Feedback Control Of Dynamic Systems Research Articles

Optimal feedback control of dynamical systems via value-function approximation

Optimal feedback control of dynamical systems via value-function approximation

Understanding and Engineering Chromatin as a Dynamical System across Length and Timescales.

Connecting the molecular structure and function of chromatin across length and timescales remains a grand challenge to understanding and engineering cellular behaviors. Across five orders of magnitude, dynamic processes constantly reshape chromatin structures, driving spaciotemporal patterns of gene expression and cell fate. Through the interplay of structure and function, the genome operates as a highly dynamic feedback control system. Recent experimental techniques have provided increasingly detailed data that revise and augment the relatively static, hierarchical view of genomic architecture with an understanding of how dynamic processes drive organization. Here, we review how novel technologies from sequencing, imaging, and synthetic biology refine our understanding of chromatin structure and function and enable chromatin engineering. Finally, we discuss opportunities to use these tools to enhance understanding of the dynamic interrelationship of chromatin structure and function.

Comparison of binary and fuzzy logic in feedback control of dynamic systems

The purpose of this paper is to present a performance comparison of expert systems with production rules, based on classical binary logic and fuzzy logic, for feedback control of dynamic systems. The expert system based on binary logic, called ES-PR-BL, was developed in Prolog language, and the system based on fuzzy logic, called ES-PR-FL, was implemented using a Mamdani type inference process. The work presents simulation results for three types of dynamic system: level control in a tank, control of the angular velocity of a DC motor, and control of the linear velocity of a vehicle. The results demonstrate the specificities of each technique and could be used to guide the development of new hybrid control methods, with the aim of improving efficiency in the control of dynamic processes employing expert systems based on production rules. The findings were highly satisfactory and demonstrated the specificities and applicabilities of the two expert systems studied.

Data-driven surrogates of value functions and applications to feedback control for dynamical systems

Dealing with high-dimensional feedback control problems is a difficult task when the classical dynamic programming principle is applied. Existing techniques restrict the application to relatively low dimensions since the discretizations typically suffer from the curse of dimensionality. In this paper we introduce a novel approximation technique for the value function of an infinite horizon optimal control. The method is based on solving optimal open loop control problems on a finite horizon with a sampling of the global value function along the generated trajectories. For the interpolation we choose a kernel orthogonal greedy strategy, because these methods are able to produce extreme sparse surrogates and enable rapid evaluations in high dimensions. Two numerical examples prove the performance of the approach and show that the method is able to deal with high-dimensional feedback control problems, where the dimensionality prevents the approximation by most existing methods.

An LMI approach to design extended predictor feedback controllers for dynamical systems with input delay

ABSTRACTThe stabilisation of dynamical systems with input delay by an extended predictor feedback controller is investigated. After considering a more general case of the predictor feedback controllers, the design procedure is transformed into the stabilisation problem of the system controlled by a dynamic output feedback controller. By proposing appropriate Lyapunov-Krasovskii functionals, the predictor feedback gains are then synthesised from the stability conditions which are obtained in form of linear matrix inequalities. Such design approach is more flexible and extendable in comparison to one used by the conventional predictor feedback control. As a simulation example, the designed extended predictor feedback controller is applied on an active suspension system and is used to stabilise an unstable system with input delays. The obtained results demonstrate the effectiveness of the design method.

Design and Analog Circuit Implementation of a Dynamic Feedback Control System Based on RLC Series Circuit

Design and Analog Circuit Implementation of a Dynamic Feedback Control System Based on RLC Series Circuit

Design of Linear Feedback Controllers for Dynamic Systems With Hysteresis

This paper proposes an approach to deal with the control of a class of dynamical systems affected by hysteresis, which is particularly common in applications of smart materials to motion control. The controlled plant is assumed to be a combination of a linear system with a hysteretic operator that can appear either in series or in a feedback path with respect to the linear component, while the controller is defined as a linear combination of the tracking error, its integral and derivatives. This paper mainly focuses on tracking behavior with constant references, and formulates the output regulation as a problem of stability of a polytopic linear differential inclusion, which does not require the identification of an accurate (direct or inverse) model of the hysteresis. The resulting conditions allow the user to seek for controller parameters that guarantee the achievement of a predefined control goal by solving a linear matrix inequality problem. Beside validation through numerical simulation, the method is successfully applied to control a challenging and innovative system, which uses two bars of magnetic shape memory alloy as the active elements of a multistable precise positioning device.

Feedforward and Feedback Control of Dynamic Systems

Recently the control methods based on disturbance rejection have largely renewed our understanding of automatic control, especially the role of feedforward control. With the renewed understanding, this work presents a feedforward and feedback approach for control of general dynamic systems under a state tracking framework. This is realized by introducing a fictitious system model and employing a proper state and disturbance estimator. The resultant control scheme embodies a close cooperation between feedforward and feedback controls: Feedforward control rejects the general disturbance and embeds a reference state trajectory, whilst feedback control cancels the fictitious dynamics and enforces desired tracking error dynamics. A notable advantage of the approach is that control designs of linear and nonlinear systems can follow a common routine and the closed-loop stability is guaranteed under standard conditions.

High precision dynamic alignment and gap control for optical near-field nanolithography

The authors demonstrate the use of interferometric-spatial-phase-imaging (ISPI) to control a gap distance of the order of nanometers for parallel optical near-field nanolithography. In optical near-field nanolithography, the distance between the optical mask and the substrate needs to be controlled within tens of nanometers or less. The ISPI technique creates interference fringes from checkerboard gratings fabricated on the optical mask, which are used to determine the gap distance between the mask and the substrate surfaces. The sensitive of this gapping technique can reach 0.15 nm. With the use of ISPI and a dynamic feedback control system, the authors can precisely align the mask and the substrate and keep variation of the gap distance below 6 nm to realize parallel nanolithography.

Neural networks for action representation: a functional magnetic-resonance imaging and dynamic causal modeling study

Automatic mimicry is based on the tight linkage between motor and perception action representations in which internal models play a key role. Based on the anatomical connection, we hypothesized that the direct effective connectivity from the posterior superior temporal sulcus (pSTS) to the ventral premotor area (PMv) formed an inverse internal model, converting visual representation into a motor plan, and that reverse connectivity formed a forward internal model, converting the motor plan into a sensory outcome of action. To test this hypothesis, we employed dynamic causal-modeling analysis with functional magnetic-resonance imaging (fMRI). Twenty-four normal participants underwent a change-detection task involving two visually-presented balls that were either manually rotated by the investigator's right hand (“Hand”) or automatically rotated. The effective connectivity from the pSTS to the PMv was enhanced by hand observation and suppressed by execution, corresponding to the inverse model. Opposite effects were observed from the PMv to the pSTS, suggesting the forward model. Additionally, both execution and hand observation commonly enhanced the effective connectivity from the pSTS to the inferior parietal lobule (IPL), the IPL to the primary sensorimotor cortex (S/M1), the PMv to the IPL, and the PMv to the S/M1. Representation of the hand action therefore was implemented in the motor system including the S/M1. During hand observation, effective connectivity toward the pSTS was suppressed whereas that toward the PMv and S/M1 was enhanced. Thus, the action-representation network acted as a dynamic feedback-control system during action observation.

Mapping the flow of information within the putative mirror neuron system during gesture observation

The putative mirror neuron system may either function as a strict feed-forward system or as a dynamic control system. A strict feed-forward system would predict that action observation leads to a predominantly temporal→parietal→premotor flow of information in which a visual representation is transformed into motor-programs which contribute to action understanding. Instead, a dynamic feedback control system would predict that the reverse direction of information flow predominates because of a combination of inhibitory forward and excitatory inverse models. Here we test which of these conflicting predictions best matches the information flow within the putative mirror neuron system (pMNS) and between the pMNS and the rest of the brain during the observation of comparatively long naturalistic stretches of communicative gestures. We used Granger causality to test the dominant direction of influence. Our results fit the predictions of the dynamic feedback control system: we found predominantly an information flow within the pMNS from premotor to parietal and middle temporal cortices. This is more pronounced during an active guessing task than while passively reviewing the same gestures. In particular, the ventral premotor cortex sends significantly more information to other pMNS areas than it receives during active guessing than during passive observation.

Reinforcement Learning for Partially Observable Dynamic Processes: Adaptive Dynamic Programming Using Measured Output Data

Approximate dynamic programming (ADP) is a class of reinforcement learning methods that have shown their importance in a variety of applications, including feedback control of dynamical systems. ADP generally requires full information about the system internal states, which is usually not available in practical situations. In this paper, we show how to implement ADP methods using only measured input/output data from the system. Linear dynamical systems with deterministic behavior are considered herein, which are systems of great interest in the control system community. In control system theory, these types of methods are referred to as output feedback (OPFB). The stochastic equivalent of the systems dealt with in this paper is a class of partially observable Markov decision processes. We develop both policy iteration and value iteration algorithms that converge to an optimal controller that requires only OPFB. It is shown that, similar to Q -learning, the new methods have the important advantage that knowledge of the system dynamics is not needed for the implementation of these learning algorithms or for the OPFB control. Only the order of the system, as well as an upper bound on its "observability index," must be known. The learned OPFB controller is in the form of a polynomial autoregressive moving-average controller that has equivalent performance with the optimal state variable feedback gain.

Inverses of Positive Linear Operators and State Feedback Design for Time-Delay Systems*

Abstract The problem of designing feedback controllers for dynamical systems with time-delay is addressed in this paper. Previous work has imposed significant restrictions on the structure of the candidate Control Lyapunov Functions in order to develop appropriate LMI conditions for the design. This paper addresses this issue and provides two new results. The first result is a step towards controller synthesis using the “complete quadratic” Lyapunov functional. Specifically given such a “complete quadratic” functional, defined by polynomials, we give an algorithm for constructing the inverse of the linear operator which defines that functional. Following this, we derive semidefinite programming conditions, expressed as a Sum-of-Squares program, for state feedback synthesis of these systems using a restricted structure of the Lyapunov functional.

Issues on Stability of ADP Feedback Controllers for Dynamical Systems

This paper traces the development of neural-network (NN)-based feedback controllers that are derived from the principle of adaptive/approximate dynamic programming (ADP) and discusses their closed-loop stability. Different versions of NN structures in the literature, which embed mathematical mappings related to solutions of the ADP-formulated problems called "adaptive critics" or "action-critic" networks, are discussed. Distinction between the two classes of ADP applications is pointed out. Furthermore, papers in "model-free" development and model-based neurocontrollers are reviewed in terms of their contributions to stability issues. Recent literature suggests that work in ADP-based feedback controllers with assured stability is growing in diverse forms.

Delayed feedback control of dynamical systems at a subcritical Hopf bifurcation

We consider the delayed feedback control of a torsion-free unstable periodic orbit originated in a dynamical system at a subcritical Hopf bifurcation. Close to the bifurcation point the problem is treated analytically using the method of averaging. We discuss the necessity of employing an unstable degree of freedom in the feedback loop as well as a nonlinear coupling between the controlled system and controller. To demonstrate our analytical approach the specific example of a nonlinear electronic circuit is taken as a model of a subcritical Hopf bifurcation.

Robust output feedback controllers for dynamical systems including delayed perturbations

The problem of output feedback stabilization of uncertain dynamical systems including time-varying delay is discussed. Here we assume that the uncertainties satisfy the so-called matching conditions, and that the time-varying delay is any bounded and continuous non-negative function. For such a class of uncertain time-delay systems, we show that under the assumption that the transfer function matrix of the nominal system is strictly feedback positive real, there always exist a class of stabilizing output feedback controllers. We first propose a linear output feedback controller which can guarantee always uniform ultimate boundedness of closed-loop dynamical systems. Furthermore, we modify this linear controller by adding a nonlinear part to obtain a nonlinear output feedback controller which can guarantee always uniform asymptotic stability of closed-loop dynamical systems. As the proposed output feedback controllers are independent of the delay, the results obtained in this paper are applicable to dynamical systems without exact knowledge of the delays, i.e. systems with perturbed delays. Finally, a numerical example is given to demonstrate the validity of the results.

Half-period delayed feedback control for dynamical systems with symmetries

Half-period delayed feedback control for dynamical systems with symmetries

A New Class of Robust Feedback Controllers for Dynamical Systems in the Absence of Matching Conditions

A New Class of Robust Feedback Controllers for Dynamical Systems in the Absence of Matching Conditions

Two-stage neural network architecture for feedback control of dynamic systems

In this paper we investigate system identification and the design of a controller using neural networks. A two-stage neural network design for controllers using single-layer structures with functional enhancements is introduced. This neural network architecture allows the design of a controller with less a priori knowledge about the plant as well as allowing for nonlinear plants. The paper also addresses the special characteristics and problems concerning the use of neural networks in control and demonstrates their performance by showing the successful implementation of a nonlinear control example via simulation.

Dynamic performance of vibration induced anterior-posterior sway during upright posture in normal subjects.

Human postural control works as a dynamic feedback control system. The dynamic performance of postural control for anterior-posterior movements during upright posture are defined by three parameters. These parameters reflect the stiffness, the damping and the swiftness of a response to an induced perturbation. In the present study 23 normal subjects were investigated. Both with open and closed eyes, there was a negative correlation between swiftness and stiffness. With open eyes there was also a weak correlation between swiftness and damping. When the subjects were tested with open eyes there was a prominent and highly significant increase of stiffness and a reduction of swiftness of the responses. It was found that proprioceptive information from the calf muscles contributes in postural control of movements up to 1 Hz and visual information is important for movements up to 0.05 Hz. The present findings suggest that postural control changes dynamic strategies depending on the available sensory feedback.