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Research Papers

Observer-Based ℋ∞ Feedback Control for Arbitrarily Time-Varying Discrete-Time Systems With Intermittent Measurements and Input Constraints

[+] Author and Article Information
Hui Zhang

Department of Mechanical Engineering,  University of Victoria, P.O. Box 3055, STN CSC, Victoria, BC, V8W 3P6, Canadahuizhang@uvic.ca

Yang Shi1

Department of Mechanical Engineering,  University of Victoria, P.O. Box 3055, STN CSC, Victoria, BC, V8W 3P6, Canadayshi@uvic.ca

1

Corresponding author.

J. Dyn. Sys., Meas., Control 134(6), 061008 (Sep 13, 2012) (12 pages) doi:10.1115/1.4006070 History: Received December 15, 2010; Revised November 17, 2011; Published September 13, 2012; Online September 13, 2012

In this paper, we investigate the observer-based ℋ∞ feedback control problem for discrete-time systems subject intermittent measurements and constrained control inputs. To characterize the practical scenario of the intermittent measurement phenomenon, we model it using a stochastic Bernoulli approach. We assume that the control action is constrained to be below a prescribed level. Sufficient conditions are obtained for the observer-based ℋ∞ feedback control problem. The estimator and the controller are derived by solving a linear matrix inequality (LMI)-based optimization problem. Moreover, the proposed method is extended to systems with arbitrarily time-varying parameters within a polytope with unknown vertices. Three examples are given to illustrate the effectiveness and efficacy of the proposed method.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

The observer-based control problem

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Figure 2

Cart and inverted pendulum system

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Figure 3

Ellipse of the initial values for the states when the constraint is 10

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Figure 4

Control actions under the initial conditions X = 0 and θ = 0.05

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Figure 5

Control actions under the initial conditions X = 2 and θ = 0.09

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Figure 6

Control actions under the initial conditions X = 4 and θ = 0.04

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Figure 7

Ellipse of the initial values for the states when the constraint is 50

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Figure 8

Control actions with the Luenberger estimator under the initial conditions X = 0 and θ = 0.05

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Figure 9

Control actions with the Luenberger estimator under the initial conditions X = 2 and θ = 0.09

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Figure 10

Control actions with the Luenberger estimator under the initial conditions X = 4 and θ = 0.04

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Figure 11

Step response for the inverse pendulum with PID controller (without missing measurement and constraint on the control action)

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Figure 12

Sine response for the inverse pendulum with PID controller (without missing measurement and constraint on the control action)

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Figure 13

Measured output trajectory for the inverse pendulum with PID controller (with missing measurement and constraint on the control action)

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Figure 14

Measured output trajectory for the inverse pendulum with designed observer and controller (with missing measurement and constraint on the control action)

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Figure 15

Control actions for the inverse pendulum with different control strategies (with missing measurement and constraint on the control action)

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Figure 16

Disturbance (Gaussian white noise) in the control action of example 2

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Figure 17

Control actions in example 2

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Figure 18

Controlled output zk in example 2

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Figure 19

Ellipse of the initial values for the states in example 2

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Figure 20

Time-varying value for the (2,2) element of the system matrix

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Figure 21

The missing measurement index rk

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Figure 22

Disturbance (Gaussian white noise) in the control action of example 3

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Figure 23

Measurement noise in example 3

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Figure 24

Control action in example 3

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