Control Scheme For Nonlinear Systems Research Articles

Combined Iterative Learning and Model Predictive Control Scheme for Nonlinear Systems

Combined Iterative Learning and Model Predictive Control Scheme for Nonlinear Systems

Disturbance rejections of polynomial fuzzy systems under equivalent-input-disturbance estimator approach

This paper proposes an integrated robust stabilization and anti-disturbance control scheme for nonlinear systems using a polynomial fuzzy model approach. To estimate unknown disturbances, an equivalent-input-disturbance (EID) estimator is employed. The proposed approach incorporates a novel fuzzy model assisted by EID estimator into the sum-of-squares-based approach, utilizing a polynomial fuzzy model-based observer to estimate the disturbance effect. A suitable fuzzy rule-based control law is developed by utilizing the parallel distributed compensation approach and the output of the EID estimator. To ensure stability, fuzzy membership functions are converted into sum-of-square polynomials using a polynomial curve fitting approach, allowing their exact shape information to be used in the stability condition. The addressed system is transformed into an augmented system by incorporating the system, observer, and filter states, simplifying the analysis. Gain matrices for the controller and observer are obtained using Lyapunov stability theory and sum-of-squares methods to confirm asymptotic stabilization of the fuzzy system. Two numerical examples are presented to demonstrate the effectiveness of the proposed control design method.

Robust exponential arbitrary time control of nonlinear systems with input delay

In this study, we aim to present an exponential arbitrary-time control scheme for nonlinear systems subjected to input time delay and additive disturbances. To this end, a new finite-time controller was developed for certain nonlinear systems, which ensures exponential tracking in a time independent of initial conditions. Due to the presence of unknown disturbances, predictors cannot be directly used to control the system, being a challenging issue. Therefore, to utilize predictor feedback in disturbed nonlinear input delay systems, a disturbance observer was designed. The proposed disturbance observer guarantees the exponential arbitrary time estimation of unknown disturbances. Next, an adaptive exponential arbitrary time controller was designed for the system using the proposed disturbance observer. In addition, the Lyapunov theorem was utilized to prove the disturbance observer and tracking errors converged to the origin in an arbitrary time. In the end, the state tracking error was analyzed accurately. It was ensured that the upper bound of the tracking error was bounded and converged to zero in the adjusted arbitrary time. Ultimately, the main results of this study will be illustrated and validated by simulation and experimental results.

Suboptimal Safety-Critical Control for Continuous Systems Using Prediction–Correction Online Optimization

This article presents an innovative efficient safety-critical control scheme for nonlinear systems by combining techniques of control barrier function (CBF) and online time-varying optimization. The idea lies in that when directly calling the complete optimization solvers used in the CBF method, such as CBF-based quadratic programming (CBF-QP), is computationally inefficient for complex tasks, the suboptimal solutions obtained from online learning techniques can be an alternatively reliable choice for ensuring both efficiency and control performance. By using the barrier-based interior point method, the original optimization problem with CBF constraints is reduced to an unconstrained one with approximate optimality. Then, Newton-and gradient-based continuous dynamics are introduced to generate alternative cheap solutions while ensuring safety. By further considering the lag effect of online tracking, a prediction term is added to the dynamics. In this way, the online cheap solutions are proven to exponentially converge to the time-varying suboptimal solutions of the interior point method. Furthermore, the safety criteria are established, and the robustness of the designed algorithms is analyzed theoretically. Finally, the effectiveness is illustrated by conducting two experiments on obstacle avoidance and anti-swing tasks.

Adaptive Event-Triggered Control for Nonlinear Systems With Asymmetric State Constraints: A Prescribed-Time Approach

Finite/Fixed-time control yields a promising tool to optimize a system&#x0027;s settling time, but lacks the ability to separately define the settling time and the convergence domain (known as <i>practically prescribed-time stability</i>, PPTS). We provide a sufficient condition for PPTS based on a new piecewise exponential function, which decouples the settling time and convergence domain into separately user-defined parameters. We propose an adaptive event-triggered prescribed-time control scheme for nonlinear systems with asymmetric output constraints, using an exponential-type barrier Lyapunov function. We show that this PPTS control scheme can guarantee tracking error convergence performance, while restricting the output state according to the prescribed asymmetric constraints. Compared with traditional finite/fixed-time control, the proposed methodology yields separately user-defined settling time and convergence domain without the prior information on disturbance. Moreover, asymmetric state constraints can be handled in the control structure through bias state transformation, which offers an intuitive analysis technique for general constraint issues. Simulation and experiment results on a heterogeneous teleoperation system demonstrate the merits of the proposed control scheme.

Adaptive neural network observer‐based filtered backstepping control for nonlinear systems with fuzzy dead‐zone and uncertainty

SummaryThis study proposes a high gain observer‐based filtered backstepping control scheme for nonlinear systems with unknown dynamics and dead‐zone constraint. Majority of the previously papers describe dead‐zone by the conventional certain models, assume that all state variables are available and invoke the backstepping or conventional dynamic surface control (CDSC) approaches for controller design. This work describes the dead‐zone by the fuzzy model, invokes radial basis function neural network (RBFNN) to model the unknown functions and proposes a RBFNN‐based high gain observer to estimate unmeasurable states. To avoid the complexity explosion in the backstepping approach and eliminate the sensitivity to the time‐constant of the first‐order filters in the CDSC, a nonlinear tracking differentiator (NTD) with finite time convergence property is used instead of the first‐order filters in the CDSC to obtain derivative of the virtual inputs. Moreover, the error compensation mechanism and auxiliary signal are proposed to eliminate the influence of the filtering error and input nonlinearity, respectively. Despite the fuzzy dead‐zone, the proposed scheme makes the closed‐loop signals uniformly ultimately bounded. In comparison with the existing results, (i) some assumptions like certain model of dead‐zone and full state measurement are removed, (ii) “explosion of complexity” and sensitivity to the time constant of the first‐order filters are eliminated, (iii) effect of the filtering error and input nonlinearity are compensated, (iv) number of adjustable parameters and online computational burden are decreased effectively. Simulation results on the two well‐known examples verify the effectiveness and applicability of the proposed new design technique.

State Quantized Output Feedback Control for Nonlinear Systems via Event-Triggered Sampling

The current article proposes a novel output feedback event-triggered control scheme for nonlinear systems considering state quantization. First, we construct a state observer to track the unavailable system states. Second, a dynamic event-triggered and quantized mechanism is constructed to handle the state sampling and quantization. By designing the event-triggered mechanism to sample the system state, and using the quantizer to filtrate the sampled signals, the wasted resources in the data channels can be effectively reduced, and the communication efficiency can be improved. Then, based on the input-to-state stability method, the asymptotic stability is ensured for the closed-loop systems. Moreover, we propose an event-triggered and quantized control scheme for the nonlinear systems with input delay, and the asymptotic stability is ensured using the Lyapunov–Krasovskii functional method. The proposed output feedback event-triggered and quantized mechanisms can guarantee a positive lower bound of the transmission interval times of communication channels, which means that the Zeno behavior is avoided. Finally, a simulation example is presented to verify the feasibility of the proposed control schemes.

Adaptive fuzzy output feedback control for a class of uncertain nonlinear systems in the presence of sensor attacks

In this paper, an adaptive fuzzy output feedback control scheme is proposed for a class of unknown nonlinear systems with sensor attacks. The fuzzy logic systems are employed to approximate the uncertain nonlinearities, and the backstepping technique is implemented to construct controllers. The unknown output feedback coefficient is handled by using a Nussbaum function in the first step of backstepping design, eventually developing an adaptive controller to accommodate sensor attacks. Compared to the current control schemes for nonlinear systems under sensor attacks, the benefit of the proposed adaptive controller is that it can apply to nonlinear systems with both uncertainty and unmeasurable states. Finally, two examples validate the efficacy of the proposed control scheme.

Simplified artificial neural network based online adaptive control scheme for nonlinear systems

Simplified artificial neural network based online adaptive control scheme for nonlinear systems

Adaptive asymptotic tracking control for multi-input and multi-output nonlinear systems with unknown hysteresis inputs

With the advantages in resolution, response speed, and reliability, smart materials such as piezoelectric ceramics and shape memory alloys are widely used in modern industries, and the hysteresis phenomenon in such smart materials has also received extensive attention. The existing tracking control schemes for nonlinear systems with backlash-like hysteresis inputs may have singularity problems, and it is difficult to obtain a high-precision tracking effect. To resolve the above issues, a novel adaptive asymptotic tracking control strategy is proposed for multi-input and multi-output nonlinear systems with unknown backlash-like hysteresis inputs, where the dependence on the system model is removed through fuzzy logic systems and elaborately designed adaptive laws. In contrast, the proposed tracking control scheme is free of any singularity problem, and the constructed controllers and adaptive laws including positive and continuous functions with zero limit make the output tracking error asymptotically converge to zero rather than near the origin. Moreover, this asymptotic convergence is proven by rigorous theoretical analysis. Finally, the effectiveness and robustness of the proposed tracking control scheme are also verified by numerical and practical simulations.

Continuous-Time Nonlinear Model Predictive Tracking Control with Input Constraints Using Feedback Linearization

This paper presents a tracking control scheme for nonlinear systems with input constraints by combining the continuous-time model predictive control and the feedback linearization. Although there are some similar combinations for nonlinear systems presented in literature, their formulations are complex and massive computations are unavoidable. This study aims to simplify the formulations and reduce the computational loads by imposing the Laguerre functions to approximate the control signals. Since the Laguerre functions have the property of orthogonality, the tracking control problem, by applying the combination, leads to a constrained quadratic optimization problem in terms of the coefficients associated with the Laguerre functions, where the input constraints are converted so as to be state-dependent, based on feedback linearization. The Hildreth’s quadratic programming algorithm is used to solve the optimization problem, so as to determine the coefficients. Moreover, this study also summarizes some common linearization schemes and shows their pros and cons. Furthermore, the proposed approach is applied to two illustrative examples, and the control performances are compared with those by linear control strategies combined with those linearization schemes.

Machine learning-based reduced-order modeling and predictive control of nonlinear processes

In this work, we develop a model predictive control scheme for nonlinear systems using autoencoder-based reduced-order machine learning models. First, an autoencoder is developed for model order reduction by projecting the process states onto a low-dimensional space using data generated from open-loop simulations of the nonlinear system in the original high-dimensional space. Subsequently, reduced-order recurrent neural networks (RNN) are developed to capture the dominant dynamics of the nonlinear system using the low-dimensional data. Lyapunov-based model predictive control (MPC) scheme using RNN models in low-dimensional space is developed to stabilize the nonlinear system. Finally, a diffusion-reaction process example is used to demonstrate the effectiveness of the proposed reduced-order RNN modeling approach and RNN-based predictive control method.

Multivariable control based on incomplete models via feedback linearization and continuous‐time derivative estimation

AbstractModels of nonlinear dynamical systems are typically composed of unknown and known parts due to the existence of mismatch between the true nonlinear system dynamics and their models. This article presents a multivariable control strategy for nonlinear systems that deals explicitly with the existence of incomplete models in a data‐driven framework. The proposed strategy uses feedback linearization and continuous‐time estimation of the unknown derivatives to achieve satisfactory closed‐loop performance for fast sampling applications with simple tuning of design parameters in the absence of a fully known system model. It is shown that this strategy possesses useful steady‐state properties, such as elimination of steady‐state error and rejection of constant input disturbances without any integral term, and ensures exponential convergence to the setpoints. Another contribution of this article is the development of methods for quantitative analysis of the stability and performance of the control strategy in the continuous‐time case. The approach is illustrated via a simulated example of reactor control. The proposed control strategy is broadly applicable and simplifies control design significantly for a large variety of systems.

Novel neural observer based fault estimation, reconstruction and fault-tolerant control scheme for nonlinear systems

This research is concerned with the adaptive neural network observer based fault approximation and fault-tolerant control of time-varying nonlinear systems. A new strategy for adaptively updating the weights of neural network parameters is proposed to enhance fault detection accuracy. Lyapunov function theory (LFT) is applied for adaptively updating the learning parameters weights of multi-layer neural network (MLNN). The purpose of using adaptive learning rates to update the weight parameters of MLNN is to obtain the global minima for highly nonlinear functions without increasing the computational complexities and costs and increase the efficacy of fault detection. Results of the proposed adaptive MLNN observer are compared with conventional MLNN observer and high gain observer. The effects of various faults or failures are studied in detail. The proposed strategy shows more robustness to disturbances, uncertainties, and unmodelled system dynamics compared to the conventional neural network, high gain observer and other existing techniques in literature. Fault tolerant control (FTC) schemes are also proposed to account for the presence of various faults and failures. Separate sliding mode control (SMC) based FTC schemes are designed for each observer to ensure stability of the faulty system. The suggested strategy is validated on Boeing 747 100/200 aircraft. Results demonstrate the effectiveness of both the proposed adaptive MLNN observer and the FTC based on the proposed adaptive MLNN compared to the conventional MLNN, high gain observer and other existing schemes in literature. Comparison of the performance of all the strategies validates the superiority of the proposed strategy and shows that the FTC based on proposed adaptive MLNN strategy provides better robustness to various situations such as disturbances and uncertainties. It is concluded that the proposed strategy can be integrated into the aircraft for the purpose of fault diagnosis, fault isolation and FTC scheme for increasing the performance of the system.

Command Filter-Based Adaptive Neural Control Design for Nonstrict-Feedback Nonlinear Systems With Multiple Actuator Constraints.

This article proposes an adaptive neural-network command-filtered tracking control scheme of nonlinear systems with multiple actuator constraints. An equivalent transformation method is introduced to address the impediment from actuator nonlinearity. By utilizing the command filter method, the explosion of complexity problem is addressed. With the help of neural-network approximation, an adaptive neural-network tracking backstepping control strategy via the command filter technique and the backstepping design algorithm is proposed. Based on this scheme, the boundedness of all variables is guaranteed and the output tracking error fluctuates near the origin within a small bounded area. Simulations testify the availability of the designed control strategy.

State prediction based control schemes for nonlinear systems with input delay and external disturbance

State prediction based control schemes for nonlinear systems with input delay and external disturbance

Event-triggered controllers based on the supremum norm of sampling-induced error

The paper proposes a novel event-triggered control scheme for nonlinear systems. Specifically, the closed-loop system is associated with a pair of auxiliary input and output. The auxiliary output is defined as the derivative of the continuous-time input function, while the auxiliary input is defined as the input disturbance caused by the sampling or equivalently the integral of the auxiliary output over the sampling period. As a result, it forms a cyclic mapping from the input to the output via the system dynamics and back from the output to the input via the integral. The event-triggered law is constructed to make the mapping contractive such that the stabilization is achieved and an easy-to-check Zeno-free condition is provided. Within this framework, we develop a theorem for the event-triggered control of interconnected nonlinear systems which is employed to solve the event-triggered control for lower-triangular systems with dynamic uncertainties.

Fuzzy Robust Constrained Control for Nonlinear Systems With Input Saturation and External Disturbances

This article proposes a high-order disturbance observer (HODO) and dynamic surface control (DSC) technique-based adaptive fuzzy control scheme for nonlinear systems subjected to input saturation and external time-varying disturbances. First, based on a Sigmoid function, the saturation input is tackled by utilizing a well-defined nonlinear smooth function. Furthermore, HODO and fuzzy logic systems are used to estimate the external disturbances and to handle the lumped unknown functions, respectively. Then, by using the backstepping method and DSC technique, a HODO-based adaptive fuzzy tracking control scheme is proposed for nonlinear systems with saturation nonlinearity, uncertainties, and external disturbances. The Lyapunov analysis method is used to prove that all signals in the entire system are semiglobally uniformly ultimately bounded (SGUUB). In addition, the tracking error converges to a compact set with a tunable error bound determined by some design parameters. Finally, a numerical simulation of two-stage chemical reactor shows the effectiveness of the developed tracking control strategy.

Analysis of the Zhang Neural Network and its Application for the control of Nonlinear Dynamical Systems

This research article presents a development of the Zhang Recurrent Neural Network (Z-RNN) model to estimate the on-line solution to linear time-varying matrix equations. This Z-RNN model is further used to develop a control strategy for nonlinear systems by estimating the solution to a Lyapunov equation on-line, without approximations and linearization. The proposed concept is validated using a 4th order Inverted Pendulum on a Cart model and it has been compared with the Linear Quadratic Regulator. The proposed technique offers a significantly lower cost and better performance. The issues with stability of the Z-RNN and sampling rate is also discussed in detail, along with the choice of parameters involved.

Multi-model cascade control strategy design based on gap metric for nonlinear processes

ABSTRACT A multi-model control system in cascade configuration using hard and soft switching for the nonlinear process is addressed in this research. Cascade control is a widely known strategy in process plants to improve control performance in the presence of disturbances. It has been found that the incorporation of conventional cascade controllers was ineffective when applied to nonlinear processes. Multi-model control schemes are capable of providing enhanced performance when compared to the conventional control schemes for nonlinear systems. This paper presents the multi-model approach (MMA) in the cascade control strategy by using hard and soft switching for selection of the controller. Simulation studies are demonstrated on nonlinear processes (isothermal CSTR, conical tank and spherical tank) and experimentally applied on the conical tank process. The performance of the cascade multi-model control strategy is superior when compared to the classical multi-model control strategy. It is observed that the cascade multi-model control strategy has provided faster response and improved disturbance rejection.