CONTINUOUS FEEDBACK CONTROL STRATEGY WITH MAXIMAL CAPTURE ZONE IN A CLASS OF PURSUIT GAMES

2005 ◽  
Vol 07 (01) ◽  
pp. 1-24 ◽  
Author(s):  
VLADIMIR TURETSKY ◽  
VALERY Y. GLIZER
Keyword(s):  
Feedback Control ◽  
Differential Game ◽  
Linear Feedback ◽  
Capture Zone ◽  
State Variables ◽  
Linear Quadratic ◽  
Kinematical Model ◽  
Continuous Feedback ◽  
Feedback Control Strategy ◽  
Noisy Measurements

An interception problem of a highly maneuverable target is considered using a linearized kinematical model with first order acceleration dynamics of the interceptor and the target. The problem is interpreted as a differential game of pursuit. An admissible pursuer (interceptor) feedback strategy, continuous with respect to the state variables and having a maximal capture zone, is constructed. This strategy is the saturated version of a linear feedback control, obtained from the solution of an auxiliary linear-quadratic differential game with cheap controls. This strategy is evaluated by Monte-Carlo simulation of the interception with noisy measurements.

Feedback Control of Two Beam, Two Joint Systems With Distributed Flexibility

1975 ◽  
Vol 97 (4) ◽  
pp. 424-431 ◽  
Author(s):  
W. J. Book ◽  
O. Maizza-Neto ◽  
D. E. Whitney
Keyword(s):  
Feedback Control ◽  
Joint Angle ◽  
Relative Merit ◽  
Linear Feedback ◽  
State Variables ◽  
Linear Feedback Control ◽  
Velocity Feedback ◽  
Control Schemes

The control of the flexible motion in a plane of two pinned beams is addressed with application to remote manipulators. Three types of linear feedback control schemes are considered: joint angle and velocity feedback with (GRC) and without (IJC) cross joint feedback, and feedback of flexible state variables (FFC). Two models of the distributed flexibility are presented along with some results obtained from them. The relative merit of the three control schemes is discussed.

scholarly journals Charging a quantum battery with linear feedback control

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 500
Author(s):  
Mark T. Mitchison ◽  
John Goold ◽  
Javier Prior
Keyword(s):  
Feedback Control ◽  
Control Strategies ◽  
Field Amplitude ◽  
Linear Feedback ◽  
Storage Device ◽  
Level System ◽  
Linear Feedback Control ◽  
Equilibrium Dynamics ◽  
Quantum Feedback ◽  
Continuous Feedback

Energy storage is a basic physical process with many applications. When considering this task at the quantum scale, it becomes important to optimise the non-equilibrium dynamics of energy transfer to the storage device or battery. Here, we tackle this problem using the methods of quantum feedback control. Specifically, we study the deposition of energy into a quantum battery via an auxiliary charger. The latter is a driven-dissipative two-level system subjected to a homodyne measurement whose output signal is fed back linearly into the driving field amplitude. We explore two different control strategies, aiming to stabilise either populations or quantum coherences in the state of the charger. In both cases, linear feedback is shown to counteract the randomising influence of environmental noise and allow for stable and effective battery charging. We analyse the effect of realistic control imprecisions, demonstrating that this good performance survives inefficient measurements and small feedback delays. Our results highlight the potential of continuous feedback for the control of energetic quantities in the quantum regime.

A Control Scheme for an Opposed Recumbent Tandem Human-Powered Bicycle

1996 ◽  
Vol 12 (4) ◽  
pp. 480-492
Author(s):  
Scott O. Cloyd ◽  
Mont Hubbard ◽  
LeRoy W. Alaways
Keyword(s):  
Feedback Control ◽  
Linear Quadratic Regulator ◽  
Optimal Feedback Control ◽  
State Variables ◽  
Linear Quadratic ◽  
Lateral Deviation ◽  
Control Scheme ◽  
Control Schemes ◽  
Lean Angle ◽  
Human Powered

Feedback control of a human-powered single-track bicycle is investigated through the use of a linearized dynamical model in order to develop feedback gains that can be implemented by a human pilot in an actual vehicle. The object of the control scheme is to satisfy two goals: balance and tracking. The pilot should be able not only to keep the vehicle upright but also to direct the forward motion as desired. The two control inputs, steering angle and rider lean angle, are assumed to be determined by the rider as a product of feedback gains and “measured” values of the state variables: vehicle lean, lateral deviation from the desired trajectory, and their derivatives. Feedback gains are determined through linear quadratic regulator theory. This results in two control schemes, a “full” optimal feedback control and a less complicated technique that is more likely to be usable by an inexperienced pilot. Theoretical optimally controlled trajectories are compared with experimental trajectories in a lane change maneuver.

Smart Fluid Damping: Shaping the Force/Velocity Response through Feedback Control

2000 ◽  
Vol 11 (12) ◽  
pp. 945-958 ◽  
Author(s):  
Neil D. Sims ◽  
Roger Stanway ◽  
Andrew R. Johnson ◽  
David J. Peel ◽  
William A. Bullough
Keyword(s):  
Feedback Control ◽  
Linear Feedback ◽  
Order Function ◽  
Bingham Plastic ◽  
Smart Fluids ◽  
Fluid Damping ◽  
Variable Damping ◽  
Velocity Characteristic ◽  
Force Velocity ◽  
Feedback Control Strategy

It is now well known that smart fluids [electrorheological (ER) and magnetorheological (MR)] can form the basis of controllable vibration damping devices. With both types of fluid, however, the force/velocity characteristic of the resulting damper is significantly non-linear, possessing the general form associated with a Bingham plastic. In a previous paper the authors showed that by using a linear feedback control strategy it is possible to produce the equivalent of a viscous damper with a continuously variable damping coefficient. In the present paper the authors illustrate an extension of the technique, by showing how the shape of the force/velocity characteristic can be controlled through feedback control. This is achieved by using a polynomial function to generate a set point based upon the damper velocity. The response is investigated for polynomial functions of zero, 1st and 2nd order. It is shown how the damper can accurately track higher order polynomial shaping functions, while the zero-order function is particularly useful in illustrating the dynamics of the closed-loop system.

scholarly journals Synchronization of Hyperchaotic Circuits via Continuous Feedback Control with Application to Secure Communications

1998 ◽  
Vol 08 (10) ◽  
pp. 2031-2040 ◽  
Author(s):  
Michele Brucoli ◽  
Donato Cafagna ◽  
Leonarda Carnimeo ◽  
Giuseppe Grassi
Keyword(s):  
Nonlinear Dynamics ◽  
Feedback Control ◽  
Secure Communication ◽  
Secure Communications ◽  
State Variables ◽  
Control Scheme ◽  
Feedback Matrix ◽  
Analytic Expressions ◽  
Continuous Feedback ◽  
Error System

In this paper a synthesis technique for the synchronization of hyperchaotic circuits with application to secure communications is developed. It is well known that information-bearing signals can be considered as causes of perturbations, when a secure communication system based on a masking technique is implemented. Starting from this consideration, in this paper a feedback control scheme is developed to guarantee synchronization between transmitter and receiver. The control scheme involves as many state variables in the feedback as the number of information signals to be transmitted. After deriving the nonlinear dynamics of the synchronization error system, the feedback matrix is determined by finding a suitable Lyapunov function and by imposing the conditions which assure the global asymptotic stability of the origin of the error system. The method is illustrated by considering hyperchaotic circuits constituted by coupled Chua's oscillators, for which analytic expressions of the feedback gains are derived.

scholarly journals Linear feedback stabilization of point-vortex equilibria near a Kasper wing

2017 ◽  
Vol 827 ◽  
pp. 121-154 ◽  
Author(s):  
R. Nelson ◽  
B. Protas ◽  
T. Sakajo
Keyword(s):  
Feedback Control ◽  
Point Vortex ◽  
Basins Of Attraction ◽  
Feedback Stabilization ◽  
Linear Feedback ◽  
Linear Quadratic ◽  
Linear Control Theory ◽  
Single Plate ◽  
Point Vortex Equilibria ◽  
Almost All

This paper concerns feedback stabilization of point-vortex equilibria above an inclined thin plate and a three-plate configuration known as the Kasper wing in the presence of an oncoming uniform flow. The flow is assumed to be potential and is modelled by the two-dimensional incompressible Euler equations. Actuation has the form of blowing and suction localized on the main plate and is represented in terms of a sink–source singularity, whereas measurement of pressure across the plate serves as system output. We focus on point-vortex equilibria forming a one-parameter family with locus approaching the trailing edge of the main plate and show that these equilibria are either unstable or neutrally stable. Using methods of linear control theory we find that the system dynamics linearized around these equilibria is both controllable and observable for almost all actuator and sensor locations. The design of the feedback control is based on the linear–quadratic–Gaussian (LQG) compensator. Computational results demonstrate the effectiveness of this control and the key finding of this study is that Kasper wing configurations are in general not only more controllable than their single-plate counterparts, but also exhibit larger basins of attraction under LQG feedback control. The feedback control is then applied to systems with additional perturbations added to the flow in the form of random fluctuations of the angle of attack and a vorticity shedding mechanism. Another important observation is that, in the presence of these additional perturbations, the control remains robust, provided the system does not deviate too far from its original state. Furthermore, except in a few isolated cases, introducing a vorticity-shedding mechanism enhanced the effectiveness of the control. Physical interpretation is provided for the results of the controllability and observability analysis as well as the response of the feedback control to different perturbations.

scholarly journals A Multistage Feedback Control Strategy for Producing 1,3-Propanediol in Microbial Continuous Fermentation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Honghan Bei ◽  
Lei Wang ◽  
Jing Sun ◽  
Liwei Zhang
Keyword(s):  
Feedback Control ◽  
Linear Combination ◽  
Control Strategy ◽  
Continuous Fermentation ◽  
Continuous Functions ◽  
Linear Feedback ◽  
Control Parameterization ◽  
Nonlinear Mathematical Programming ◽  
Feedback Control Strategy ◽  
Mathematical Programming Problems

In this paper, we consider a multistage feedback control strategy for producing 1,3-propanediol in microbial continuous fermentation. Both the dilution rate and the concentration of glycerol in the input feed are used as control variables, and these variables are further assumed to be in the form of a linear combination of biomass and glycerol concentrations. Unlike the general form of linear feedback control, the coefficients of linear combination are continuous functions with respect to time. Inspired by the control parameterization method, we use the piecewise-constant functions to approximate the coefficient functions; then we get the multistage feedback control law by solving nonlinear mathematical programming problems. Numerical results indicate the flexibility and effectiveness of our strategy.

scholarly journals Stochastic Linear Quadratic Stackelberg Differential Game with Overlapping Information

2020 ◽  
Vol 26 ◽  
pp. 83
Author(s):  
Jingtao Shi ◽  
Guangchen Wang ◽  
Jie Xiong
Keyword(s):  
Differential Game ◽  
Direct Calculation ◽  
Stackelberg Equilibrium ◽  
Equilibrium Strategy ◽  
Optimal Controls ◽  
State Variables ◽  
Linear Quadratic ◽  
Stochastic Filtering ◽  
Stackelberg Differential Game ◽  
The Cost

This paper is concerned with the stochastic linear quadratic Stackelberg differential game with overlapping information, where the diffusion terms contain the control and state variables. Here the term “overlapping” means that there are common part between the follower’s and the leader’s information, while they have no inclusion relation. Optimal controls of the follower and the leader are obtained by the stochastic maximum principle, the direct calculation of the derivative of the cost functional and stochastic filtering. A new system of Riccati equations is introduced to give the state estimate feedback representation of the Stackelberg equilibrium strategy, while its solvability is a rather difficult open problem. A special case is then studied and is applied to the continuous-time principal-agent problem.

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