Asymmetric Nonlinearity Research Articles

On a semilinear fourth order elliptic problem with asymmetric nonlinearity

In this work, we address the existence of solutions for a biharmonic elliptic equation with homogeneous Navier boundary condition. The problem is asymmetric and has linear behavior on $-\infty$ and superlinear on $+\infty$. To obtain the results we apply topological methods.

Neural Network-Based Adaptive Boundary Control of a Flexible Riser With Input Deadzone and Output Constraint.

In this article, vibration abatement problems of a riser system with system uncertainty, input deadzone, and output constraint are considered. For obtaining better control precision, a boundary control law is constructed by employing the backstepping method and Lyapunov's theory. The output constraint is guaranteed by utilizing a barrier Lyapunov function. Adaptive neural networks are designed to cope with the uncertainty of the riser and compensate for the effect caused by the asymmetric deadzone nonlinearity. With the designed controller, the output constraint is satisfied, and the system stability is guaranteed through Lyapunov synthesis. In the end, numerical simulation results are provided to display the performance of the developed adaptive neural network boundary control law.

Adaptive Finite-Time Command Filtered Controller Design for Nonlinear Systems With Output Constraints and Input Nonlinearities.

This work addresses a finite-time tracking control issue for a class of nonlinear systems with asymmetric time-varying output constraints and input nonlinearities. To guarantee the finite-time convergence of tracking errors, a novel finite-time command filtered backstepping approach is presented by using the command filtered backstepping technique, finite-time theory, and barrier Lyapunov functions. The newly proposed method can not only reduce the complexity of computation of the conventional backstepping control and compensate filtered errors caused by dynamic surface control but also can ensure that the output variables are restricted in compact bounding sets. Moreover, the proposed controller is applied to robot manipulator systems, which guarantees the practical boundedness of all the signals in the closed-loop system. Finally, the effectiveness and practicability of the developed control strategy are validated by a simulation example.

Asymmetric Bouc-Wen hysteresis modeling for MFC actuator via hybrid APSO-TRR identification algorithm

Macro fiber composite (MFC) is widely used in active vibration and deformation control. The intrinsic asymmetric hysteresis nonlinearity of MFC affects the control accuracy. In this paper, a modified Bouc-Wen (MBW) model based on the sigmoid function is proposed to describe the asymmetric hysteresis characteristics of MFC, and its parameters are identified by a hybrid algorithm composed of the trust-region reflection method and asynchronous particle swarm optimization. The accuracy of the proposed MBW model is verified though hysteresis tests of MFC under different drive frequencies. The results show that the MBW model can accurately model the asymmetrical hysteresis of the MFC actuator, the modeling error is reduced by 72% compared with the classic Bouc-Wen model. The proposed hybrid parameter identification method saves 95% of the time compared with the particle swarm optimization and asynchronous particle swarm optimization algorithms. • A modified Bouc-Wen (MBW) model is proposed to describe the asymmetric hysteresis characteristics of MFC actuators. • A hybrid algorithm (APSO - TRR) with global and local search ability is proposed for parameter identification. • Performance of proposed APSO - TRR is compared with classical PSO、APSO and TRR algorithms. • Accuracy of proposed asymmetric Bou–Wen model is compared with classical Bou–Wen model.

An efficient and flexible window function for a memristor model and its analog circuit application

The memristor is a novel nanostructured resistive tuning two-terminal electronic device that has been widely explored in the areas of neuromorphic computing systems, memory, digital circuits, analog circuits, and many more new applications. In this article, an efficient and flexible window function is presented for a linear drift memristor model. The proposed parametric cubic parabolic window function provides a unique feature (controllable window function discontinuity at the boundaries) to a linear drift memristor model by which the distorted pinched hysteresis loop problem is resolved and the number of programming resistance states of the memristor is improved. Five control parameters are introduced in the proposed window function in order to correct the existing problems (such as boundary effect, boundary lock and inflexibility) and are able to provide asymmetric nonlinearity at the boundaries of the device, making it feasible for tracking the resistive switching dynamic of a futuristic oxide-based memristive device with different inert electrodes. The proposed model is validated with a solution-processed ZnO-based fabricated memristive device. A programmable analog gain amplifier circuit is ultimately executed to simulate the utilization of the evolved memristor model, and the effect of memristance resolution is investigated.

Periodic solutions of indefinite planar systems with asymmetric nonlinearities via rotation numbers

We consider an indefinite planar system under asymmetric non‐resonance conditions and obtain the existence of ‐periodic solutions by combining a rotation number approach together with the Poincaré‐Bohl theorem. We allow that the angular velocity of solutions of is controlled by the angular velocity of solutions of two positively homogeneous systems and then characterize the rotation behavior of solutions of the planar system by the rotation numbers of the positively homogeneous systems. Because the system under consideration is strongly asymmetric and controlled by two positively homogeneous systems on the left half‐plane, the time that solutions stay in the left half‐plane in ‐period is intermittent; therefore, we estimate the angle difference of the dwell time of solution orbits in the half phase plane and develop a system method of “tracking” the angle difference of solutions of system on each small interval on the given side under the sign‐varying conditions.

Adaptive Estimation of Asymmetric Dead-Zone Parameters for Sandwich Systems

This brief presents a novel one-step adaptive parameter estimation framework for identification of unknown asymmetric dead-zone characteristic parameters (e.g., width and slopes) in the sandwich systems, which avoids using the intermediate variables or carrying out a two-step recursive identification procedure. By applying a continuous piecewise linear neural network (CPLNN), the asymmetric dead-zone nonlinearities can be represented into a parameterized form, where the dead-zone characteristic parameters can be derived based on the online updated CPLNN weights. Moreover, after representing the sandwich system into an augmented system, an adaptive observer is designed to reconstruct the immeasurable internal variables, and an adaptive law with guaranteed convergence is used to online update the CPLNN weights so as to estimate the dead-zone parameters. In this adaptive law, the parameter estimation error information is extracted using simple filters and introducing several auxiliary variables. It is proven that the observation error and estimation error both converge to a small set around zero. The efficiency of the estimation method is exemplified via practical experiments on an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Y$ </tex-math></inline-formula> positioning platform.

Demonstration of synaptic characteristics of polycrystalline-silicon ferroelectric thin-film transistor for application of neuromorphic computing

In this work, the synaptic characteristics together with 5 bits (32 states) operation based on polycrystalline-silicon (poly-Si) ferroelectric thin-film transistor (FeTFT) with HfZrO x gate dielectric are demonstrated for the first time. A 1.2 V threshold voltage shift of memory window is obtained. The impacts of pulse time on the potentiation and depression states are studied by a modulation scheme with incremental pulse voltages. The potentiation and depression rates of the conductance (G d) states of FeTFTs are found to be asymmetric and become more severe when increasing the pulse time. In order to realize high recognition rate and accuracy of neuromorphic computing, low asymmetric nonlinearity of potentiation () and depression () of poly-Si FeTFTs can be achieved with the reduction of operation voltage. Low asymmetry = 0.71 and high G d ratio ∼40 of FeTFTs are obtained based on the small pulse time of 50 ns and low average potentiation/depression voltages of 2.63/–2.69 V. When the pulse time is increased from 50 to 150 ns, the average potentiation/depression voltages can be further reduced to ∼1.59/–1.69 V for low asymmetry = 0.25 due to the enhanced G d potentiation and depression rates, and the G d ratio is also reduced to 9.96 with the reduction of potentiation/depression voltages. The small pulse time and potentiation/depression voltages of FeTFTs are responsible for the polarization switching of the ferroelectric layer following the minor operation-loop. Compared to the depression state, it leads to more stable retention and endurance behavior of the potentiation state due to the different depolarization electric fields.

A Fractional-Order Normalized Bouc–Wen Model for Piezoelectric Hysteresis Nonlinearity

This article presents a new fractional-order normalized Bouc–Wen (BW) (FONBW) model to describe the asymmetric and rate-dependent hysteresis nonlinearity of piezoelectric actuators (PEAs). In view of the fact that the classical BW (CBW) model is only efficient for the symmetric and rate-independent hysteresis description, the FONBW model is devoted to characterizing the asymmetric and rate-dependent behaviors of the hysteresis in PEAs by adopting an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> th-order polynomial input function and two fractional operators, respectively. Different from the traditional modified BW models, the proposed FONBW model also eliminates the redundancy of parameters in the CBW model via the normalization processing. By this way, the developed FONBW model has a relatively simple mathematic expression with fewer parameters to simultaneously characterize the asymmetric and rate-dependent hysteresis behaviors of PEAs. Model parameters are identified by the self-adaptive differential evolution algorithm. To validate the effectiveness of the proposed model, a series of model verification and inverse-multiplicative-structure-based feedforward control experiments are carried out on a PEA system. Results show that the proposed model is superior to the CBW model and traditional modified BW model in modeling accuracy and hysteresis compensation.

Controlled Bistable Transmission Non-Reciprocity in a Four-Mode Optomechanical System

We examine the bistable transmission non-reciprocity in a four-mode optomechanical system, where a mechanical oscillator interacts with one of three coupled optical cavities so as to generate an asymmetric optomechanical non-linearity. Two transmission coefficients in opposite directions are found to exhibit non-reciprocal bistable behaviors due to this asymmetric optomechanical non-linearity as the impedance-matching condition is broken for a not too weak input field. Such a bistable transmission non-reciprocity can be well manipulated to exhibit reversible higher isolation ratios in tunable wider ranges of the input field power or one cavity mode detuning by modulating relevant parameters like optical coupling strengths, optomechanical coupling strengths, and mechanical frequencies. This optomechanical system provides a flexible platform for realizing transmission non-reciprocity of weal light signals and may be extended to optical networks with more coupled cavities.

Stability Analysis of Periodic Solutions of Van Der Pol-Duffing Forced Oscillator with Asymmetric Nonlinearities

Stability Analysis of Periodic Solutions of Van Der Pol-Duffing Forced Oscillator with Asymmetric Nonlinearities

Three solutions for a fractional elliptic problem with asymmetric critical Choquard nonlinearity

In this paper, we study the existence and multiplicity of weak solutions for the following asymmetric nonlinear Choquard problem on fractional Laplacian: \begin{align*} (-\Delta)^s u & = -\lambda|u|^{q-2}u + au + b \Big ( \int_{\Omega} \frac{(u^{+}(y))^{2^{*}_{\mu ,s}}} {|x-y|^ \mu}\, dy \Big ) (u^{+})^{2^{*}_{\mu ,s}-2}u \quad\text{in} \; \Omega,\\ u & = 0\quad \text{in} \; \mathbb{R}^{N}\backslash\Omega, \end{align*} where $\Omega$ is open bounded domain of $\mathbb{R}^{N}$ with $C^2$ boundary, $N > 2s$ and $s \in (0,1)$. Here, $(-\Delta)^s$ is the fractional Laplace operator, $\lambda > 0$ is a real parameter, $q \in (1, 2)$, $a > 0$ and $b > 0$ are given constants, $0 < \mu < \min\{N,4s\}$ and $2^{*}_{\mu ,s} = \frac{2N-\mu}{N-2s}$ is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality and the notation $u^{+} = \max \{u, 0\}$. We prove that the above problem has at least three nontrivial solutions using the Mountain pass Lemma and Linking theorem.

Neumann problems of superlinear elliptic systems at resonance

We prove existence of weak solutions of Neumann problem of nonhomogeneous elliptic system with asymmetric nonlinearities that may resonant at − ∞ and superlinear at + ∞ . The proof is based on Mawhin's coincidence theory and the product formula of Brouwer degree.

All state constrained decentralized adaptive implicit inversion control for a class of large scale nonlinear hysteretic systems with time-delays

This paper proposes an all state constrained decentralized adaptive implicit inversion control scheme for a class of large scale nonlinear systems with unknown time delays and asymmetric saturated hysteresis. First, to address the states constrained problem, the asymmetric barrier Lyapunov function is introduced to keep the error surface within an appropriate range from the view of engineering practice to ensure the performance and safety, such as for attitude tracking of rigid spacecraft, for spacecraft approach and intersection. Second, the transmission delays between different subsystems are considered and approximated through the incorporation of the neural-network approximators and the finite coverage lemma. Third, a new hysteresis implicit inverse algorithm is designed to effectively mitigate asymmetric and saturated hysteresis nonlinearities. It should be noted that the implicit inverse implies that the analytical inverse of the asymmetric and saturated hysteresis is not required. Instead, the decoupling algorithms are designed to extract the actual control signal from the temporarily hysteretic control signal , which reduces the preliminary work of the control algorithm. Finally, all of the signals in the closed-loop system are proved to be semi-globally ultimately uniformly bounded and the tracking errors converge to an arbitrarily small residual set. The experimental results on two-machine excitation power systems in the hardware-in-loop system are presented to illustrate the effectiveness of the proposed scheme.

Uncertainty quantification of nonlinear system stochastic response estimates based on the Wiener path integral technique: A Bayesian compressive sampling treatment

The Wiener path integral (WPI) technique for determining the stochastic response of diverse nonlinear systems is enhanced herein based on a Bayesian compressive sampling (CS) treatment. Specifically, first, sparse expansions for the system response joint probability density function (PDF) are employed. Next, exploiting the localization capabilities of the WPI technique for direct evaluation of specific PDF points leads to an underdetermined linear system of equations for the expansion coefficients. Further, relying on a Bayesian CS solution formulation yields a posterior distribution for the expansion coefficient vector. In this regard, a significant advantage of the herein developed methodology relates to the fact that the uncertainty of the response PDF estimates obtained by the WPI technique is quantified. Furthermore, an adaptive scheme is proposed based on the quantified uncertainty of the estimates for optimal selection of PDF sample points. This yields considerably fewer boundary value problems to be solved as part of the WPI technique, and thus, the associated computational cost is significantly reduced. Two indicative numerical examples pertaining to a Duffing nonlinear oscillator and to an oscillator with asymmetric nonlinearities are considered for demonstrating the capabilities of the developed technique. Comparisons with pertinent Monte Carlo simulation data are included as well.

Modeling and parametric identification of Hammerstein systems with time delay and asymmetric dead-zones using fractional differential equations

The parametric identification of Hammerstein structured nonlinear systems with discontinuous asymmetric (two segment piecewise-linear with a dead-zone) nonlinearity and input time delay is presented using a fractional-order modeling technique. The effect of the unknown dead-zone nonlinearity is separated from the linear dynamics using special excitation signals to simplify the identification process. The use of fractional calculus permits reduced order modeling of the linear dynamics. An interactive block-based strategy is then introduced to simultaneously estimate the separated nonlinear and linear parameters, including the fractional differentiation order(s) and input time delay, which usually require separate algorithms in such cases. The proposed method utilizes block pulse functions to mitigate the computational complexity of fractional differential operations. Numerical examples are provided to validate the efficacy in comparison to existing methods. A DC servo motor application is used to demonstrate the proposed nonlinear modeling approach.

Data filtering-based multi-innovation forgetting gradient algorithms for input nonlinear FIR-MA systems with piecewise-linear characteristics

The piecewise-linear characteristics often appear in the nonlinear systems that operate in different ways in different input regions. This paper studies the identification issue of a class of block-oriented systems with piecewise-linear characteristics. The asymmetric piecewise-linear nonlinearity is expressed as a linear parametric representation through introducing an appropriate switching function, then the identification model of the system is derived by using the key term separation technique. On this model basis, a multi-innovation forgetting gradient algorithm is presented to estimate the unknown parameters. To further enhance the identification accuracy, the filtering identification model of the system is derived by changing the structure of the system without changing the relationship between the input and output. Further, a data filtering-based multi-innovation forgetting gradient algorithm is proposed through the use of the data filtering technique. A simulation example is employed to illustrate that the proposed approaches are effective for parameter estimation and the data filtering-based multi-innovation forgetting gradient algorithm has better estimation performance.

Adaptive prescribed performance control of nonlinear asymmetric input saturated systems with application to AUVs

In this paper, the adaptive prescribed performance tracking control of nonlinear asymmetric input saturated systems in strict-feedback form is addressed under the consideration of model uncertainties and external disturbances. A radial basis function neural network (RBF-NN) is utilized to handle the model uncertainties. By prescribed performance functions, the transient performance of the system can be guaranteed. The continuous Gaussian error function is represented as an approximation of asymmetric saturation nonlinearity such that the backstepping technique can be leveraged in the control design. Based on the Lyapunov synthesis, residual function approximation inaccuracies and external disturbances are compensated by constructed adaptive control laws. As a consequence, all the signals in the closed-loop system are uniformly ultimately bounded and the tracking errors bounded by prescribed functions converge to a small neighbourhood of zero. The proposed method is applied to the autonomous underwater vehicles (AUVs) with extensive simulation results demonstrating the effectiveness of the proposed method.

Design and dynamic modeling of a continuum and compliant manipulator with large workspace

This paper focuses on the design and dynamic modeling of a novel multi-section continuum and compliant robotic manipulator with large workspace. In large scales, many of the design techniques and actuator types which have proved advantageous in creating continuum robots at smaller scales are not applicable. Fluidic muscles, a class of pneumatic muscle actuators (PMAs) with large scale movements, high actuation forces and compliant nature, are utilized in the design of the continuum manipulator. However, these actuators are capable of applying axial contracting forces and cannot produce bending movements. Moreover, their asymmetric hysteresis nonlinearity causes difficulties in the accurate control procedure. These drawbacks are addressed in the design and presented model of the manipulator. The presented model is based on constant curvature method and concentrated masses. The Bouc–Wen hysteretic function is modified to describe the asymmetric force/length hysteresis of the utilized PMAs in this model. Experimental results show that the proposed model has a proper performance to characterize the asymmetric hysteresis loop of the actuators. Finally, the design and dynamic model of the robot are validated experimentally on the implemented manipulator.

Asymmetric Determinants of Oil Price Movements in Pakistan

In this research we are interested to investigate the presence of asymmetries in the long run and short run relationship between Pakistan oil prices and a set of major determinants of oil prices namely, Saudi oil production, world oil production, exchange rate and spread.We use nonlinear autoregressive distributed lag (NARDL) bounds testing approach that allows possible asymmetric effect in both short and long run. Results provide the evidence of asymmetries in both short and long run relationship among Pakistan oil prices and determinants under consideration. Considering the importance of asymmetric non-linearity in this context, it is shown that exchange rate bears more, a moderate of world oil production and Saudi oil production and up-to a lesser extent spread constitute an important determinant of Pakistan oil prices.Our findings have relevant implications for investors, speculators and particularly for policy makers of Pakistan’s economy.