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(IJACSA) International Journal of Advanced Computer Science and Applications,Vol. 8, No. 2, 2017Time Varying Back Propagating Algorithm forMIMO Adaptive Inverse ControllerIbrahim Mustafa MehediCenter of Excellence in Intelligent Engineering Systems (CEIES)Department of Electrical and Computer EngineeringKing Abdulaziz University, Jeddah - 21589, Saudi ArabiaAbstract—In the field of automatic control system design,adaptive inverse is a powerful control technique. It identifies thesystem model and controls automatically without having priorknowledge about the dynamics of plant. In this paper neuralnetwork based adaptive inverse controller is proposed to controla MIMO system. Multi layer perception and back propagation arecombinedly used in this investigation to design the NN learningalgorithm. The developed structure represents the ability toidentify and control the MIMO system. Mathematical derivationand simulation results for both plant identification and controlare shown in this paper. Further, to prove the superiority of theproposed technique, performances are compared with recursiveleast square (RLS) method for the same MIMO system. RLSbased adaptive inverse scheme is discussed in this paper for plantidentification and control. Also the obtained simulated resultsare compared for both plant parameter estimation and trackingtrajectory performance.Keywords—Adaptive inverse control; neural network; MIMO;multilayer perceptionI.I NTRODUCTIONPrior knowledge is an important factor for almost everyconventional control system. Such as in continuous time system, number of poles and zeros or the limit of upper boundson the order of the plant are assumed to be known [1], [2],[3], [4]. Again the known time delay is crucial for discretetime systems [5], [6], [7]. To overcome these difficulties,the adaptive control methods were developed. Because it canwork even if the system structure and critical parameters areunknown [6], [10]. There are several approaches are proposedto develop the adaptive controllers [8] and already been implemented for different robotic applications. Such an applicationis presented in [9]. In this example work, an adaptive neuralnetwork control approach is used to enhance the performanceof a flexible manipulator. Adaptive controllers, based on selfTuning method were proposed to avoid the problem of uncancellable zeros for the system transfer function [11], but thereference model of the adaptive control depends on transferfunction of the plant. Due to this problem, the desired outputis not independent of the plant characteristics. The adaptiveinverse control is one of the solutions to overcome thesedifficulties. It is a method to design an automatic controlsystem. It learns over time to control a particular dynamicsystem [12]. Adaptive filtering technique proceeds with threeconcurrent learning steps and eventually develops adaptiveinverse control method [13]. At the beginning, the modeledadaptive plant identifies the system dynamics. Next, the controldynamics of the plant is learned by a feed-forward controller.Finally, the disturbance affecting the plant is canceled byan adaptive feedback disturbance canceler. These controllersapproximately compensate the effect of numerator polynomialat the output with the help of approximate inverse of the plant[4], [10]. The desired trajectory is approximately followed bythe output of the plant with some delay which can be estimated.The plant dynamics is controlled by several neural network(NN) approaches. A dual step controller based on neuralnetwork is used to obtain feedback linearizion and learning ofthe plant dynamics [14]. The calculation complexities of computing inverse dynamic are reduced by using neural networkmethod. It also improves the precision by learning procedure.A different neural network technique is considered using afeed-forward inverse recurrent method based PD controller[15]. Inversion error is compensated and disturbances arerejected using this technique. Past investigations show thebetter performance while using neural network controllers forcontrolling the nonlinear plant dynamics [16]. Gain tuning isalso performed for PD controller using NN [17].All of these techniques used for neural network controllershave firm restrictions. In general, they require to know thefairly precise plant model before hand. Adaptive inverse control technique is considered in this paper, which is based onneural network using multi layer perception for MIMO system.A simplified architecture of the NN models are incorporatedin which the modeling of the system approximate inverse ofthe plant are obtained directly. Then the approximate inversemodel is used for the learning process to control the plantdynamics.The rest of the paper is presented as follows: The problemstated for the purpose of this investigation is mentioned inthe the next section. Architecture of adaptive inverse controltechnique is explained in Section 3 for multi input and multioutput (MIMO) system. Multilayer perception based neuralnetwork concept is discussed in Section 4. In Section 5,back propagation based learning algorithm is explained todesign adaptive inverse controller. Simulation results and theirdiscussion for a dual input and dual output system is presentedin Section 6 while using NN based adaptive inverse controlscheme. Plant identification algorithm of RLS method andadaptive inverse control scheme is discussed in Section 8.Also the obtained simulated results are compared for bothplant parameter estimation and tracking trajectory performanceevaluation in this Section. The Section 8 concluded the investigation.www.ijacsa.thesai.org370 P a g e

(IJACSA) International Journal of Advanced Computer Science and Applications,Vol. 8, No. 2, 2017Fig. 1.Schematic diagram of basic adaptive inverse controlII.S TATEMENT OF P ROBLEMConsidering a multi input and multi output (MIMO) discrete time linear system described by:y(z) P (z)u(z) V (z)Fig. 2.Adaptive inverse- plant estimation for MIMO systemFig. 3.Adaptive inverse- plant control for MIMO system(1)where, multi outputsy(z) [y1 (z) y2 (z) y3 (z) T yM (z)] uN (z)] VM (z)](2)multi inputsu(z) [u1 (z) u2 (z) u3 (z) T(3)disturbancesV (z) [V1 (z) V2 (z) V3 (z) T(4)and the discrete transfer function P11 (z) P12 (z) P13 (z) P1N (z) P (z) PM 1 (z) PM 2 (z) PM 3 (z) PM N (z)(5)In the above equations, u(z) is the inputs and y(z) isthe outputs of the measurable plant while V (z) denotes forbounded disturbances. P (z) is the discrete transfer functionmetrics. The aim of the neural network based inverse adaptiveis to obtain a set of control inputs which are bounded. Withthe impact of these bounded control inputs, the outputs y(z)should follow the reference inputs.III.A RCHITECTURE OF A DAPTIVE I NVERSEC ONTROLLERAdaptive inverse controller is not similar to the traditionalclosed loop controllers. The main concept of inverse adaptivecontrol is to govern the system with a control command fromthe controller. The controller transfer function is the inverse ofplant transfer function. The principal idea of inverse adaptivecontrol is shown in Figure (1). Obtaining better trackingperformance for the plant output is the main objective of thissystem. A true plant inverse need to be created by adapting thecontroller parameters because the plant is usually unknown.Comparing the plant output and command input, an errorsignal is produced to use for the adjusting process of thecontroller’s parameters through an adaptive algorithm. Purposeof this algorithm is to minimize the error in terms of squaremean. But this configuration has some demerits. Such as theadaptation process of the controller can not be done directlyby the algorithm. Because the algorithm (for example, LMS)needs an error refereed to the plant input. Therefore a differentconfiguration of adaptive inverse controller is proposed toovercome this problem and shown in Figure (2) and (3) fora MIMO system.Rapid adaptation process and control action with plantdisturbance represented in Figure (2) and (3). The plantidentification and control mechanism are described as follows: Step 1: A MIMO plant model P̂ (z) of the originalplant P (z) is identified on real time basis by usingback propagating adaptive algorithm shown in Figure(2). Step 2: Updated parameters of controller Ĉ(z) isgenerated from a digital copy of P̂ (z) either on-lineor off-line and it is shown in Figure (3). Step 2: Finally the obtained updated Ĉ(z) can be usedas a cascaded controller with the original plant P (z)as presented in Figure (2).www.ijacsa.thesai.org371 P a g e

(IJACSA) International Journal of Advanced Computer Science and Applications,Vol. 8, No. 2, 2017Identification of the plant output10.08Actual plantIdentified plant0.060.04Amplitude0.020 0.02 0.04 0.06 0.08 0.10Fig. 4.IV.Multi-layer neural 10000Fig. 5. MIMO plant identification without disturbance for output-1 (Sinusoidal input)N EURAL N ETWORK WITH M ULTI L AYER P ERCEPTIONA multi layer neural network contains multiple neurons,those are organized into different layers . The primary layersare placed at input side, the output layers are organized at theend and the middle area of the input and output is known ashidden layers [18]. It is already known that neural networkis capable to execute in the presence of system nonlinearitiesbecause NN is a nonlinear filter. This property encourages toimplement NN in the adaptive inverse problem. The neuronsare connected towards forward direction without having anyfeed back connections between input and output. Therefore, inthis work, the adaptive inverse control is implemented by usingmulti layer feed forward neural network (MLFFNN) [19] andshown in Figure (4). The active functions of successive layerscan differ from each other. Connection link between input andneurons contain some weight. Neuron output is applicable tothe nonlinear function.V.1000A DAPTING C ONTROLLER V IA L EARNING A LGORITHMThe learning algorithm of this study is supported byback propagation technique for the NN based controller. Theactivation function induced by local field at the input is shownin Eq.(6). where, yi (n) is the output of ith neuron for the nthiteration. The synaptic weight of the connecting link betweenoutput of ith neuron and jth neuron is denoted by wji (n). Thetotal number of inputs applied to the neuron j is indicated bym.nXvj (n) wji (n)yi (n)(6)where δj is responsible for local gradient related withjth neuron while the learning rate is denoted by η(n). Thislearning rate is updated using following technique:η(n) ψ(n) ψ(n 1) ψ(n m)(9)m 1hereψ αη(n 1) γ k e(n) k2 .Mathematical expression of the local gradient δj is definedby Eq.(10) for j output neuron.0δj (n) ej (n)Φj (vj (n))(10)where error ej is measured between the output and desiredresponse dj (n). Again the local gradient can be calculatedwhile the neuron comes from hidden layer and expressed bythe Eq.(11).X0δj (n) Φj (vj (n))δk (n)wkj (n)(11)kVI.S IMULATION R ESULTS AND D ISCUSSIONTransfer function of a MIMO system is used for thisinvestigation. To obtain direct and inverse model of MIMOsystem, we have used back propagating algorithm based onfeed forward multi layer perception. The transfer function ofdouble inputs and double outputs MIMO plant is shown in Eq.(12).i 0The output at the jth neuron is shown in Eq.(7) while thenonlinear function φ() is applied to the output of any neuron.yj (n) φj (vj (n))P (z) z 1 (0.1182 0.1531z 1 )1 1.385z 1 0.4724z 2z 1 ( 0.1174 0.09145z 1 )1 1.385z 1 0.4724z 2(7)The synaptic weights is updated according to the backpropagation algorithm and it is expresses by the Eq.(8).wji (n 1) wji (n) η(n)δj (n)yi (n)"(8)z 1 (0.1378 0.1378z 1 )1 1.385z 1 0.4724z 2z 1 (0.09867 0.1683z 1 )1 1.385z 1 0.4724z 2#(12)A. Plant identificationPrimarily the system is identified through adaptive inverseback propagation technique with random weight values whileno disturbance is considered. Sinusoidal signal is given as thewww.ijacsa.thesai.org372 P a g e

(IJACSA) International Journal of Advanced Computer Science and Applications,Vol. 8, No. 2, 2017Identification of the plant output21.5Identification of the plant output1Actual plantIdentified plant0.08Actual plantIdentified plant10.060.040.5AmplitudeAmplitude0.020 0.50 0.02 0.04 1 0.06 ationsFig. 6. MIMO plant identification without disturbance for output-2 (Sinusoidal input) 0.080Fig. 0900010000MIMO plant identification with disturbance for output-1 (SinusoidalIdentification of the Plant2Actual Plant OutputPlant IdentifiedIdentification of the plant output21.51.5Actual PlantIdentified plant110.50AmplitudeAmplitude0.5 0.50 1 0.5 1.5 2010002000300040005000Iterrations6000700080009000 110000 1.501000200030004000Fig. 9.input)In both cases, an adaptive inverse with back propagationtechnique was found the satisfactorily identified system. Thesystem was driven by uniform control signal. It is shownin the Figure (5) to (10) that the neural networks couldbe trained to identify the plant nearly perfect manner withand without disturbances. Usually with the disturbance, theplant dynamics should be disturbed. With the implementationof adaptive inversed based back propagation technique, the600070008000900010000MIMO plant identification with disturbance for output-2 (Sinusoidalreference input signal. Identified plant is shown in Figure (5)and (6) with respect to output-1 and output-2. It is observedthat the plants are identified perfectly. To see the impact ofchanging the input signal the simulation was run again usingsquare wave (reference input) as shown in Figure (7). Due tothe changes of input signal the proposed technique found theplant identification nearly perfect.Identification of the Plant2Actual Plant OutputPlant Identified1.510.5AmplitudeThe same simulation was repeated with random weightvalues in the presence of disturbance. With the same sinusoidalinput signal, the identified plant is shown in Figure (8) and (9).Again the sample result of MIMO plant identification is shownin Figure (10) with disturbance condition while the input signalis changed from sinusoidal to square wave.5000IterrationsFig. 7. MIMO plant identification for square input signal without disturbances(sample result)0 0.5 1 1.5 0000Fig. 10. MIMO plant identification for square input signal with disturbances(sample result)www.ijacsa.thesai.org373 P a g e

(IJACSA) International Journal of Advanced Computer Science and Applications,Vol. 8, No. 2, 2017Tracking Trajectory for the plant output 1Tracking Trajectory for the Plant output 11.5Reference inputPlant output1Reference inputPlant output10.5AmplitudeAmplitude0.500 0.5 0.5 1 1.50 1100020003000400050006000Iterrations700080009000 1.5010000Fig. 11. Tracking trajectory for MIMO plant without disturbance for output-1Fig. cking Trajectory for the Plant output 2Reference inputPlant output1Reference inputPlant output10.5Amplitude0.5Amplitude4000Tracking trajectory for MIMO plant with disturbance for output-1Tracking Trajectory for the plant output 200 0.5 0.5 1 1 09000 00900010000Fig. 12. Tracking trajectory for MIMO plant without disturbance for output-2Fig. 14.system identification processes matched the nominal dynamicsof the plant. These proves the theoretical prediction.again using square wave (reference input) as shown in Figure(15).B. Plant controlVII.Once the plant identification is done then the controlaction is implemented using adaptive inverse technique tothe MIMO system. Reference input is chosen as sinusoidalsignal. Primarily the plant is experienced with no disturbances.The result is presented in Figure (11) and (11). The desiredplant output ( blue dashed line) and the true system output(red solid line) are indicated in this result. Tracking of thesinusoidal input signal is nearly perfect while the plant doesnot experience any disturbances. A sinusoidal control signal isobserved for this MIMO plant.To observe the performance of disturbance cancellation,the disturbance signal is included in terms of noise in thealgorithm. The filter is chosen for the purpose of disturbancecancellation. The effectiveness of the canceler was testedperfectly. The result is in shown Figure (13) and (14). Thecontrol signal of the MIMO plant is also sinusoidal while thedisturbance is considered. To see the impact of changing theinput signal to control the plant output, the simulation was runTracking trajectory for MIMO plant with disturbance for output-2C OMPARISON WITH RLS BASED A DAPTIVE I NVERSEC ONTROL A LGORITHMA. Recursive Least Squares (RLS) MethodThe principle task of Recursive Least Squares (RLS)method is to calculate the state variables and observationvectors of the system. Then it compares between observationand the actual output of system. Finally it calculates the sumof squared errors. The parameter matrix is identified through acontinuous modification process while the sum of squared erroris achieved at its minimum range. Therefore, the identifiedparameters are kept closer to the actual parameters of thesystem [20]. Although RLS method is very fast process butit is highly complex in terms of computational cost.B. Summary of Identification AlgorithmMulti order filter is considered to summarize RLS algorithm. In the Fig. 16, r(m), y(m), d(m) and z(m) are input,output, disturbance noise and measured output respectively.www.ijacsa.thesai.org374 P a g e

(IJACSA) International Journal of Advanced Computer Science and Applications,Vol. 8, No. 2, 2017Tracking Trajectory for the plant output2Reference inputPlant output1.51Amplitude0.50 0.5Fig. 16.Least Squares Method(14)Fig. 17.RLS based adaptive inverse- plant control for MIMO system(15)Using suitable initial values for q and α̂ recursive operationis performed so that the residual error γ(m) is reduced enough.Hence, a minimum value is obtained for criterion function inorder to complete the identification process. 1 1.5 20Fig. 000900010000Tracking trajectory of MIMO plant for square input signal (sampleα(m) is model parameter which is unknown. The model inputis defined asr(m) [r1 (m), r2 (m), .rn (m)]Tα [α, α, .α](13)TOutput parameters of the model isz(m) rT (m)α d(m)The function of least square criterion is deduced bynXC(α) [z(m) rT (m)α]2(16)m 1α is estimated for the minimum value of C(α) and then α̂is called the parameter values of least square estimation. Nowthe recursive least square (RLS) method is expressed through α̂(m) [r(m)T r(m)] 1 r(m)T z(m)(17)q(m) 1 r(m)T r(m)Where q(m) is symmetric matrix positively decrease withthe increase of y. The derived formulas for recursive methodsare as follows:α̂(m) α̂(m 1) M (m)[r(m) θT α̂(m 1)](18)Here, M (m) is gain matrix and defined as:M (m) q(m 1)θ(m)1 1)θ(m)θT (m)q(mq(m) [I M (m)θT ]q(m 1)C(m) C(m 1) (19)(20)[z(m 1) rT (m 1)α(m 1)]21 θT (m 1)q(m 1)θ(m 1)(21)Therefore, the residual is expressed as:γ(m) [z(m 1) rT (m 1)α(m 1)]21 θT (m 1)q(m 1)θ(m 1)(22)C. RLS Based Adaptive Inverse ControlFigure 17 shows a schematic diagram of RLS basedadaptive control for MIMO system. Structure contains severalblocks like original model of the plant, inverse plant, adaptivealgorithm, plant estimation algorithm, and feedback module.In this control architecture, plant is identified using RLSalgorithm and expressed into S-function and converted intoinverse system which combined with original plant connectedin series. State feedback block forms a closed loop controlarchitecture.D. Simulation results of RLS Based Adaptive Inverse Control- A comparisonAThe same MIMO system defined in Eq. 12 is identifiedthrough RLS based adaptive inverse technique with randomweight values. A square signal is given as the reference inputsignal. Identified plant is shown in Figure (18) and (19) withrespect to output-1 and output-2. It is observed and comparedwith the result produced through back propagation basedadaptive inverse control shown in Fig. 7 (without disturbance)and Fig. 10 (with disturbance). A better identification for plantparameters is obtained than RLS based estimation technique interms of overshoot. Specifically, RLS based adaptive inversealgorithm of MIMO plant identification for square input signalwith respect to output-2 contains very high overshoot. Therefore, the identified plant using neural network based controlleris more perfect over RLS based estimation technique.www.ijacsa.thesai.org375 P a g e

(IJACSA) International Journal of Advanced Computer Science and Applications,Vol. 8, No. 2, 2017Identification of the PlantTracking Trajectory for the Plant output 11.5Actual PlantRLS AICReference InputRLS AIC Output110.50.5AmplitudeAmplitude1.500 0.5 0.5 1 1 0 1.5010000Fig. 18. MIMO plant identification for square input signal with respect tooutput-1 using RLS based adaptive inverse 00900010000Fig. 20. Tracking trajectory of MIMO plant for square input signal withrespect to output-1 using RLS based adaptive inverse algorithmTracking Trajectory for the Plant output 22.5Reference InputRSL AIC Output2Identification of the Plant5Actual PlantRLS AIC41.513Amplitude0.5Amplitude210 0.50 1 1 1.5 2 2 3 2.50 4 010000Fig. 21. Tracking trajectory of MIMO plant for square input signal withrespect to output-2 using RLS based adaptive inverse algorithmFig. 19. MIMO plant identification for square input signal with respect tooutput-2 using RLS based adaptive inverse algorithmVIII.Next step of plant parameter identification is to controlthe system. RLS based adaptive inverse technique is used tocontrol the outputs of the same MIMO system. Referenceinput is chosen as square signal for this simulation. The plantcontrolled results are presented in Figure (20) and (21) withrespect to output-1 and output-2. The desired plant output (blue dashed line) and the true system output (red solid line) areindicated in these results. It is observed that using RLS basedadaptive inverse algorithm, tracking trajectory of MIMO plantfor square input signal with respect to output-2 contains veryhigh overshoot. For the comparison with NN based adaptiveinverse control technique, the plant is experienced with nodisturbances which is shown in Fig. 15. It is found that thetracking trajectory of MIMO plant is more perfect while usingback propagating algorithm based adaptive inverse controltechnique because its overshoot is with acceptable range. Dueto the higher overshoot obtained in Fig. 21, it may causeinstability of the system.C ONCLUSIONIn this paper, back propagation based adaptive inverse control technique is proposed to find the approximate inverse ofthe system. It has been shown that the proposed control methodcan perform well for MIMO system. It has also been shownnearly perfect performance while the disturbance is injectedin term of noise. Therefore, the results verify the ability ofneural network based adaptive inverse technique to controlMIMO system. To prove the superiority of the proposed technique, the performance is compared with recursive least square(RLS) method for the same MIMO system. Plant identificationalgorithm of RLS method and adaptive inverse control schemeis discussed in this paper. Also the obtained simulated resultsare compared for both plant parameter estimation and trackingtrajectory performance.ACKNOWLEDGMENTThis article was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah. Therefore,the authors acknowledge with thanks DSR financial support.www.ijacsa.thesai.org376 P a g e

(IJACSA) International Journal of Advanced Computer Science and Applications,Vol. 8, No. 2, 2017R 3][14][15][16][17][18][19][20]S. Alkhalaf, Improvement of Control System Performance by Modificationof Time Delay, (IJACSA) International Journal of Advanced ComputerScience and Applications, 6(2), pp. 181-185, 2015.B. Audone, M. Audone and I. Marziali, On the use of the minimumphase algorithm in EMC data processing, International Symposium onElectromagnetic Compatibility (EMC EUROPE), pp. 1-6, 2012.J. Lu, M. Shafiq and T. Yahagi, A design method of model referenceadaptive control for SISO non-minimum phase continuous-time systemsusing approximate inverse systems, Transaction IEEE of Japan, 117-C(3),pp. 315-321, 1997.J. Lu, M. Shafiq and T. Yahagi, A design method of model referenceadaptive control for SISO non-minimum phase continuous-time systemsbased on pole-zero placement, IEICE Transaction Fundamentals, E80A(6), pp. 1109-1115, 1997.B. H’mida and S. Dhaou, Discrete-Time Approximation for NonlinearContinuous Systems with Time Delays, (IJACSA) International Journalof Advanced Computer Science and Applications, 7(5), pp. 431-437,2016.K. Astrom and M. B Witten, Adaptive control, Addison-Wesely, NewYork, 1995.J. Lu, M. Shafiq and T. Yahagi, A new method for self tuning controlof non-minimum phase discrete-time systems in the presence of disturbances, Transaction IEEE of Japan, 117-C(2), pp. 110-116, 1997.A. Peiman, K. Abdollah and H. Khayrollah, A novel adaptive fullydifferential GM-C filter, tuneable with a CMOS fuzzy logic controllerfor automatic channel equalization after digital transmissions, AEU International Journal of Electronics and Communications, 63(5), pp. 374386, 2017.A. R Maouche and H. Meddahi, A Fast Adaptive Artificial Neural Network Controller for Flexible Link Manipulators, (IJACSA) InternationalJournal of Advanced Computer Science and Applications, 7(1), pp. 298308, 2016.T. Yahagi and J. Lu, On self-tuning control of non minimum phasediscrete time systems using approximate inverse systems, Journal ofDynamic Systems, Measurement, and Control, Transaction AMSE, 115,pp. 12-18, 1993.K. Astrom and M. B Witten, self-tuning controller based on pole-zeroplacement, IEEE Proceedings. 120-D, pp. 120-130, 1980.B. Widrow and G. L Plett, Adaptive inverse control based on linear andnonlinear adaptive filtering, Proceedings of International Workshop onNeural Networks for Identification, Control, Robotics and signal/imageprocessing, Venice, Italy, pp. 30-38, 1996.G. L Plett, Adaptive inverse control of plants with disturbance, PhDThesis, Stanford University, Stanford, CA, 1998.B. S Kim and A. J Calise, Nonlinear flight control using neuralnetworks, Journal of Guidance Control and Dynamics, 20(1), pp. 26-33,1997.L. Yan and C. J Li, Robot learning control based of recurrent neuralnetwork inverse model, Journal of Robotic Systems, 14(3), pp. 199-212,1997.K. S Narendra and K. Parthasarathy, Identification and control of dynamical system using neural networks, IEE transaction, Neural Network,1(1), pp. 4-27, 1990.D. L Tien, H. J Kang, Y. S Suh and Y. S Ro, An online self-gaintuning method using neural networks for nonlinear PD computed torquecontroller of a 2-dof parallel manipulator, Neurocomputing, 116, pp.53-61, 2013.F. Laurene, ”Fundamentals Of Neural Networks Architectures,Algorithms and Applications, Prentice Hall, ISBN:0133341860,9780133341867, 1994.H. S Adheed and A. Sulaiman, Multi-Layer Feed Forward NeuralNetwork Application In Adaptive Beamforming Of Smart Antenna System, International Conference on Multidisciplinary in IT and Communication Science and Applications (AIC-MITCSA), DOI: 10.1109/AICMITCSA.2016.7759925, pp. 1-6, 2016.Z. Jianhui and C. Siqin Adaptive Inverse System Control of Electromagnetic Linear Actuator, International Journal of Control and 12.12, 8(12), pp. 131-144, 2015.www.ijacsa.thesai.org377 P a g e

The adaptive inverse control is one of the solutions to overcome these difficulties. It is a method to design an automatic control system. It learns over time to control a particular dynamic system [12]. Adaptive filtering technique proceeds with three concurrent learning steps and eventually develops adaptive inverse control method [13].

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.3 ISA / ANSI, ANSI-A300, Standards for Tree Care Operations. 2.2 Planting Layout, Massing and Plant Selection.1 Consider the limits and frequencies of institutional maintenance practices at UBC, and design accordingly for efficiency, servicing accessibility, low maintenance, weed control, pest, disease and drought tolerance. .1 Regardless of whether irrigation will be installed on site, the .