product Model ◽  
Embedded Control ◽  
Loop Control ◽  
Control Loops ◽  
Human Control ◽  
Cognitive Simulation ◽  
Human Models ◽  
Interaction Simulation

To include interactions with human users in simulations of the use of products, the most common approach is to couple human subjects to the behavioral product model in the simulation loop using interfaces based on VR and haptics. Replacing human subjects by human models with simulation capabilities could offer a cost-saving alternative. Currently available human models have not yet been deployed this way. This paper explores the possibilities to achieve mutual closed-loop coupling between human models and artifact models for enabling fully software-based interaction simulations. We have not only investigated human control in simulations, but also solutions to include embedded control in artifacts. The paper critically reviews existing (partial) solutions to simulate or execute control behaviors, and to close the control loops we identified in human-artifact interaction simulation. We concluded that closed-loop control of interaction simulations can be achieved by selectively combining existing partial solutions. Inclusion of decision-making appears to be the biggest challenge. Promising solutions are (i) cognitive simulation and (ii) execution of conjectured interactions specified as logical instructions, typically in the form of scenarios. Based on scenarios, which we expect to be more intuitive for designers, a new approach is now being developed.

scholarly journals The Optimal Solution of a Non-Convex State-Dependent LQR Problem and Its Applications

PLoS ONE ◽  
2014 ◽  
Vol 9 (4) ◽  
pp. e94925 ◽  
Author(s):  
Xudan Xu ◽  
J. Jim Zhu ◽  
Ping Zhang
Keyword(s):  
Optimal Solution ◽  
State Dependent ◽  
Lqr Problem
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