Self-triggered model predictive control for networked control systems based on first-order hold. (English) Zbl 1390.93297
Summary: In this work, a new self-triggered model predictive control (STMPC) algorithm is proposed for continuous-time networked control systems. Compared with existing STMPC algorithms, the proposed STMPC is implemented based on linear interpolation (first-order hold) rather than the standard zero-order hold, which helps further reduce the difference between the self-triggered control signal and the original time-triggered counterpart and thus reduce the rate of triggering. Based on the first-order hold implementation, a self-triggering condition is derived and the corresponding theoretical properties of the closed-loop system are analyzed. Finally, the comparison between the proposed algorithm and the zero-order hold-based STMPC is carried out through both theoretical analysis and a simulation example to illustrate the effectiveness of the proposed method.
MSC:
| 93B40 | Computational methods in systems theory (MSC2010) |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 93C10 | Nonlinear systems in control theory |
Keywords:
first-order hold; model predictive control; networked control systems; self-triggered controlReferences:
| [1] | ÅströmKJ, BernhardssonB. Comparison of Riemann and Lebesque sampling for first order stochastic systems. Paper presented at: Proceedings of the 41st IEEE Conference on Decision and Control; 2002; Las Vegas, NV, USA. |
| [2] | MengX, ChenT. Optimal sampling and performance comparison of periodic and event based impulse control. IEEE Trans Autom Control. 2012;57(12):3252‐3259. · Zbl 1369.93576 |
| [3] | ShiD, ChenT, ShiL. Event‐triggered maximum likelihood state estimation. Automatica. 2014;50(1):247‐254. · Zbl 1298.93322 |
| [4] | ShiD, ChenT, ShiL. An event‐triggered approach to state estimation with multiple point‐ and set‐valued measurements. Automatica. 2014;50(6):1641‐1648. · Zbl 1296.93187 |
| [5] | MahmoudMS, MemonAM. Aperiodic triggering mechanisms for networked control systems. Inform Sci. 2015;296:282‐306. · Zbl 1360.93473 |
| [6] | TabuadaP. Event‐triggered real‐time scheduling of stabilizing control tasks. IEEE Trans Autom Control. 2007;52(9):1680‐1685. · Zbl 1366.90104 |
| [7] | HanD, MoY, WuJ, WeerakkodyS, SinopoliB, ShiL. Stochastic event‐triggered sensor schedule for remote state estimation. IEEE Trans Autom Control. 2015;60(10):2661‐2675. · Zbl 1360.93672 |
| [8] | MemonAM, MahmoudMS. Two‐level design for aperiodic networked control systems. Signal Process. 2016;120:43‐55. |
| [9] | AntaA, TabuadaP. To sample or not to sample: self‐triggered control for nonlinear systems. IEEE Trans Autom Control. 2010;55(9):2030‐2042. · Zbl 1368.93355 |
| [10] | PostoyanR, TabuadaP, NešićD, AntaA. Event‐triggered and self‐triggered stabilization of distributed networked control systems. Paper presented at: 2011 50th IEEE Conference on Decision and Control and European Control Conference; 2011; Orlando, FL, USA. |
| [11] | MemonAM, MahmoudMS. Evaluation of novel self‐triggering method for optimisation of communication and control. IET Control Theory Appl. 2016;10(1):76‐83. |
| [12] | LiH, ShiY. Event‐triggered robust model predictive control of continuous‐time nonlinear systems. Automatica. 2014;50(5):1507‐1513. · Zbl 1296.93110 |
| [13] | EqtamiA, DimarogonasDV, KyriakopoulosKJ. Event‐triggered control for discrete time systems. Paper presented at: Proceedings of the American Control Conference; 2010; Baltimore, MD, USA. |
| [14] | LuL, ZouY, NiuY. Event‐triggered decentralized robust model predictive control for constrained large‐scale interconnected systems. Cogent Eng. 2016;3(1):1127 309. |
| [15] | ZhangJ, LiuS, LiuJ. Economic model predictive control with triggered evaluations: state and output feedback. J Process Control. 2014;24(8):1197‐1206. |
| [16] | ZhangJ, LiuJ. Two triggered information transmission algorithms for distributed moving horizon state estimation. Syst Control Lett. 2014;65:1‐12. · Zbl 1285.93095 |
| [17] | GommansT, HeemelsW. Resource‐aware MPC for constrained nonlinear systems: a self‐triggered control approach. Syst Control Lett. 2015;79:59‐67. · Zbl 1326.93044 |
| [18] | EqtamiA, Heshmati‐AlamdariS, DimarogonasDV, KyriakopoulosKJ. Self‐triggered model predictive control for nonholonomic systems. Paper presented at: 2013 European Control Conference (ECC); 2013; Zürich, Switzerland. |
| [19] | HashimotoK, AdachiS, DimarogonasD. Self‐triggered model predictive control for nonlinear input‐affine dynamical systems via adaptive control samples selection. IEEE Trans Autom Control. 2016;62(1):177‐189. · Zbl 1359.93279 |
| [20] | AtassiAN, KhalilHK. A separation principle for the stabilization of a class of nonlinear systems. IEEE Trans Autom Control. 1999;44(9):1672‐1687. · Zbl 0958.93079 |
| [21] | ChenH, AllgowerF. A quasi‐infinite horizon nonlinear model predictive control scheme with guaranteed stability. Automatica. 1998;34:1205‐1217. · Zbl 0947.93013 |
| [22] | MayneDQ, RawlingsJB, RaoCV, ScokaertPO. Constrained model predictive control: stability and optimality. Automatica. 2000;36(6):789‐814. · Zbl 0949.93003 |
| [23] | LehmannD, HenrikssonE, JohanssonKH. Event‐triggered model predictive control of discrete‐time linear systems subject to disturbances. Paper presented at: 2013 European Control Conference (ECC); 2013; Zürich, Switzerland. |
| [24] | MarruedoDL, AlamoT, CamachoE. Enlarging the domain of attraction of MPC controller using invariant sets. Paper presented at: 2002 15th IFAC World Congress; 2002; Barcelona, Spain. |
| [25] | JohansenTA. Approximate explicit receding horizon control of constrained nonlinear systems. Automatica. 2004;40(2):293‐300. · Zbl 1051.49018 |
| [26] | MichalskaH, MayneDQ. Robust receding horizon control of constrained nonlinear systems. IEEE Trans Autom Control. 1993;38(11):1623‐1633. · Zbl 0790.93038 |
| [27] | ZhangZ, ChongKT. Comparison between first‐order hold with zero‐order hold in discretization of input‐delay nonlinear systems. Paper presented at: International Conference on Control, Automation and Systems (ICCAS’07); 2007; Seoul, South Korea. |
| [28] | El‐FarraNH, ChristofidesPD. Integrating robustness, optimality and constraints in control of nonlinear processes. Chem Eng Sci. 2001;56(5):1841‐1868. |
| [29] | SakizlisV, PerkinsJD, PistikopoulosEN. Explicit solutions to optimal control problems for constrained continuous‐time linear systems. IEE Proc‐Control Theory Appl. 2005;152(4):443‐452. |
| [30] | ÅströmKJ, WittenmarkB. Computer‐Controlled Systems: Theory and Design. Courier Corporation, 2013; North Chelmsford, Massachusetts, USA. |
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