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Abstract

A new online identification method is presented. The identified nonlinear systems have partial-state measurement. Their inner states, parameters and structures are unknown. The design is based on the combination of a model-free state observer and a neuro identifier. First, a sliding mode observer, which does not need any information about the nonlinear system, is applied to obtain the full states. A dynamic multilayer neural network is then used to identify the whole nonlinear system. The main contributions of the paper are: a new observer-based identification algorithm is proposed; and a stable learning algorithm for the neuro identifier is given

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... Remark 6: Assumption 4 is weaker than that in [11] where |h j (t, x)| required to have a constant bound. BecauseĀ,P and h j (t, x) are selected by the user, Eq.(41) is not hard to be satisfied if ...
... Remark 7: Some standard techniques can be used to eliminate the chattering [11] (e.g., a boundary layer compensator can offer a continuous approximation of the discontinuous sliding mode inside the boundary layer and guarantees the observer error within any neighborhood of the origin ). ♦ In order to identify the current mode, a series of observers are designed as ...
... Remark 8 : Note that if we choose K k and Q k in (11), L in (40), andQ in (43) such that λ max (P k ) = λ min (P k ), λ max (P ) = λ min (P ), and |ē x | converges faster than any |e xk | for mode j without inputs, then |x −x j | is always minimal at t k + ∆t k , for any ∆t k > 0. ♦ ...
Article
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An observer-based fault tolerant control (FTC) framework is proposed for a class of periodic switched nonlinear systems (PSNS) without full state measurements. Two kinds of faults are considered for PSNS: Continuous faults that affect each mode during its dwell time period; Discrete faults that affect the switching sequence. Under the average dwell time scheme, the proposed FTC framework can maintain the stability of overall PSNS in spite of these two kinds of faults. An illustrative example is taken to show the efficiency of the proposed method.
... Remark 6 : Assumption 4 is weaker than that in [33] where |h k (x, t)| required to have a constant bound. BecauseĀ,P and h k (x, t) are selected by the user, Eq.(43) is not hard to be satisfied if ...
... Sincex i ,x k andx are all continuous and measurable, in the real implementation of the identifier, high order time derivatives of the signals can help to find the similarity (as using 1-order time derivative of signals in the simulation). Optimal selection method ofL,Q and ρ j to improve the transient performance of the model free observer can be seen in [11], [33] and references therein, which is not addressed in this paper. ...
... To avoid an unexpected oscillation of rotor, we select ξ = 2. From (44) and (47), we can also choose ρ 1 = 5. A boundary layer compensator technique [33] is used with a bound number 0.02 to eliminate the chattering. Fig. 4 shows the performance of the identifier. ...
Article
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An observer-based fault tolerant control (FTC) framework is proposed for a class of periodic switched non-linear systems (PSNS) without full state measurements. Two kinds of faults are considered: continuous faults that affect each mode during its dwell period; and discrete faults that affect the switching sequence. Under the average dwell time scheme, the proposed FTC framework can maintain the stability of overall PSNS in spite of these two kinds of fault. A switched reluctance motor example is taken to illustrate the efficiency of the proposed method.
... In fact, only one paper can be found [30], where two NNs are used to design the observer and critic function, respectively. Neural network (NN) based observer design [31], [32]− [35] has been proved to be an effective way to solve the state estimation problem for the unknown systems, which is different from the commonly used model-based observer designs such as extended Luenberger observers [36], extended Kalman filter [37], sliding mode observer [38], and the robust observer [39]. In NN based observer design, the NN weights should be updated online. ...
... Once the structure of the neural network is determined, a proper updating law should be designed to train the NN to obtainŴ 1 andŴ 2 . This can be achieved by defining a Lyapunov function candidate based on the quadratic functions of the weights and the observer errors, which can be used to guarantee the stability of the system [31], [34], [35], [43], [44]. Thus, we choose the following Lyapunov function ...
... By using the inequality ab ≤ a 2 δ/2 + b 2 /2δ with δ > 0, we can rewrite (35) aṡ ...
Article
This paper introduces an observer-based adaptive optimal control method for unknown singularly perturbed nonlinear systems with input constraints. First, a multi-time scales dynamic neural network U+0028 MTSDNN U+0029 observer with a novel updating law derived from a properly designed Lyapunov function is proposed to estimate the system states. Then, an adaptive learning rule driven by the critic NN weight error is presented for the critic NN, which is used to approximate the optimal cost function. Finally, the optimal control action is calculated by online solving the Hamilton-Jacobi-Bellman U+0028 HJB U+0029 equation associated with the MTSDNN observer and critic NN. The stability of the overall closed-loop system consisting of the MTSDNN observer, the critic NN and the optimal control action is proved. The proposed observer-based optimal control approach has an essential advantage that the system dynamics are not needed for implementation, and only the measured input U+002F output data is needed. Moreover, the proposed optimal control design takes the input constraints into consideration and thus can overcome the restriction of actuator saturation. Simulation results are presented to confirm the validity of the investigated approach.
... However, most of this work relies on exact a priori knowledge of the system nonlinearities. The adaptive learning ability neural networks (NN) makes them powerful tools for identification [15,17,54], observation [9-20,31,37– 39,42], monitoring [53] and control [47][48][49]of nonlinear system without any a priori knowledge about the system dynamics. Recent research [50,51] also shows that reinforcement learning may overcome the need for an exact model and achieve the optimality at the same time. ...
... In [52], new delay-dependent stability criteria for DNN with time-varying delay are derived by dividing the delay interval into some variable subintervals employing weighting delays. In [17], a new learning procedure with a relay term to accelerate and improve the corresponding learning process. However, off-line training based on mean least square (MLS) method was required to select the nominal parameters in [16,17]. ...
... In [17], a new learning procedure with a relay term to accelerate and improve the corresponding learning process. However, off-line training based on mean least square (MLS) method was required to select the nominal parameters in [16,17]. In [19], passivity theory is used to design the DNN observer and controller of partially known SISO nonlinear systems. ...
... Neural networks can be considered as an alternative model-free observer because they offer potential benefit for nonlinear modeling [9]. For example, dynamic neural networks have been applied to design a Luenberger-like observer [10]. Due to neural modeling error, neural observers are not asymptotically stable. ...
... Normal combinations of neural networks and sliding mode methods are to apply them at same time, where the sliding mode observer is used to compensate modeling error of the neural observer [4]. This type of neural observers cannot assure finite time convergence [10]. In this paper, neural observer and sliding mode compensator are connected serially, it is called two-stage neural observer. ...
... where is a known matrix which will be specified later, is known upper bound of the neural modeling error, which will be defined in (19). The second-order sliding mode observer is (10) where and are the sliding mode gains, they will be determined by the theorem in the next section. The learning algorithm (6) is dead-zone one (11) If ...
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This paper proposes a novel velocity observer which uses neural network and sliding mode for unknown mechanical systems. The neural observer in this paper has two stages: 1) a dead-zone neural observer assures that the observer error is bounded and 2) a super-twisting second-order sliding-mode is used to guarantee finite time convergence of the observer. With sliding mode compensation, the two-stage neural observer ensures finite time convergence, and reduces the chattering during its discrete realization.
... The optimal structure then, is the one having the fewest units (neurons) for which the criterion is met. Neuro-Identifiers (NIDs) are basically Multi-Layer Feed-Forward artificial neural networks (MLFF) with an input layer (buffer layer), a single or multiple nonlinear hidden layer with biases and a linear/or nonlinear output layer (Yu et al., 2000;Saggar et al., 2007). The results of research have shown that linear identifiers are not capable of identifying nonlinear systems. ...
... The results of research have shown that linear identifiers are not capable of identifying nonlinear systems. Hybrid identifiers can identify simple nonlinear systems but not complex ones (Bin and Babri, 1998;Yu et al., 2000;Tanomaru, 1994). Figure 2 shows the structure of the multi-layer feed-forward neural network identifier NID, with two nonlinear hidden layers, which is used in this research. ...
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Problem statement: The problem in cryptanalysis can be described as an unknown and the neural networks are ideal tools for black-box system identification. In this study, a mathematical black-box model is developed and system identification techniques are combined with adaptive system techniques, to construct the Neuro-Identifier. Approach: The Neuro-Identifier was discussed as a black-box model to attack the target cipher systems. Results: In this study this model is a new addition in cryptography that presented the methods of block (SDES) crypto systems discussed. The constructing of Neuro-Identifier mode achieved two objectives: The first one was to construct emulator of Neuro-model for the target cipher system, while the second was to (cryptanalysis) determine the key from given plaintext-ciphertext pair. Conclusion: Present the idea of the equivalent cipher system, which is identical 100% to the unknown system and that means that an unknown hardware, or software cipher system could be reconstructed without known the internal circuitry or algorithm of it.
... The optimal structure then, is the one having the fewest units (neurons) for which the criterion is met. Neuro-Identifiers (NIDs) are basically Multi-Layer Feed-Forward artificial neural networks (MLFF) with an input layer (buffer layer), a single or multiple nonlinear hidden layer with biases and a linear/or nonlinear output layer (Yu et al., 2000;Saggar et al., 2007). The results of research have shown that linear identifiers are not capable of identifying nonlinear systems. ...
... The results of research have shown that linear identifiers are not capable of identifying nonlinear systems. Hybrid identifiers can identify simple nonlinear systems but not complex ones (Bin and Babri, 1998;Yu et al., 2000;Tanomaru, 1994). Figure 2 shows the structure of the multi-layer feed-forward neural network identifier NID, with two nonlinear hidden layers, which is used in this research. ...
Article
Problem statement: The problem in cryptanalysis can be described as an unknown and the neural networks are ideal tools for black-box syste m identification. In this study, a mathematical bla ck- box model is developed and system identification te chniques are combined with adaptive system techniques, to construct the Neuro-Identifier. Approach: The Neuro-Identifier was discussed as a black-box model to attack the target cipher systems . Results: In this study this model is a new addition in cryptography that presented the methods of block (SDES) crypto systems discussed. The constructing of Neuro-Identifier mode achieved two objectives: The first one was to construct emulator of Neuro-model for the target cipher system, while the second was to (cryptanalysis) determine the key from given plaintext-ciphertext pair. Conclusion: Present the idea of the equivalent cipher system, which is identical 100% to the unknown system and that means that an unknown hardware, or software cipher system could be reconstructed without known the internal circuitry or algorithm of it.
... (II) in Appendix A) and d m is the upper limit of uncertainty which is predicted by designer. It is necessary to be noted that ðe T PÞ is not a square matrix and therefore pseudo inverse matrix is used to calculate u s vector [21]. Stability proof of designed controller is presented in Appendix A. The block diagram of the overall UPFC control system is depicted inFig. ...
... However, in a practical system, it is considered that the system parameters are corrupted by some uncertainties. It should be mentioned that such uncertainties are usually present in any physical system and will be often limited to achieve the desired performance [21] . In this paper, the proposed controller is designed so as the uncertainty in the system is reduced. ...
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... But, it turns out that the corresponding stability analysis cannot be directly applied in the situations with the output noise (or, mixed uncertainty) presence. So, it is still a challenge to suggest a workable technique to analyze the stability of identification error generated by sliding-mode (discontinuous nonlinearity) type observers [Martinez-Guerra et al., 2004;Yu et al., 2000]. ...
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... Normal combinations of neural networks and sliding mode methods are to apply them at same time, where sliding mode is used to compensate neural modeling error [6]. This type of neural observers with sliding mode compensation cannot assure finite time convergence [21]. In this paper, neural observer and sliding mode compen­ sator are connected serially, it is called two­stage neural observer. ...
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... In NN theory, learning represents the path in the phase space of control parameters driving the system trajectories towards phase transition and bifurcations [14]. In other words, it promotes the capability of NN to approximate almost any non-linear continuous function [15]. Statistical learning theory could be used to develop efficient learning algorithms for a wide variety of problems in robust control systems analysis and synthesis [16]. ...
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... Owing to these unrealistic assumptions, it follows that these observational techniques are not being properly executed. In this situation, the use of neural networks (NNs) avoids the modelling difficulties thanks to its tangible approximation ability for a wide class of nonlinear functions, without any previous knowledge of the dynamics of the system because it sees the process of the system as a black box (Chairez et al., 2009;Yu et al., 2000). Over the last few years, there have also been studies on adaptive neural observer design. ...
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... The cancellation can assure the uncertainty errors converge to zero in finite time [30]. This technique has been implemented in nonlinear observer design [32]. ...
... In [18] a high-gain observer based identification method is proposed for parameter identification of robots with elastic joints. In [19] a sliding-mode observer-based neural network identification algorithm is proposed with application to parameter identification of a 2-DOF robot manipulator. ...
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It is demonstrated that neural networks can be used effectively for the identification and control of nonlinear dynamical systems. The emphasis is on models for both identification and control. Static and dynamic backpropagation methods for the adjustment of parameters are discussed. In the models that are introduced, multilayer and recurrent networks are interconnected in novel configurations, and hence there is a real need to study them in a unified fashion. Simulation results reveal that the identification and adaptive control schemes suggested are practically feasible. Basic concepts and definitions are introduced throughout, and theoretical questions that have to be addressed are also described
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Multilayer neural networks are used in a nonlinear adaptive control problem. The plant is an unknown feedback-linearizable continuous-time system. The control law is defined in terms of the neural network models of system nonlinearities to control the plant to track a reference command. The network parameters are updated online according to a gradient learning rule with dead zone. A local convergence result is provided, which says that if the initial parameter errors are small enough, then the tracking error will converge to a bounded area. Simulations are designed to demonstrate various aspects of theoretical results
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The input-output maps G of causal time-invariant systems are considered, and a complete characterization of those maps that can be uniformly approximated by the maps of certain simple structures is given. The criterion is that G must satisfy certain continuity and approximately-finite-memory conditions. It is proved that the conditions are satisfied by the input-output maps of control systems of a familiar type containing a sector nonlinearity for which the circle condition for stability is met. In particular, this shows that such feedback systems, with inputs drawn from a certain large set of bounded functions, possess arbitrarily good finite Volterra-series (or radial-basis-function) approximations
Neural networks for control systems-a surveyIdentification and control of dynamical systems using neural networks', IEEE TransIdentification of nonlinear dynamical systems using multilayered neural networks
  • References
  • K J Hunt
  • D Sbarbaro
  • R Zbikowski
  • P J Gawthrop
  • K S Narendra
  • K Karthasarathy
  • S Jagannathan
7 References 1 HUNT, K.J., SBARBARO, D., ZBIKOWSKI, R., and GAWTHROP, P.J.: 'Neural networks for control systems-a survey', Automatica, 1992, 28, pp. 1083-1 112 NARENDRA, K.S., and KARTHASARATHY, K.: 'Identification and control of dynamical systems using neural networks', IEEE Trans., JAGANNATHAN, S., and LEWIS, EL.: 'Identification of nonlinear dynamical systems using multilayered neural networks', Automatica,