Distributed consensus observer-based \(H_\infty\) control for linear systems with sensor and actuator networks. (English) Zbl 1316.93008
Summary: This paper proposed a Distributed Consensus Observer (DCO) based \(H_\infty\) control method for a class of Linear Time-Invariant (LTI) continuous systems with a Sensor and Actuator Network (SAN). The communication topology of the SAN under consideration is represented by a directed graph, in which the sensor nodes are not able to acquire all the control inputs applied to the target system from the actuator nodes. To overcome this difficulty, a set of novel DCOs embedded in the sensor nodes and a set of DCO-based controllers embedded in the actuator nodes are initially constructed to estimate and control the state of the target system in a fully distributed way, respectively. The constructed DCOs take full advantage of their consensus property and replace the unavailable control inputs with the approximate ones computed on the basis of the state estimates of the underlying sensor node and its neighboring sensor nodes. Subsequently, a design method of DCO-based \(H_\infty\) control is proposed in terms of Bilinear Matrix Inequality (BMI) to ensure that the closed-loop system is exponentially stable while satisfying a prescribed overall \(H_\infty\) performance of disturbance attenuation. Moreover, in order to make attenuation level as small as possible, a suboptimal \(H_\infty\) control design problem is formulated as a BMI optimization problem, and a modified path-following method is provided for solving this problem by using the existing Linear Matrix Inequality (LMI) optimization techniques. Finally, simulation results demonstrate the effectiveness of the proposed method.
MSC:
| 93A14 | Decentralized systems |
| 93B36 | \(H^\infty\)-control |
| 93C05 | Linear systems in control theory |
| 93B07 | Observability |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 94C15 | Applications of graph theory to circuits and networks |
Keywords:
sensor and actuator networks; distributed consensus observer-based controllers; bilinear matrix inequality; path-following methodSoftware:
LMI toolboxReferences:
| [1] | DOI: 10.1016/j.adhoc.2004.04.003 · doi:10.1016/j.adhoc.2004.04.003 |
| [2] | Anderson B.D., Optimal filtering (1979) |
| [3] | DOI: 10.1137/S0363012994272630 · Zbl 0892.93050 · doi:10.1137/S0363012994272630 |
| [4] | DOI: 10.1137/1.9781611970777 · Zbl 0816.93004 · doi:10.1137/1.9781611970777 |
| [5] | DOI: 10.1109/TIE.2009.2029585 · doi:10.1109/TIE.2009.2029585 |
| [6] | DOI: 10.1109/TIE.2010.2043038 · doi:10.1109/TIE.2010.2043038 |
| [7] | DOI: 10.1049/el:20081574 · doi:10.1049/el:20081574 |
| [8] | DOI: 10.1109/91.855915 · doi:10.1109/91.855915 |
| [9] | DOI: 10.1109/TAC.2011.2176154 · Zbl 1369.90170 · doi:10.1109/TAC.2011.2176154 |
| [10] | Gabinet P., LMI control toolbox for use with Matlab (1995) |
| [11] | DOI: 10.1109/TAC.2008.930190 · Zbl 1367.93696 · doi:10.1109/TAC.2008.930190 |
| [12] | DOI: 10.1109/TNET.2007.900413 · doi:10.1109/TNET.2007.900413 |
| [13] | DOI: 10.1109/ACC.1999.783595 · doi:10.1109/ACC.1999.783595 |
| [14] | Haykin S.S., Adaptive filter theory, 4. ed. (2005) · Zbl 0723.93070 |
| [15] | DOI: 10.1109/TAC.2013.2286893 · Zbl 1360.68154 · doi:10.1109/TAC.2013.2286893 |
| [16] | DOI: 10.1016/j.automatica.2007.07.004 · Zbl 1283.93019 · doi:10.1016/j.automatica.2007.07.004 |
| [17] | Lewis F.L., Optimal and robust estimation: With an introduction to stochastic control theory (2008) · Zbl 1133.93040 |
| [18] | DOI: 10.1109/TNN.2011.2105501 · doi:10.1109/TNN.2011.2105501 |
| [19] | DOI: 10.1016/j.ins.2012.10.009 · Zbl 1293.93268 · doi:10.1016/j.ins.2012.10.009 |
| [20] | DOI: 10.1016/j.sysconle.2008.01.002 · Zbl 1140.93355 · doi:10.1016/j.sysconle.2008.01.002 |
| [21] | DOI: 10.1016/j.automatica.2008.09.009 · Zbl 1158.93349 · doi:10.1016/j.automatica.2008.09.009 |
| [22] | DOI: 10.1016/j.automatica.2012.05.042 · Zbl 1267.93171 · doi:10.1016/j.automatica.2012.05.042 |
| [23] | DOI: 10.1002/9780470570517 · Zbl 1183.68015 · doi:10.1002/9780470570517 |
| [24] | DOI: 10.1109/TAC.2008.928309 · Zbl 1367.93183 · doi:10.1109/TAC.2008.928309 |
| [25] | DOI: 10.1109/TAC.2011.2163864 · Zbl 1368.90024 · doi:10.1109/TAC.2011.2163864 |
| [26] | DOI: 10.1016/j.sysconle.2008.01.011 · Zbl 1153.93034 · doi:10.1016/j.sysconle.2008.01.011 |
| [27] | DOI: 10.1016/j.jpdc.2012.02.013 · Zbl 1248.68100 · doi:10.1016/j.jpdc.2012.02.013 |
| [28] | DOI: 10.1016/j.automatica.2011.06.012 · Zbl 1223.68022 · doi:10.1016/j.automatica.2011.06.012 |
| [29] | DOI: 10.1016/j.automatica.2010.06.025 · Zbl 1204.93122 · doi:10.1016/j.automatica.2010.06.025 |
| [30] | DOI: 10.1016/j.automatica.2012.09.010 · Zbl 1257.93094 · doi:10.1016/j.automatica.2012.09.010 |
| [31] | Verdone R., Wireless sensor and actuator networks: Technologies, analysis and design (2010) |
| [32] | Wang H.O., Fuzzy control systems design and analysis: A linear matrix inequality approach (2001) |
| [33] | DOI: 10.1080/00207170701836944 · Zbl 1148.93016 · doi:10.1080/00207170701836944 |
| [34] | DOI: 10.1109/TFUZZ.2007.896351 · doi:10.1109/TFUZZ.2007.896351 |
| [35] | DOI: 10.3390/s8021099 · doi:10.3390/s8021099 |
| [36] | DOI: 10.3390/s7102157 · doi:10.3390/s7102157 |
| [37] | DOI: 10.1016/j.ins.2013.06.043 · Zbl 1320.93039 · doi:10.1016/j.ins.2013.06.043 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
