Probabilistic Control for Uncertain Systems

In this paper a new framework has been applied to the design of controllers which encompasses nonlinearity, hysteresis and arbitrary density functions of forward models and inverse controllers. Using mixture density networks, the probabilistic models of both the forward and inverse dynamics are estimated such that they are dependent on the state and the control input. The optimal control strategy is then derived which minimizes uncertainty of the closed loop system. In the absence of reliable plant models, the proposed control algorithm incorporates uncertainties in model parameters, observations, and latent processes. The local stability of the closed loop system has been established. The efficacy of the control algorithm is demonstrated on two nonlinear stochastic control examples with additive and multiplicative noise.

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Actuator Saturation and Control Design for Buildings Structural Systems with Improved Uncertainty Description

Shock and Vibration ◽

10.1155/2013/478796 ◽

2013 ◽

Vol 20 (2) ◽

pp. 297-308 ◽

Cited By ~ 6

Author(s):

Y.C. Ding ◽

F.L. Weng ◽

Z.A. Yu

Keyword(s):

Closed Loop ◽

Actuator Saturation ◽

Input Saturation ◽

Lyapunov Theory ◽

Loop System ◽

Structural Systems ◽

Control Input ◽

Closed Loop System ◽

Parameter Uncertainties ◽

Earthquake Excitation

The problem of robustly active vibration control for a class of earthquake-excited structural systems with time-delay and saturation in the control input channel and parameter uncertainties appearing in all the mass, damping and stiffness matrices is concerned in this paper. The objective of the designing controllers is to guarantee the robust stability of the closed-loop system and attenuate the disturbance from earthquake excitation. Firstly, by using the linear combination of some matrices to deal with the system's uncertainties, a new system uncertainties description, namely rank-1 uncertainty description, is presented. Then, by introducing a linear varying parameter, the input saturation model is described as a linear parameter varying model. Furthermore, based on parameter-dependent Lyapunov theory and linear matrix inequality (LMI) technique, the LMIs-based conditions for the closed-loop system to be stable are deduced. By solving those conditions, the controller, considering the actuator saturation, input delay and parameters uncertainties, is obtained. Finally, a three-storey linear building structure under earthquake excitation is considered and simulation results are given to show the effectiveness of the proposed controllers.

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PANDEMIC POLICY DESIGN VIA FEEDBACK: A MODELLING STUDY

10.1101/2021.09.23.21263924 ◽

2021 ◽

Author(s):

Klaske Van Heusden ◽

Greg Stewart ◽

Sarah Otto ◽

Guy Dumont

Keyword(s):

Public Health ◽

Decision Making ◽

Feedback Control ◽

Human Health ◽

Closed Loop ◽

Policy Design ◽

Loop System ◽

Model Parameters ◽

Closed Loop System ◽

Hospital Occupancy

The COVID-19 pandemic has had an enormous toll on human health and well-being and led to major social and economic disruptions. Public health interventions in response to burgeoning case numbers and hospitalizations have repeatedly bent down the epidemic curve in many jurisdictions, effectively creating a closed-loop dynamic system. We aim to formalize and illustrate how to incorporate principles of feedback control into pandemic projections and decision making. Starting with a SEEIQR epidemiological model, we illustrate how feedback control can be incorporated into pandemic management using a simple design (proportional-integral or PI control), which couples recent changes in case numbers or hospital occupancy with explicit policy restrictions. We then analyse a closed-loop system between the SEEIQR model and the designed feedback controller to illustrate the potential benefits of pandemic policy design that incorporates feedback. We first explored a feedback design that responded to hospital measured infections, demonstrating robust ability to control a pandemic despite simulating large uncertainty in reproduction number R0 (range: 1.04-5.18) and average time to hospital admission (range: 4-28 days). The second design compared responding to hospital occupancy to responding to case counts, showing that shorter delays reduced both the cumulative case count and the average level of interventions. Finally, we show that feedback is robust to changing public compliance to public health directives, and to systemic changes associated with new variants of concern and with the introduction of a vaccination program. The negative impact of a pandemic on human health and societal disruption can be reduced by coupling models of disease propagation with models of the decision-making process. This creates a closed-loop system that better represents the coupled dynamics of a disease and public health responses. Importantly, we show that feedback control is robust to delays in both measurements and responses, and to uncertainty in model parameters and the efficacy of control measures.

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A Study on the Effect of Driver Model Parameters on the Performance of Driver-Vehicle-Road Closed-Loop System

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.470.604 ◽

2013 ◽

Vol 470 ◽

pp. 604-608

Author(s):

Li Zeng Zhang ◽

Hsin Guan ◽

Xin Jia ◽

Ping Ping Lu ◽

Yong Shang Chen

Keyword(s):

Delay Time ◽

Closed Loop ◽

System Simulation ◽

Lag Time ◽

Loop System ◽

Driver Model ◽

Model Parameters ◽

Closed Loop System

The concept of DODF and other two evaluation indices based on DODF were proposed. Based on the optimal preview acceleration driver model, the effect of driver model parameters on the performance of driver-vehicle-road closed-loop system was studied by the closed-loop system simulation. The results show that the preview time of a driver who has good driving habits should be always larger than a certain valueTP0, the increase of both nerve delay timetdand muscle lag timeThlead to the increase ofTP0, andtdhas more effect onTP0thanThdoes. The increase of bothtdandThlead to the decrease of DODF, andtdhas more effect on DODF thanThdoes. Furthermore, the increase of bothtdandThalso lead to the increase of both tracking indexJEMand driving load indexTCM,tdhas more effect onJEMthanThdoes, andThhas more effect onTCMthantddoes.

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Safety and Feasibility of the OmniPod Hybrid Closed-Loop System in Adult, Adolescent, and Pediatric Patients with Type 1 Diabetes Using a Personalized Model Predictive Control Algorithm

Diabetes Technology & Therapeutics ◽

10.1089/dia.2017.0346 ◽

2018 ◽

Vol 20 (4) ◽

pp. 257-262 ◽

Cited By ~ 35

Author(s):

Bruce A. Buckingham ◽

Gregory P. Forlenza ◽

Jordan E. Pinsker ◽

Mark P. Christiansen ◽

R. Paul Wadwa ◽

...

Keyword(s):

Type 1 Diabetes ◽

Model Predictive Control ◽

Predictive Control ◽

Control Algorithm ◽

Closed Loop ◽

Pediatric Patients ◽

Loop System ◽

Closed Loop System ◽

Model Predictive Control Algorithm

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An alternative stability proof for “Adaptive type-2 fuzzy estimation of uncertainties in the control of electrically flexible-joint robots”

Journal of Vibration and Control ◽

10.1177/1077546318802694 ◽

2018 ◽

Vol 25 (5) ◽

pp. 977-983 ◽

Cited By ~ 6

Author(s):

Alireza Izadbakhsh ◽

Payam Kheirkhahan

Keyword(s):

Closed Loop ◽

Loop System ◽

Control Input ◽

Closed Loop System ◽

Flexible Joint ◽

Flexible Joint Robots ◽

Robust Stability Analysis ◽

The Stability ◽

Estimation Of Uncertainties

This short note points out an improvement on the robust stability analysis for electrically driven flexible joint robots (EDFJR) given in the 2017 paper by Zirkohi and Fateh, entitled “Adaptive type-2 fuzzy estimation of uncertainties in the control of electrically flexible-joint robots.” In their paper, the authors present an interval Type-2 Adaptive fuzzy control scheme for EDFJR. The nonlinearities associated with actuator input constraints have been also considered in their paper. They discussed the saturated and unsaturated region of the control input separately and neglected the transition state between these regions. Moreover, they did not guarantee the stability of the closed-loop system in the saturated area. In this note, an alternative stability proof is presented that does not require this separation, and which guarantees the stability in a more general framework. The overall closed-loop system is proven to be robust, and bounded-input, bounded-output stable, while the motor/joint position errors are uniformly-ultimately bounded based on the Lyapunov's stability concept.

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Longitudinal nonlinear adaptive autopilot design for missiles with control constraint

Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering ◽

10.1177/0954410017699002 ◽

2017 ◽

Vol 232 (9) ◽

pp. 1655-1670 ◽

Cited By ~ 3

Author(s):

Keum W Lee ◽

Sahjendra N Singh

Keyword(s):

Feedback Loop ◽

Closed Loop ◽

Angle Of Attack ◽

Trajectory Control ◽

Loop System ◽

Control Law ◽

Control Input ◽

Error Signal ◽

Closed Loop System ◽

Control Saturation

This paper develops a new nonlinear adaptive longitudinal autopilot for the control of missiles with control input constraint, in the presence of parametric uncertainties and external disturbance input. The objective here is to control the angle of attack of the missile. A saturating control law is derived for the trajectory control of the angle of attack. The control law includes an auxiliary dynamic system in the feedback loop, driven by control input error signal, caused by control saturation, to preserve stability in the closed-loop system. By the Lyapunov stability analysis, it is shown that in the closed-loop system, the system trajectories are uniformly ultimately bounded. Simulation results show that the designed autopilot with constrained input can accomplish accurate trajectory control if the control saturation period is short. It is also seen that although the tracking error increases with the saturation period, the angle of attack tends to zero, once the command input is set to zero. Furthermore this adaptive control system, including the control error signal feedback loop, performs better than the adaptive laws, designed earlier based on immersion and invariance principle, without control magnitude constraint.

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Global Adaptive Control of Stochastic Nonlinear Systems with Linearly Bounded Unmeasurable States by Output Feedback

Mathematical Problems in Engineering ◽

10.1155/2012/184624 ◽

2012 ◽

Vol 2012 ◽

pp. 1-15

Author(s):

Qiangde Wang ◽

Chunling Wei

Keyword(s):

Nonlinear Systems ◽

Output Feedback ◽

Closed Loop ◽

Inverse Dynamics ◽

Growth Conditions ◽

Loop System ◽

Stochastic Nonlinear Systems ◽

Nonlinear Functions ◽

Closed Loop System ◽

Stochastic Stabilization

The problem of the output feedback stochastic stabilization is investigated for a class of stochastic nonlinear systems with linearly bounded unmeasurable states. Under the condition that the inverse dynamics is stochastic input-to-state stable and the nonlinear functions satisfy the linear growth conditions with unknown growth rate, an adaptive output feedback controller is proposed to make the closed-loop system globally stable in probability and the states of the closed-loop system converge to zero almost surely. A simulation example is provided to show the effectiveness of the theoretical results.

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