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Stability Analysis Strategy for the Adaptive Neural Control System: A Practical Validation Via a Transesterification Reactor
Abstract
In this paper, a stability analysis strategy of nonlinear control systems is proposed. An adaptive neural control scheme composed of an emulator, and a controller with decoupled adaptive rates is considered. A Lyapunov function based on tracking error dynamic is retained and an online adjusting technique of the neural controller adaptive rate is adopted to improve the closed loop performance in terms of stability, rapidity and precision. Comparative studies and an experimental validation on a semi-batch reactor are realized to prove the efficiency of the developed strategy.
... The model was validated with data from the literature, and two controllers for the temperature of the process were proposed: one for the closed-loop system, and a proportional-integral controller (PI) generating fast and stable responses in the stationary state. Other types of controllers have been developed, such as the proposal in [24], in which a neural controller was combined with a fuzzy adaptability rate for network training, improving both the response time and precision. A neural controller was introduced in [25], applying the particle swarm optimization (PSO) to change the responsiveness rate of the controller, reducing the time to find the optimal responsiveness rate of the controller. ...
This work deals with the problem of choosing a controller for the production of biodiesel from the transesterification process through temperature control of the chemical reactor, from the point of view of automatic control, by considering such aspects as the performance metrics based on the error and the energy used by the controller, as well as the evaluation of the control system before disturbances. In addition, an improvement method is proposed via a neuro-fuzzy controller tuned with a metaheuristic algorithm to increase the efficiency of the chemical reaction in the reactor. A clear improvement is shown in the minimization of the integral of time multiplied squared error criterion (ITAE) performance index with respect to the proposed method (8.1657 ×104) in relation to the PID controller (7.8770 ×107). Moreover, the integral of the total control variation (TVU) performance index is also shown to evaluate the power used by the neuro-fuzzy controller (25.7697), while the PID controller obtains an index of (32.0287); this metric is especially relevant because it is related to the functional requirements of the system since it quantifies the variations of the control signal.
Nowadays, energy management environment is a very important issue that technologies have focused on in order to save costs and minimize energy waste. This objective can be achieved by means of an energy resource management approach through an appropriate optimization technique. However, energy savings can conflict with other objective functions, to solve the problem a multi-objective optimization that considers the minimization of the control energy can be adopted. In this paper, we propose to use a multi-objective indirect neural adaptive control concept for nonlinear systems with unknown dynamics. The control scheme consists of an adaptive instantaneous neural emulator and neural controller built on fully connected real-time recurrent learning networks (RTRL). The multi-objective particle swarm optimization (MOPSO) algorithm is used as a mechanism to find NE and NC adaptive learning rates that optimize the proposed objective functions: control energy minimization and closed-loop preservation. Comparative studies and experimental validation on a semi-batch reactor, used to generate cleaner biofuels, are performed to confirm the effectiveness of the proposed strategy.
This paper deals with a new weight-updating algorithm using Lyapunov stability theory (LST) for the training of a neural emulator (NE), of nonlinear systems, connected by an autonomous algorithm inspired from the real-time recurrent learning (RTRL). The proposed method is formulated by an inequality-constraint optimization problem where the Lagrange multiplier theory is used as the optimization tool. The contribution of this paper is the integration of the LST into the Lagrange constraint function to synthesize a new analytical adaptation gain rate satisfying the asymptotic stability of the NE and providing good emulation performances. To confirm the good performances and the convergence ability of the proposed adaptation algorithm, a numerical example and an experimental validation on a chemical reactor are proposed.
The application of neural networks can present some limitations for the control of strongly nonlinear systems. In this paper, a new control scheme based on a neural multicontroller (NMC) is proposed. Indeed, the developed strategy considers a set of local neural controllers which adapt their parameters thanks to an online adaptation algorithm. The instantaneous choice of the adequate local controller is based on a switching mechanism. The advantages of the proposed method are (1) to avoid the computational complexity issues due to the search for an optimal adapting rate when a single neural controller is used, and in presence of strongly nonlinear systems, and (2) to improve the control law by selecting the suitable controller which generates the most valid control law satisfying the desired closed-loop performances. Numerical examples are illustrated to evaluate the performance of the proposed control scheme compared to the classical one. An application of the new strategy on a chemical reactor model validates satisfactory results.
A new adaptive neural control method, with the actuators multiple constraints of amplitude and rate into consideration, is proposed in this paper for the flexible air-breathing hypersonic vehicle (AHV). In order to better reflect the characteristics of the actual AHV model, we regard the AHV as a completely unknown non-affine system in the control law design process, which is different from the existing AHV control methods, thus ensuring the reliability of the designed control law. On the basis of the implicit function theorem, the radial basis function neural network (RBFNN) is introduced to approximate the model. Meanwhile, the minimum learning parameter algorithm is adopted to adaptively adjust the weight vector of RBFNN, then the design of the ideal control law is completed. When the amplitude and rate of the actuator are saturated, the designed novel auxiliary error compensation system is used to effectively compensate for the ideal control law, and the stability of the closed-loop control system is proved via the Lyapunov stability theory. In addition, to avoid the “explosion of terms” problem in the control law design process, the finite-time-convergence-differentiator is introduced to accurately estimate the differential signal. Finally, the effectiveness of the control method designed in this paper is verified by simulation.
In actuality, the dead zones and failures often occur in actuators, but the existing algorithms have difficulty simultaneously tolerating dead zones and actuator failures in multi-agent systems. In this paper, the directed topology, uncertain dynamics, unknown dead zones and actuator failures are simultaneously taken into account for the multi-agent systems. By introducing distributed backstepping technique, the radial basis function neural networks and a bound estimation approach, the distributed fault-tolerant tracking controllers and relative adaptive laws for each follower are proposed, which guarantee all followers reach the synchronization and obtain the ideal tracking performance. Comparing with the existing results, it is a new attempt for strict-feedback multi-agent system to take unknown dead zones and unknown actuator failures into consideration. Moreover, the basis function vectors in RBF NNs are no longer required for controllers to decrease computational burden significantly. In the end, the efficiency of our proposed algorithm is verified by comparison simulation results.
This paper proposes to use a recurrent neural network for black-box modelling of nonlinear audio systems, such as tube amplifiers and distortion pedals. As a recurrent unit structure, we test both Long Short-Term Memory and a Gated Recurrent Unit. We compare the proposed neural network with a WaveNet-style deep neural network, which has been suggested previously for tube amplifier modelling. The neural networks are trained with several minutes of guitar and bass recordings, which have been passed through the devices to be modelled. A real-time audio plugin implementing the proposed networks has been developed in the JUCE framework. It is shown that the recurrent neural networks achieve similar accuracy to the WaveNet model, while requiring significantly less processing power to run. The Long Short-Term Memory recurrent unit is also found to outperform the Gated Recurrent Unit overall. The proposed neural network is an important step forward in computationally efficient yet accurate emulation of tube amplifiers and distortion pedals.
This paper deals with a new fuzzy adapting rate for a neural emulator of nonlinear systems with unknown dynamics. This method is based on an online intelligent adaptation by using a fuzzy supervisor. The satisfactory obtained simulation results are compared with those registered in the case of the classical choice of adapting rate and show very good emulation performances. An experimental validation of the proposed fuzzy adapting rate on a chemical reactor is also proposed to confirm the good performances in terms of speed of convergence and precision of representation.
In this paper, a neural network (NN) based event trigger control problem of electromagnetic active suspension system is solved. Due to the limitation of vehicle communication resources, the control schemes utilizing fixed threshold and relative threshold are presented respectively to reduce the communication burden between actuator and controller. Firstly, the fixed threshold-based trigger mechanism is developed while the algebraic loop problem is addressed using the special characteristics of NN basis function. Second, to further avoid a large measurement error, the time-varying threshold-based event trigger approach is built. The designed event trigger controllers can make the vertical displacement and speed of the electromagnetic suspension system near zero. In the design process, the radial basis function neural networks (RBFNNs) are employed to approximate unknown terms. Then, all signals in the resulted system are proved to be bounded, and the Zeno behavior is avoided successfully. Finally, the feasibility and rationality of the two methods are proved by the simulation analysis base on the electromagnetic suspension system.
Filter design for nonlinear systems, especially time delayed nonlinear systems, has always been an important and challenging problem. This brief investigates the filter design problem of nonlinear systems with multiple constraints: time delay, actuator, and sensor faults, and a new adaptive neural network-based filter design method is proposed. Comparing with the existing works where there is a shortcoming that the designed filters contain unknown time delay(s), the design method proposed in this brief overcomes the shortcoming and only the estimation of the unknown time delay exists in the filter. Furthermore, not only the system states can be estimated, but also the unknown time delay with actuator and sensor faults can be estimated in this brief. Finally, simulation results are given to show the effectiveness of the proposed new design method.
The paper introduces a novel adaptive neural network fractional-order nonsingular terminal sliding mode controller using conformable fractional-order (CFO) derivative for a class of uncertain nonlinear systems. For this purpose, a new conformable fractional-order nonlinear sliding surface is proposed and the corresponding control law is designed using Lyapunov stability theorem in order to satisfy the sliding condition in finite time. To deal with uncertainties, the lumped uncertainty is approximated by neural networks and adaptation laws are designed using Lyapunov stability concept. As adaptive neural network uses small switching control gain in the presence of large time varying uncertainties the chattering phenomenon is omitted. The proposed adaptive neural network conformable fractional-order nonsingular terminal sliding mode controller (ANN-CFONTSMC) exhibits better control performance, guaranties finite-time convergence and robust stability of the closed-loop control system. Finally, the effectiveness of the proposed controller is illustrated through the numerical simulations.
This paper focuses on tuning parameters of fractional order PID controller (FOPID) by using neural networks (NNs). For tuning the coefficients of the controller and orders of fractional derivative and integrator, five exclusive NNs are employed. Moreover, an emulator is used to identify the plant’s behavior. Extended Kalman Filter (EKF) algorithm is used to update the weights of the controller’s NNs, and Back Propagation (BP) algorithm is used for the weight updating procedure of the emulator’s NNs. The proposed neural fractional order PID controller (NFOPID) is capable of being applied to various plants. Thus, two plants with different dynamics are examined. One is vibration damping of a Euler–Bernoulli beam, which has a fast dynamic, and the other is a time-delayed system like temperature control of a tempered glass furnace. The controller could deal appropriately with these tasks and is compared for accuracy and robustness with other controllers. The results were satisfactory for both systems.
In this article, observer‐based decentralized adaptive neural control is proposed for uncertain interconnected nonlinear systems with input quantization and time‐varying output restrictions. Decentralized hysteresis quantizer is employed to handle input signal. The unmeasured states are estimated by designing K‐filters. A Lyapunov description is used to dispose of state unmodeled dynamics. The constrained interconnected nonlinear systems are transformed into novel interconnected nonlinear systems without output constraints by constructing invertible nonlinear mappings. Dynamic surface control technique and a hyperbolic tangent function are adopted to design decentralized controller, which has a simpler structure. Stability analysis indicates that all the signals in the closed‐loop system are semiglobally uniformly ultimately bounded and system outputs satisfy the constraints. Two numerical examples are used to verify the effectiveness of the theoretical findings.
This work addresses one aspect of the overparameterization problem in using artificial/recurrent neural networks (ANN/RNN) based dynamic models for model predictive control (MPC) implementations. The manuscript presents an approach to handle situations where the training data may not be sufficiently rich, and in particular, for handling historical data with correlated inputs. Two approaches are proposed. The key idea in the first method is perform principal component analysis (PCA) on input space and then utilize the scores to build a PCA-RNN model. Next, a PCA-RNN-based MPC is designed to compute the optimized values of scores and subsequently determined the manipulated inputs. An alternative solution is proposed in the second approach by proposing a new constraint on squared prediction error (SPE) statistic in the RNN-based MPC to make prescribed inputs follow the PCA model constructed for training input data. Finally, an approach is presented that allows to break the correlation in the MPC implementation while maintaining model validity. This is done by first generating richer closed-loop data by implementing the SPE based MPC with slightly relaxed constraints (thus compromising only slightly on the closed loop performance). Then the new data is utilized to re-identify the model, and for use in the MPC. The efficacy of the proposed approaches to handle the problem of set-point tracking is evaluated using a chemical reactor example. The results are compared with a nominal MPC design, and the superior performance under the proposed formulations demonstrated.
In this work, physics-based recurrent neural network (RNN) modeling approaches are proposed for a general class of nonlinear dynamic process systems to improve prediction accuracy by incorporating a priori process knowledge. Specifically, a hybrid modeling method is first introduced to integrate first-principles models and RNN models. Subsequently, a partially-connected RNN modeling method that designs the RNN structure based on a priori structural process knowledge, and a weight-constrained RNN modeling method that employs weight constraints in the optimization problem of the RNN training process are developed. The proposed physics-based RNN models are utilized in model predictive controllers and applied to a chemical process network example to demonstrate their improved approximation performance compared to the fully-connected RNN model that is developed as a black box model.
Chemical looping is a novel and promising technology that converts fossil fuels to electricity and high value chemicals with in-situ carbon capture without significant cost penalties. Smooth and controlled solid circulation is the key to the successful operation of the chemical looping system. Bridging or arching, which may occur in the moving bed standpipe of the system, caused by a combination of fines accumulation and gas flows, is a major impediment to the smooth solid circulation and can lead to the failure of the entire system operation. Thus, early detection of the tendency of bridging or arching is important. This paper describes a model that applies the long short-term memory based recurrent neural network scheme to detect the tendency of arching in the standpipe of a chemical looping system. The arching tendency can be ascertained by early detection of the bubble formation in the standpipe. The bubble movement or local fluidization is recognized to precede the arching formation due to local accumulation of fine particles generated from coarse particle attrition. The early detection of the bubbles thus renders it possible to prevent arching through the prompt action of fines removal from the system. In this study, the recurrent neural network model which detects the fines induced fault manifested as bubbles in the standpipe is developed. It is over the data generated from an experimental sub-pilot scale, cold-flow chemical looping unit. To improve the robustness of the diagnosis, a number of networks with different structures are considered, and an ensemble decision strategy is used to conduct the diagnosis. The recall value obtained of the diagnosed result, which represents the extent of the fraction of real bubbles that are detected, can reach higher than 86.7%. This result reflects a good accuracy of the recurrent neural network model in the fault detection for the chemical looping system.
This work demonstrates an adaptive fuzzy backstepping control for a two cascaded continuous stirred tank reactors (CSTRs) system based on the dynamic surface control (DSC). The proposed controller is able to ensure the internal stabilization of the closed-loop system and render outputs track their reference signals asymptotically, although the CSTRs system is highly nonlinear and strong coupling. The effective and robust performance of the proposed controller in this research is certificated by the simulation analysis. Compared with previous researches, the on-line computation of controller is effectively reduced, which means that the proposed controller is easy to implement in engineering. The adaptive fuzzy dynamic surface control appears the potential for CSTRs process in mill operation.
In this study, a fractional-order sliding mode control (FSMC) scheme using a recurrent neural network (RNN) approximator is introduced to achieve better control performance for a class of dynamic systems. The proposed recurrent neural network fractional-order sliding mode control (RNNFSMC) scheme combines a fractional-order control method and a RNN structure. The primary objective of the proposed RNNFSMC scheme is to construct a fractional-order sliding mode controller. The RNN estimator is applied to approximate the unknown nonlinear part online. In the case study, the proposed RNNFSMC scheme is used for a dynamic model of an active power filter to realize the current harmonic compensation control. Simulation experiment proves that the proposed scheme is effective and robust and has a good tracking effect for dynamic system.
This paper presents an adaptive neural network output feedback control method for stochastic nonlinear systems with full state constraints. The barrier Lyapunov functions are used to conquer the effect of state constraints to system performance. The neural network state observer is established to estimate the unmeasured states. By using dynamic surface control technique, the "explosion of complexity" issue existing in the backstepping design is overcome. The proposed control scheme can guarantee that all signals of the system are bounded and the system output can follow the desired signal. Finally, two examples are given to verify the effectiveness of our control method.
In this research, the controller design problem is considered for non-strict-feedback systems with input delay. An appropriate auxiliary system is utilized to deal with the difficulties appeared in input delay. By the utilization of backstepping and adaptive neural control, a state-feedback stabilization controller is developed. The designed controller enables the variables in the closed-loop system to be semi-globally uniformly ultimately bounded in a small interval around the origin. The main significance of this research is that an intelligent control scheme is extended to a class of nonlinear systems with non-strict-feedback form and input delay, simultaneously. Finally, an example is given to show the effectiveness of the control method.
This paper investigates the finite-time adaptive neural control and almost disturbance decoupling problems for multi-input/multi-output (MIMO) nonlinear systems with disturbances and non-strict-feedback structure. In the design procedure of the adaptive controller, neural networks are employed to estimate the unknown nonlinearities and Young’s inequality is utilized to cope with the disturbance terms derived from all subsystems. In order to characterize the disturbance attenuation performance of finite-time adaptive control, a criterion named finite-time almost disturbance decoupling is first developed. Under this criterion, an adaptive neural controller is designed via the backstepping method and the appropriate selection of Lyapunov function. It is revealed that the proposed controller can guarantee all variables of the closed-loop system are bounded, and the performance of finite-time almost disturbance decoupling is realized. Finally, a practical example is employed to validate the effectiveness of the designed controller.
This work reports on a novel approach to effective design of iterative learning control of repetitive nonlinear processes based on artificial neural networks. The essential idea discussed here is to enhance the iterative learning scheme with neural networks applied for controller synthesis as well as for system output prediction. Consequently, an iterative control update rule is developed through efficient data-driven scheme of neural network training. The contribution of this work consists of proper characterization of the control design procedure and careful analysis of both convergence and zero error at convergence properties of the proposed nonlinear learning controller. Then, the resulting sufficient conditions can be incorporated into control update for the next process trial. The proposed approach is illustrated by two examples involving control design for pneumatic servomechanism and magnetic levitation system.
Despite ever wider use of neural computers (NC) and their simulators − neural emulators − in medicine, their further use comes up against the fundamental impossibility of using them to solve tasks of systemic synthesis (finding the most important diagnostic signs, , in medicine). This article presents two new principles (the chaotic organization of the initial state of weightings Wi0 of xi features and the principle of multiple reverberations), which can be solved using NC for systemic synthesis. Examples of the use of such special operating modes in cardiovascular physiology are presented. Uncertainties of types 1 and 2 in medicine are considered; these cannot be resolved within the framework of stochastics.
This paper addresses the problem of adaptive tracking control for a class of strict-feedback nonlinear state constrained systems with input delay. To alleviate the major challenges caused by the appearances of full state constraints and input delay, an appropriate barrier Lyapunov function and an opportune backstepping design are used to avoid the constraint violation, and the Pade approximation and an intermediate variable are employed to eliminate the effect of the input delay. Neural networks are employed to estimate unknown functions in the design procedure. It is proven that the closed-loop signals are semiglobal uniformly ultimately bounded, and the tracking error converges to a compact set of the origin, as well as the states remain within a bounded interval. The simulation studies are given to illustrate the effectiveness of the proposed control strategy in this paper.
Mine main fan switchover system (MMFSS) consists of two main fans, which are equipped with a horizontal air door and a vertical air door, respectively. The purpose of operating MMFSS is to ensure small fluctuation of the underground airflow quantity and to guarantee safe operations of both fans simultaneously by controlling the four air doors during switchover from working to standby fan. MMFSS has time-varying dynamics under different operating conditions, strong coupling, high nonlinearities and uncertainty in character, applying conventional control methods can not lead to satisfactory performances. In this study, an adaptive intelligent decoupling proportional-integral-derivative (PID) control method is proposed, where the unmodelled dynamics are estimated and compensated by neural networks, the coupling effect is eliminated by the designed decoupling compensator, and a switching mechanism among multiple models is employed to deal with the effect of time-varying dynamics. By inspiring from the generalised minimum variance control law concept, the parameters of the developed controller are determined. The stability of the close-loop system and the convergence of tracking error are examined. Finally, simulations of MMFSS show the feasibility and effectiveness of the obtained results.
This paper studies the tracking control problem for an uncertain n-link robot with full-state constraints. The rigid robotic manipulator is described as a multiinput and multioutput system. Adaptive neural network (NN) control for the robotic system with full-state constraints is designed. In the control design, the adaptive NNs are adopted to handle system uncertainties and disturbances. The Moore-Penrose inverse term is employed in order to prevent the violation of the full-state constraints. A barrier Lyapunov function is used to guarantee the uniform ultimate boundedness of the closed-loop system. The control performance of the closed-loop system is guaranteed by appropriately choosing the design parameters. Simulation studies are performed to illustrate the effectiveness of the proposed control.
This work investigates an uncoupled multimodel emulator for non-linear system control design. Efficiency of the proposed multimodel emulator is illustrated by comparison with the neural one by their application to SISO indirect adaptive neural control. Neither an initialisation parameter and nor online adaptation is required for multimodel emulator unlike the neural one. The effectiveness of the proposed multimodel emulator is shown through numerical simulations. The obtained results using multimodel emulator are far better than neural emulator.
This paper deals with a new indirect adaptive control scheme with decoupled adaptive rates, developed for complex square systems with unknown dynamics. This scheme, based on fully connected neural networks, is inspired from the real time recurrent learning (RTRL) algorithm. Both neural emulator and neural controller networks do not learn the plant dynamics but only adapt their parameters using an online adaptation algorithm in order to track the process variations. The contributions of this paper are to propose a new structure of neural control with a full structure of neural controller and to demonstrate the efficiency of the relaxation of networks parameters relative to the new proposed structure. Advantages of Neural controller with full structure and relaxation of its parameters from neural emulator ones are suggested according to simulation of nonlinear system. Effectiveness of the new proposed control structure is established by its application to the well-known Tennessee Eastman Challenge Process.
This paper adresses a Lyapunov stability analysis of nonlinear systems control. We consider an adaptive control scheme based on recurrent neural networks emulator and controller with decoupled adaptive rates. Lyapunov sufficient stability conditions for decoupled adaptive rates of the emulator and controller are proposed. In order to guarantee the fast convergence, the optimal adaptive rate of controller is derived in the sense of Lyapunov exponential stability taking into account the stability of the emulator. The good performances of the proposed stable control design are shown with numerical simulations results.
This paper investigates adaptive control design for nonlinear square MIMO systems. The control scheme is based on recurrent neural networks emulator and controller with decoupled adaptive rates. Networks' parameters are updated according to an autonomous algorithm inspired from the Real Time Recurrent Learning (RTRL). The contributions of this paper are the determination of Lyapunov sufficient stability conditions for decoupled adaptive rates of the emulator and controller and the development of new adaptation strategies based on the tracking error dynamics and Lyapunov stability analysis to improve the closed loop performances. Efficiency of the proposed controller is illustrated with nonlinear system simulations. An application of the developed approaches to a hot-air blower is presented in order to validate simulations results.
Biodiesel has become more attractive recently because of its environmental benefits and the fact that it is made from renewable resources. The cost of biodiesel, however, is the main hurdle to commercialization of the product. The used cooking oils are used as raw material, adaption of continuous transesterification process and recovery of high quality glycerol from biodiesel by-product (glycerol) are primary options to be considered to lower the cost of biodiesel. There are four primary ways to make biodiesel, direct use and blending, microemulsions, thermal cracking (pyrolysis) and transesterification. The most commonly used method is transesterification of vegetable oils and animal fats. The transesterification reaction is affected by molar ratio of glycerides to alcohol, catalysts, reaction temperature, reaction time and free fatty acids and water content of oils or fats. The mechanism and kinetics of the transesterification show how the reaction occurs and progresses. The processes of transesterification and its downstream operations are also addressed.
Control system education must include experimental exercises that complement the theory presented in lectures. These exercises include modelling, analysis and design of a control system. Key concepts and techniques in the area of intelligent systems and control have been discovered and developed over the past few decades. While some of these methods have significant benefits to offer, engineers are often reluctant to utilise new intelligent control techniques, for several reasons. In this paper fuzzy logic controllers have been developed using speed and mechanical power deviations, and a neural network has been designed to tune the gains of the fuzzy logic controllers. Student feedback indicates that theoretical developments in lectures on control systems were only appreciated after the laboratory exercises.
With the motivation of using more information to update the parameter estimates to achieve improved tracking performance, composite adaptation that uses both the system tracking errors and a prediction error containing parametric information to drive the update laws, has become widespread in adaptive control literature. However, despite its obvious benefits, composite adaptation has not been widely implemented in neural network-based control, primarily due to the neural network (NN) reconstruction error that destroys a typical prediction error formulation required for the composite adaptation. This technical note presents a novel approach to design a composite adaptation law for NNs by devising an innovative swapping procedure that uses the recently developed robust integral of the sign of the error (RISE) feedback method. Semi-global asymptotic tracking is proven for a Euler-Lagrange system. Experimental results are provided to illustrate the concept.
An adaptive control technique for nonlinear stable plants with unmeasurable state is presented. It is based on a recurrent neural network employed as a dynamical model of the plant. Using this dynamical model, a feedback linearizing control is computed and applied to the plant. Parameters of the model are updated on-line to allow for partially unknown and time-varying plant. The stability of the scheme is shown theoretically, and its performance and limitations of the assumptions are illustrated in simulations. It is argued that appropriately structured recurrent neural networks can provide conveniently parameterized dynamic models for many nonlinear systems for use in adaptive control.
Biodiesel has become more attractive recently because of its environmental benefits and the fact that it is made from renewable resources. The cost of biodiesel, however, is the main hurdle to commercialization of the product. The used cooking oils are used as raw material, adaption of continuous transesterification process and recovery of high quality glycerol from biodiesel by-product (glycerol) are primary options to be considered to lower the cost of biodiesel. There are four primary ways to make biodiesel, direct use and blending, microemulsions, thermal cracking (pyrolysis) and transesterification. The most commonly used method is transesterification of vegetable oils and animal fats. The transesterification reaction is affected by molar ratio of glycerides to alcohol, catalysts, reaction temperature, reaction time and free fatty acids and water content of oils or fats. The mechanism and kinetics of the transesterification show how the reaction occurs and progresses. The processes of transesterification and its downstream operations are also addressed.
In this paper, we consider the problem of adaptive stabilizing
unknown nonlinear systems whose state is contaminated with external
disturbances that act additively. A uniform ultimate boundedness
property for the actual system state is guaranteed, as well as
boundedness of all other signals in the closed loop. It is worth
mentioning that the above properties are satisfied without the need of
knowing a bound on the “optimal” weights, providing in this
way higher degrees of autonomy to the control system. Thus, the present
work can be seen as a first approach toward the development of
practically autonomous systems
Introduction The purpose of this chapter is to provide an introductory overview of some of the current research efforts directed toward adapting the weights in connectionist networks having feedback connections. While much of the recent emphasis in the field has been on multilayer networks having no such feedback connections, it is likely that the use of recurrently connected networks will be of particular importance for applications to the control of dynamical systems. Following the approach taken in the previous chapter by Andy Barto, this chapter will emphasize the relationship of connectionist research in this area to strategies used in more conventional engineering circles for modelling and controlling dynamical systems, while at the same time noting what there is in the connectionist approach that is novel. In particular, I will argue that while much of the connectionist approach to adapting the weights in recurrent networks having interesting dynamics rests on the same s
Commande neuronale adaptative des systemes non linéaires
- S Zerkaoui