Aiming at the online control problem of microbial fuel cells, this article presents a class of explicit model-predictive control methods based on the machine learning data model. The proposed method is divided into two stages: off-line design and on-line control. In the off-line design stage, (1) a feasible data set is collected by sampling the admissible state in the feasible region and solving the optimal model predictive control law for each sampling data point off-line, (2) a feasible sample discriminator is constructed based on the support vector machine–based binary classification in order to judge the whether the real sampling state is feasible, and (3) according to the feasible samples and the corresponding optimal control law, the control surface of explicit model predictive controller is constructed based on the machine learning methods. In the on-line control stage, the process data are collected in real time and the feasible control output is calculated by using the trained explicit predictive control surface. Extensive testing and comparison among the different machine learning algorithms, such as artificial neural network, extreme learning machine, Gaussian process regression, and relevance vector machine, are performed on the benchmark model of a class of microbial desalination fuel cells. These results demonstrate that the proposed explicit model predictive control method can avoid the exhausting optimization computing and is easy to realize on-line with good control performance.
CusickRDKimYLoganBE.Energy capture from thermolytic solutions in microbial reverse-electrodialysis cells. Science2012; 335(6075): 1474–1477.
2.
LoganBE.Peer reviewed: extracting hydrogen and electricity from renewable resources. Environ Sci Technol2004; 38(9): 160–167.
3.
KimJRMinBLoganBE.Evaluation of procedures to acclimate a microbial fuel cell for electricity production. Appl Microbiol Biot2005; 68(1): 23–30.
4.
LoganBE.Exoelectrogenic bacteria that power microbial fuel cells. Nat Rev Microbiol2009; 7(5): 375–381.
5.
HeZMinteerSDAngenentLT.Electricity generation from artificial wastewater using an upflow microbial fuel cell. Environ Sci Technol2005; 39(14): 5262–5267.
6.
LiuHRamnarayananRLoganBE.Production of electricity during wastewater treatment using a single chamber microbial fuel cell. Environ Sci Technol2004; 38(7): 2281–2285.
7.
ZhuXTokashJCHongYet al. Controlling the occurrence of power overshoot by adapting microbial fuel cells to high anode potentials. Bioelectrochemistry2013; 90(2): 30–35.
8.
YousefiVMohebbi-KalhoriDSamimiAet al. Effect of separator electrode assembly (SEA) design and mode of operation on the performance of continuous tubular microbial fuel cells (MFCs). Int J Hydrogen Energ2016; 41(1): 597–606.
9.
WangHParkJDRenZ.Active energy harvesting from microbial fuel cells at the maximum power point without using resistors. Environ Sci Technol2012; 46(9): 5247–5252.
10.
PengSLiangDWDiaoPet al. Nernst-ping-pong model for evaluating the effects of the substrate concentration and anode potential on the kinetic characteristics of bioanode. Bioresour Technol2013; 136(3): 610–616.
11.
GargAVijayaraghavanVMahapatraSSet al. Performance evaluation of microbial fuel cell by artificial intelligence methods. Expert Syst Appl2014; 41(4): 1389–1399.
12.
WuHCaoLWangJ.Gray-box modeling and control of polymer molecular weight distribution using orthogonal polynomial neural networks. J Process Contr2012; 22(9): 1624–1636.
13.
MagniLRaimondoDMAllgwerF.Nonlinear model predictive control: towards new challenging applications. Berlin, Heidelberg: Springer, 2009.
14.
SzucsAKvasnicaMFikarM. A memory-efficient representation of explicit MPC solutions. In: Proceedings of 2011 50th IEEE conference on decision control and European control conference (CDCECC), Orlando, FL, 12–15 December 2011, pp.1916–1921. New York: IEEE.
15.
BemporadABorrelliFMorariM.Model predictive control based on linear programming—the explicit solution. IEEE T Automat Contr2003; 47(12): 1974–1985.
16.
BemporadAMorariMDuaVet al. The explicit linear quadratic regulator for constrained systems. Automatica2002; 38(1): 3–20.
17.
RaimondoDMHuberODarupMSet al. Constrained time-optimal control for nonlinear systems: a fast explicit approximation. IFAC P Vol2012; 45: 113–118.
18.
AxehillDBesselmannTRaimondoDMet al. A parametric branch and bound approach to suboptimal explicit hybrid MPC. Automatica2014; 50(1): 240–246.
19.
RubagottiMBarcelliDBemporadA.Robust explicit model predictive control via regular piecewise-affine approximation. Int J Control2014; 87(12): 2583–2593.
20.
ChenWHBallanceDJGawthropPJ.Optimal control of nonlinear systems: a predictive control approach. Automatica2003; 39(4): 633–641.
21.
JohansenTA.Approximate explicit receding horizon control of constrained nonlinear systems. Automatica2004; 40(2): 293–300.
22.
GrancharovaAJohansenTA.Computation, approximation and stability of explicit feedback min-max nonlinear model predictive control. Automatica2009; 45(5): 1134–1143.
23.
BemporadAFilippiC.Suboptimal explicit receding horizon control via approximate multiparametric quadratic programming. J Optimiz Theory App2003; 117(1): 9–38.
24.
SummersSRaimondoDMJonesCNet al. Fast explicit nonlinear model predictive control via multiresolution function approximation with guaranteed stability. IFAC P Vol2010; 43(14): 533–538.
25.
ChakrabartyADinhVBuzzardGTet al. Robust explicit nonlinear model predictive control with integral sliding mode. In: Proceedings of American control conference, Portland, OR, 4–6 June 2014, pp.2851–2856. New York: IEEE.
26.
GrancharovaAJohansenTA.Explicit nonlinear model predictive control. Berlin; Heidelberg: Springer, 2012.
27.
ChakrabartyABuzzardGTZakSH.Output-tracking quantized explicit nonlinear model predictive control using multi-class support vector machines. IEEE T Ind Electron2017; 64(5): 4130–4138.
28.
WangJWangQ. Output tracking explicit nonlinear model predictive control for microbial desalination cells. In: Proceedings of international conference on control, decision and information technologies (CoDit’18), Thessaloniki, 10–13 April 2018. pp.1–6. New York: IEEE.
29.
ParisiniTZoppoliR.A receding-horizon regulator for nonlinear systems and a neural approximation. Automatica1995; 31(10): 1443–1451.
30.
ParisiniTSanguinetiMZoppoliR.Nonlinear stabilization by receding horizon neural regulators. Int J Control1998; 70(3): 341–362.
31.
KessonBMToivonenHT.A neural network model predictive controller. J Process Contr2006; 16(9): 937–946.
32.
AswaniAGonzalezHSastrySSet al. Provably safe and robust learning-based model predictive control. Automatica2013; 49(5): 1216–1226.
33.
OngCJSuiDGilbertEG.Enlarging the terminal region of nonlinear model predictive control using the support vector machine method. Automatica2006; 42(6): 1011–1016.
34.
GengZDongJChenJet al. A new self-organizing extreme learning machine soft sensor model and its applications in complicated chemical processes. Eng Appl Artif Intel2017; 62: 38–50.
35.
LiuLNanYWangJet al. PLS-based process analysis for glycosylation reaction. In: Proceedings of 12th world congress on intelligent control and automation, Guilin, China, 12–15 June 2016, pp.126–131. New York: IEEE.
36.
WangJWangQWangXet al. Operation space design of microbial fuel cells combined anaerobic-anoxic-oxic process based on support vector regression inverse model. Eng Appl Artif Intel2018; 72: 340–349.
37.
PingQZhangCChenXet al. Mathematical model of dynamic behavior of microbial desalination cells for simultaneous wastewater treatment and water desalination. Environ Sci Technol2014; 48(21): 13010–13019.
VapnikVN.The nature of statistical learning theory. Berlin: Springer, 1995, pp.988–999.
40.
DumaisSChenH. Hierarchical classification of web content. In: Proceedings of 23rd annual international ACM SIGIR conference research development information retrieval, Athens, 24–28 July 2000, pp.256–263. New York: ACM.
41.
VapnikVN.Statistical learning theory. New York: Wiley, 1998.
42.
LuongLHSSpeddingTA. A neural-network system for predicting machining behaviour. J Mater Process Tech1995; 52(2): 585–591.
43.
HuangGBZhouHDingXet al. Extreme learning machine for regression and multiclass classification. IEEE T Syst Man Cy B2012; 42(2): 513–529.
44.
TippingMESmolaA.Sparse Bayesian learning and the relevance vector machine. J Mach Learn Res2001; 1(3): 211–244.
