New Nonlinear Observer Design With Application to Electrostatic Micro-Actuators

2005 ◽  
Author(s):  
Venkat Durbha ◽  
S. N. Balakrishnan
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Correction Term ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Optimal Feedback Control ◽  
Actuator Dynamics ◽  
One Dimensional ◽  
Practical Applications ◽  
The Cost

In many practical applications it is not possible to measure all the states required to control the system. In such instances observer/filter is used to give a good estimate of the states of the system. The objective of the observer is to estimate the states such that the error between the actual and computed measurements goes to zero and obtain the “best” estimates of the states of a given system. In the current study a new nonlinear observer structure is proposed. The development of the observer is based on optimal control theory. A cost function is defined in terms of the measurement residual and the magnitude of correction term. The observer gains are obtained by minimizing the cost function with respect to the magnitude of corrections. The proposed observer is used to estimate the states of a one-dimensional electrostatic micro-actuator. The states of the actuator dynamics are, charge on the capacitor plates, the distance between the plates and the relative velocity between the plates. The regulation of the actuator states to desired trajectories is achieved through optimal control based state feedback. However in practice it is very difficult to measure the relative position and velocity of the plates. In this paper optimal feedback control based on the state estimates provided by the observer is used to regulate the actuator states to the desired location.

scholarly journals Diagnostics on the cost-function in variational assimilations for meteorological models

2014 ◽  
Vol 21 (1) ◽  
pp. 187-199 ◽  
Author(s):  
Y. Michel
Keyword(s):  
Hypothesis Testing ◽  
Cost Function ◽  
Quadratic Forms ◽  
Standard Theory ◽  
Variational Assimilation ◽  
One Dimensional ◽  
Perfect System ◽  
The Cost ◽  
Meteorological Models ◽  
Variational Formulations

Abstract. Several consistency diagnostics have been proposed to evaluate variational assimilation schemes. The "Bennett-Talagrand" criterion in particular shows that the cost-function at the minimum should be close to half the number of assimilated observations when statistics are correctly specified. It has been further shown that sub-parts of the cost function also had statistical expectations that could be expressed as traces of large matrices, and that this could be exploited for variance tuning and hypothesis testing. The aim of this work is to extend those results using standard theory of quadratic forms in random variables. The first step is to express the sub-parts of the cost function as quadratic forms in the innovation vector. Then, it is possible to derive expressions for the statistical expectations, variances and cross-covariances (whether the statistics are correctly specified or not). As a consequence it is proven in particular that, in a perfect system, the values of the background and observation parts of the cost function at the minimum are positively correlated. These results are illustrated in a simplified variational scheme in a one-dimensional context. These expressions involve the computation of the trace of large matrices that are generally unavailable in variational formulations of the assimilation problem. It is shown that the randomization algorithm proposed in the literature can be extended to cover these computations, yet at the price of additional minimizations. This is shown to provide estimations of background and observation errors that improve forecasts of the operational ARPEGE model.

scholarly journals Optimal Control of Virus Spread under Different Conditions of Resources Limitations

Information ◽  
2019 ◽  
Vol 10 (6) ◽  
pp. 214
Author(s):  
Paolo Di Giamberardino ◽  
Daniela Iacoviello
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Virus Spread ◽  
Human Virus ◽  
Positive Diagnosis ◽  
Control Actions ◽  
The People ◽  
Different Types ◽  
The Cost ◽  
Instantaneous Control

The paper addresses the problem of human virus spread reduction when the resources for the control actions are somehow limited. This kind of problem can be successfully solved in the framework of the optimal control theory, where the best solution, which minimizes a cost function while satisfying input constraints, can be provided. The problem is formulated in this contest for the case of the HIV/AIDS virus, making use of a model that considers two classes of susceptible subjects, the wise people and the people with incautious behaviours, and three classes of infected, the ones still not aware of their status, the pre-AIDS patients and the AIDS ones; the control actions are represented by an information campaign, to reduce the category of subjects with unwise behaviour, a test campaign, to reduce the number of subjects not aware of having the virus, and the medication on patients with a positive diagnosis. The cost function considered aims at reducing patients with positive diagnosis using as less resources as possible. Four different types of resources bounds are considered, divided into two classes: limitations on the instantaneous control and fixed total budgets. The optimal solutions are numerically computed, and the results of simulations performed are illustrated and compared to put in evidence the different behaviours of the control actions.

LEARNING AND RECOGNITION OF HUMAN ACTIONS USING OPTIMAL CONTROL PRIMITIVES

2009 ◽  
Vol 06 (03) ◽  
pp. 459-479
Author(s):  
SUMITRA GANESH ◽  
RUZENA BAJCSY
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Estimation Method ◽  
Nonlinear Least Squares ◽  
Performance Criterion ◽  
Human Motion ◽  
Human Actions ◽  
Mode Estimation ◽  
Nonlinear Least Squares Problem ◽  
The Cost

We propose a unified approach for recognition and learning of human actions, based on an optimal control model of human motion. In this model, the goals and preferences of the agent engaged in a particular action are encapsulated as a cost function or performance criterion, that is optimized to yield the details of the movement. The cost function is a compact, intuitive and flexible representation of the action. A parameterized form of the cost function is considered, wherein the structure reflects the goals of the actions, and the parameters determine the relative weighting of different terms. We show how the cost function parameters can be estimated from data by solving a nonlinear least squares problem. The parameter estimation method is tested on motion capture data for two different reaching actions and six different subjects. We show that the problem of action recognition in the context of this representation is similar to that of mode estimation in a hybrid system and can be solved using a particle filter if a receding horizon formulation of the optimal controller is adopted. We use the proposed approach to recognize different reaching actions from the 3D hand trajectory of subjects.

scholarly journals Inverse KKT: Learning cost functions of manipulation tasks from demonstrations

2017 ◽  
Vol 36 (13-14) ◽  
pp. 1474-1488 ◽  
Author(s):  
Peter Englert ◽  
Ngo Anh Vien ◽  
Marc Toussaint
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Cost Functions ◽  
Quadratic Program ◽  
Relevant Task ◽  
Kernel Hilbert Spaces ◽  
The Cost ◽  
Linear Parameterization

Inverse optimal control (IOC) assumes that demonstrations are the solution to an optimal control problem with unknown underlying costs, and extracts parameters of these underlying costs. We propose the framework of inverse Karush–Kuhn–Tucker (KKT), which assumes that the demonstrations fulfill the KKT conditions of an unknown underlying constrained optimization problem, and extracts parameters of this underlying problem. Using this we can exploit the latter to extract the relevant task spaces and parameters of a cost function for skills that involve contacts. For a typical linear parameterization of cost functions this reduces to a quadratic program, ensuring guaranteed and very efficient convergence, but we can deal also with arbitrary non-linear parameterizations of cost functions. We also present a non-parametric variant of inverse KKT that represents the cost function as a functional in reproducing kernel Hilbert spaces. The aim of our approach is to push learning from demonstration to more complex manipulation scenarios that include the interaction with objects and therefore the realization of contacts/constraints within the motion. We demonstrate the approach on manipulation tasks such as sliding a box, closing a drawer and opening a door.

On the optimal control of stationary diffusion processes with natural boundaries and discounted cost

1971 ◽  
Vol 8 (3) ◽  
pp. 561-572 ◽  
Author(s):  
R. Morton
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Cost Function ◽  
Diffusion Processes ◽  
Expected Cost ◽  
Discounted Cost ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Stationary Diffusion ◽  
Natural Boundaries

SummaryResults similar to those in [3] are obtained for one-dimensional diffusion processes with discounted cost. The stronger assumption that at least one of the inaccessible boundaries is natural enables us to identify the solution of a differential equation corresponding to the future expected cost function.

On the optimal control of stationary diffusion processes with natural boundaries and discounted cost

1971 ◽  
Vol 8 (03) ◽  
pp. 561-572
Author(s):  
R. Morton
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Cost Function ◽  
Diffusion Processes ◽  
Expected Cost ◽  
Discounted Cost ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Stationary Diffusion ◽  
Natural Boundaries

Summary Results similar to those in [3] are obtained for one-dimensional diffusion processes with discounted cost. The stronger assumption that at least one of the inaccessible boundaries is natural enables us to identify the solution of a differential equation corresponding to the future expected cost function.

scholarly journals The reserve of joint torque determines movement coordination

2021 ◽  
Author(s):  
Germain Faity ◽  
Denis Mottet ◽  
Simon Pla ◽  
Jérôme Froger
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Degrees Of Freedom ◽  
Minimum Cost ◽  
Joint Torque ◽  
Movement Coordination ◽  
Trunk Motion ◽  
Additional Load ◽  
The Cost ◽  
Healthy Participants

AbstractHumans coordinate biomechanical degrees of freedom to perform tasks at minimum cost. When reaching a target from a seated position, the trunk-arm-forearm coordination moves the hand to the well-defined spatial goal, while typically minimising hand jerk and trunk motion. However, due to fatigue or stroke, people visibly move the trunk more, and it is unclear what cost can account for this. Here we show that people recruit their trunk when the torque at the shoulder is too close to the maximum. We asked 26 healthy participants to reach a target while seated and we found that the trunk contribution to hand displacement increases from 11% to 27% when an additional load is handled. By flexing and rotating the trunk, participants spontaneously increase the reserve of anti-gravitational torque at the shoulder from 25% to 40% of maximal voluntary torque. Our findings provide hints on how to include the reserve of torque in the cost function of optimal control models of human coordination in healthy fatigued persons or in stroke victims.

scholarly journals OPTIMAL CONTROL OF A CONVECTIVE-DIFFUSIVE FLUID PROBLEM

1995 ◽  
Vol 05 (02) ◽  
pp. 225-237 ◽  
Author(s):  
SUZANNE LENHART
Keyword(s):  
Optimal Control ◽  
Performance Criterion ◽  
Equation Modeling ◽  
Parabolic Differential Equation ◽  
Convective Velocity ◽  
Final Time ◽  
One Dimensional ◽  
Flow Through ◽  
Differential Equation Modeling ◽  
The Cost

We consider optimal control of a parabolic differential equation, modeling one-dimensional fluid flow through a soil-packed tube in which a contaminant is initially distributed. A fluid is pumped through the tube to remove the contaminant. The convective velocity due to the fluid pumping is the nonlinear control action. The goal is to minimize a performance criterion which is a combination of the total contaminant at the final time and the cost of the control. The optimal control is characterized by an optimality system.

scholarly journals Optimal control techniques based on infection age for the study of the COVID-19 epidemic

2020 ◽  
Vol 15 ◽  
pp. 48
Author(s):  
J. Frédéric Bonnans ◽  
Justina Gianatti
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Numerical Experiments ◽  
Age Classes ◽  
Control Techniques ◽  
Infection Age ◽  
Death Toll ◽  
Infected Population ◽  
The Future ◽  
The Cost

We propose a model for the COVID-19 epidemic where the population is partitioned into classes corresponding to ages (that remain constant during the epidemic). The main feature is to take into account the infection age of the infected population. This allows to better simulate the infection propagation that crucially depend on the infection age. We discuss how to estimate the coefficients from data available in the future, and introduce a confinement variable as control. The cost function is a compromise between a confinement term, the hospitalization peak and the death toll. Our numerical experiments allow to evaluate the interest of confinement varying with age classes.

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