Output Feedback Dynamic Surface Control Research Articles

Command filter and high gain observer based adaptive output feedback control for stochastic nonlinear systems with prescribed performance and input quantization

SummaryIn this paper, an adaptive output feedback dynamic surface control (DSC) strategy is proposed for strict‐feedback stochastic nonlinear systems with input quantization, prescribed performance and dynamic uncertainties. A new quantizer is used to process the input signal, which can avoid the chattering of the quantization signal and keep the upper bound of the quantization error constant. Radial basis functions are used to approximate unknown smooth functions, unmodeled dynamics are processed by dynamic signals, and unmeasurable states are estimated by high gain observer. Hyperbolic tangent functions are employed to handle prescribed performance. The second order command filter is used to replace the first order filter used in general DSC, and the compensation term is added in each step of DSC. By the Lyapunov stability analysis, all signals in the controlled system are semi‐globally uniformly ultimately bounded (SGUUB) in probability. Two examples further prove that the control scheme designed in this paper is reasonable and effective.

Decentralized adaptive output feedback dynamic surface control for stochastic nonstrict‐feedback interconnected nonlinear systems with actuator failures and input quantization via command filter

AbstractIn this article, a new decentralized adaptive neural output feedback control scheme based on first‐order command filter is proposed for stochastic nonstrict‐feedback interconnected systems with prescribed performance, input quantization, actuator failures and unmodeled dynamics. The unknown smooth functions are eliminated by using the radial basis function neural networks. The immeasurable states in the system are estimated using the decentralized K‐filters, unmodeled dynamics is processed using dynamic signal, and the hyperbolic tangent function is applied to the construction of the prescribed performance function. The hysteretic quantizer and actuator failure are denoted in the form of linearization, and a smoothing function is introduced to compensate for the effects of quantization and bounded stuck faults. Based on the dynamic surface control (DSC) method and using the properties of Gaussian function to deal with stochastic nonstrict‐feedback interconnected systems, the first‐order command filter is used to replace the first‐order filter in the traditional DSC to eliminate the influence of filtering error on the systems, and an error compensation signal is introduced at the recursive each step of the design to construct a new error dynamic surface, which simplifies the derivation process and the design of the controller. Finally, the Lyapunov method is used to prove that all the signals in the whole controlled system are semiglobally uniformly ultimately bounded in probability and the tracking error is within the time‐varying constraint. The effectiveness of the proposed decentralized adaptive control method is verified by a numerical simulation and an example simulation.

Anti-Disturbance Dynamic Surface Control for Position Tracking of Interior Permanent Magnet Synchronous Motor Based on Nonlinear Extended State Observer

In this paper, an anti-disturbance output feedback dynamic surface control (DSC) method is proposed for the position tracking of interior permanent magnet synchronous motor subject to unknown nonlinearities and time-varying disturbances. Specifically, a nonlinear extended-state-observer (NLESO) based on exponential functions is designed to estimate the total disturbance composed of system uncertainties and external disturbances. Then, by compensating for the total disturbance via the NLESO, an anti-disturbance output feedback law is designed based on the DSC approach. The salient features of the proposed approach is twofold. First, the total uncertainty including internal and external disturbances can be accurately estimated by an NLESO in real time. Second, the desired anti-disturbance performance of the servo control system can be achieved regardless of the position measurement only. The stability of the closed-loop control system is proved by using the cascade theory and input-to-state stability theory. Both simulation and experiment results are conducted to illustrate the effectiveness of the proposed control method.

Improved Adaptive Fuzzy Output-Feedback Dynamic Surface Control of Nonlinear Systems With Unknown Dead-Zone Output

This article presents an adaptive fuzzy output-feedback dynamic surface control (DSC) for the nonlinear systems with dead-zone output nonlinearity. First, a novel smooth approximation of the output dead zone is given to conveniently fuse with the backstepping technique. After that a nonlinear fuzzy state observer is constructed to estimate the unmeasurable states, by employing the fuzzy logic systems for identifying the unknown compounded nonlinear functions, which releases the limitation in the existing references that the state observer needs to be linear in the presence of dead-zone output nonlinearity. Then, to reduce the effect of unknown dead-zone coefficients, an adaptive compensation mechanism is introduced by using the characteristic of hyperbolic tangent function, which can replace the widely used Nussbaum-type function-based control strategy. Furthermore, a novel DSC method based on the nonlinear filters is proposed, which not only avoids the issue of explosion of complexity inherent in the backstepping procedure, but also improves the system control performance. Under the certain assumptions, the stability of the closed-loop system is proved by use of Lyapunov function stability theory. Finally, the applicability of the proposed control method is rigorously verified by a single-link robot arm simulation example.

Adaptive Output-Feedback Control of a Class of Nonlinear Systems with Unknown Sensor Sensitivity and Its Experiment for Flexible-Joint Robots

This paper investigates an adaptive output-feedback stabilization problem for a class of uncertain nonlinear systems with an unknown sensor sensitivity. A high-gain observer based on an inexact system output is designed to estimate unmeasurable state variables and an adaptive output-feedback dynamic surface control strategy is established to accomplish the robust stabilization in the presence of the unknown sensor sensitivity. Compared with the existing control results dealing with the unknown sensor sensitivity, the primary contribution of this paper is that the proposed adaptive control strategy does not require the information of the sensor sensitivity and its bound where the effect of the unknown sensor sensitivity is compensated by designing an adaptation structure. From the Lyapunov stability analysis, the ultimate uniform boundedness of all closed-loop signals and the convergence of the stabilization error to an adjustable neighborhood of the origin are ensured. A simulation for a numerical example and an experiment for a flexible-joint robot are provided to validate the effectiveness of the proposed theoretical approach.

Reduced-Order Observer-Based Adaptive Backstepping Control for Fractional-Order Uncertain Nonlinear Systems

This article presents two adaptive fuzzy output-feedback dynamic surface control schemes for single-input-single-output (SISO) strict-feedback fractional-order uncertain nonlinear systems under the complete smooth nonlinearity and partial piecewise-smooth nonlinearity, respectively. For the former, complete smooth nonlinear functions are approximated by employing fuzzy logic systems, based on which a novel fractional-order reduced-order observer is constructed to estimate the unmeasurable states. For the latter, a new switched approximation and estimate strategy is proposed to deal with the problem of piecewise-smooth nonlinearity. Meanwhile, fuzzy basis function property is utilized to eliminate the assumption requirement that the nonlinear functions must satisfy the Lipschitz condition inherent in the output-feedback control, which is suitable for two cases. Under certain assumptions, the stability of two closed-loop systems are proved via fractional-order Lyapunov function stability criterion. Specifically, the stability proof of the second case is built on the foundation of the common Lyapunov function method. Finally, two diverse Chua's circuit simulation examples are provided to, respectively, validate the effectiveness of the proposed two control strategy.

Prescribed performance adaptive neural output feedback dynamic surface control for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics

SummaryThis paper studies the output feedback tracking control problem for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics using a prescribed performance adaptive neural dynamic surface control design approach. A nonlinear mapping technique is employed to address the state constraints. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. The unmodeled dynamics is addressed by introducing an available dynamic signal. Subsequently, we construct the controller and parameter adaptive laws using a backstepping technique. Based on Lyapunov stability theory, it is shown that all signals in the closed‐loop system are semiglobally uniformly ultimately bounded and that the tracking error always remains within the prescribed performance bound. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

High-order ESO based output feedback dynamic surface control for quadrotors under position constraints and uncertainties

This paper investigates the trajectory tracking and attitude stabilization problem with only position measurements for quadrotors subject to position constraints and uncertainties. By introducing the one-to-one nonlinear mapping (NM) to prevent position state violation, an output constrained trajectory tracking law is developed by transforming the original restricted translational dynamics into an equivalent unconstrained subsystem. To address the uncertainties arising from parametric deviations and external disturbances, with given model information incorporated into observer design, we develop a high-order extended state observer (ESO), capable of simultaneously online estimating the uncertainties and full-states of quadrotors. Then, an output feedback based trajectory tracking and attitude stabilization approach is synthesized by integrating NM and high-order ESO via dynamic surface control (DSC), leading to a much simpler control structure and reduced implementation costs. The salient feature is that position constraints, uncertainties as well as output feedback difficulties can be comprehensively handled with acceptable control performance. It is shown via Lyapunov stability that all signals in the closed-loop system are guaranteed to be uniformly ultimately bounded. Simulation results are provided to validate the benefits and effectiveness of the proposed method.

Adaptive quantized output feedback DSC of uncertain systems with output constraints and unmodeled dynamics based on reduced-order K-filters

Abstract This paper is concerned with adaptive output feedback tracking control for a class of uncertain nonlinear systems with quantized input and unmodeled dynamics as well as output constraints. Quantized reduced-order K-filters are designed to observe parts of unmeasured states. The considered system is of two types of uncertainties. To deal with these uncertainties, we adopts global exponential stability technique of the state unmodeled dynamics with a Lyapunov description and the fuzzy approximation approach to those uncertain functions. To avoid the chattering of the quantized control signal, a hysteretic quantizer is introduced, and by designing a novel control law based on dynamic surface control (DSC) method, many assumptions of the quantized system in early literatures are removed. Combining quantized DSC with an one to one mapping from output error to the first dynamic surface, the robust quantized adaptive controller is constructed to guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB), and the tracking error is restricted within the prescribed output constraints. A numerical simulation example shows the effectiveness of the proposed approach.

Decentralized Adaptive Neural Output-Feedback DSC for Switched Large-Scale Nonlinear Systems

In this paper, for a class of switched large-scale uncertain nonlinear systems with unknown control coefficients and unmeasurable states, a switched-dynamic-surface-based decentralized adaptive neural output-feedback control approach is developed. The approach proposed extends the classical dynamic surface control (DSC) technique for nonswitched version to switched version by designing switched first-order filters, which overcomes the problem of multiple "explosion of complexity." Also, a dual common coordinates transformation of all subsystems is exploited to avoid individual coordinate transformations for subsystems that are required when applying the backstepping recursive design scheme. Nussbaum-type functions are utilized to handle the unknown control coefficients, and a switched neural network observer is constructed to estimate the unmeasurable states. Combining with the average dwell time method and backstepping and the DSC technique, decentralized adaptive neural controllers of subsystems are explicitly designed. It is proved that the approach provided can guarantee the semiglobal uniformly ultimately boundedness for all the signals in the closed-loop system under a class of switching signals with average dwell time, and the tracking errors to a small neighborhood of the origin. A two inverted pendulums system is provided to demonstrate the effectiveness of the method proposed.

Observer-based adaptive sliding mode backstepping output-feedback DSC for spin-stabilized canard-controlled projectiles

This article presents a complete nonlinear controller design for a class of spin-stabilized canard-controlled projectiles. Uniformly ultimate boundedness and tracking are achieved, exploiting a heavily coupled, bounded uncertain and highly nonlinear model of longitudinal and lateral dynamics. In order to estimate unmeasurable states, an observer is proposed for an augmented multiple-input-multiple-output (MIMO) nonlinear system with an adaptive sliding mode term against the disturbances. Under the frame of a backstepping design, an adaptive sliding mode output-feedback dynamic surface control (DSC) approach is derived recursively by virtue of the estimated states. The DSC technique is adopted to overcome the problem of “explosion of complexity” and relieve the stress of the guidance loop. It is proven that all signals of the MIMO closed-loop system, including the observer and controller, are uniformly ultimately bounded, and the tracking errors converge to an arbitrarily small neighborhood of the origin. Simulation results for the observer and controller are provided to illustrate the feasibility and effectiveness of the proposed approach.

Single-parameter-learning-based fuzzy fault-tolerant output feedback dynamic surface control of constrained-input nonlinear systems

This paper addresses the problem of adaptive fuzzy fault-tolerant dynamic surface control for a class of constrained-input nonlinear systems. To resolve this problem, the design of an observer-based single-parameter-learning (SPL) control method using output feedback is proposed. The Takagi-Sugeno (T-S) fuzzy system is used to identify and approximate online the uncertain nonlinear dynamics, requiring no knowledge. The barriers that restrict the applications of the traditional backstepping and approximation-based approach, including the explosion of complexity and the dimension curse problems, are circumvented via dynamic surface control and SPL techniques. The merit of the proposed method lies in that only one parameter in the entire control scheme requires online adjustment, regardless of the number of parameters in the T-S fuzzy system that characterizes the fuzzy rules; the calculation burden, in this sense, is reduced to the extent of the minimum value. The truncated adaptation method is used to avoid the chattering and instability caused by constrained input. It is shown with rigorous proof using the Lyapunov and invariant set theorems that all the closed-loop signals are guaranteed semi-globally uniformly ultimately bounded. The output tracking error is adjustable by means of design parameters in an explicit form, and can be adjusted to an arbitrarily small value around zero by appropriately chosen control parameters, even under faulty and constrained actuators. Simulation and comparative results are provided to demonstrate the effectiveness of the proposed control approach.

Adaptive output feedback control of nonlinear systems with prescribed performance and MT-filters

In this paper, adaptive prescribed performance output feedback control is investigated for a class of nonlinear systems with unmodeled dynamics. Neural networks are used to approximate the unknown nonlinear functions. MT-filters are employed to estimate the unmeasured states. The unmodeled dynamics is dealt with by introducing an available dynamic signal. Adaptive output feedback dynamic surface control and parameter adaptive laws are proposed based on introducing the prescribed performance function and output error transformation. It is proved that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Simulation results are provided to demonstrate the effectiveness of the proposed approach.

Dynamic surface error constrained adaptive fuzzy output feedback control for switched nonlinear systems with unknown dead zone

This paper investigates the adaptive fuzzy output-feedback dynamic surface control (DSC) approach with prescribed performance for a class of uncertain switched nonlinear systems with unknown dead-zone. In this research, fuzzy logic systems are used to identify the unknown nonlinear functions, a fuzzy switched state observer is established to observe the unmeasured states. Based on DSC backstepping control design technique and incorporated by the predefined performance theory and the average dwell time method, a new adaptive fuzzy output-feedback control method is developed. It is proved that the proposed control approach can ensure that all the signals of the resulting closed-loop system are bounded, and the tracking errors are within the prescribed performance bounds for all times. Simulation studies illustrate the effectiveness of the proposed approach.

Adaptive neural networks output feedback dynamic surface control design for MIMO pure-feedback nonlinear systems with hysteresis

An adaptive neural networks (NNs) output feedback tracking control approach is proposed for a class of multi-input and multi-output (MIMO) pure-feedback nonlinear systems with unknown backlash-like hysteresis and immeasurable states. Radial basis function neural networks (RBF NNs) are utilized to approximate the unknown nonlinear functions of the controlled systems, and a state observer is designed to estimate the unmeasured states. The filtered signals are introduced to circumvent algebraic loop problem encountered in the implementation of the controller, and an adaptive compensation technique are used to solve the problem of unknown backlash-like hysteresis. Based on the designed state observers, and combining the backstepping and dynamic surface control (DSC) techniques, an adaptive NN output feedback tracking control approach is developed. The proposed method not only overcomes the problem of “explosion of complexity” inherent in the backstepping control design but also guarantees that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking errors converge to a small neighborhood of the origin. Two simulation examples are provided to show the effectiveness of the proposed approach.

Output-feedback dynamic surface control for a class of nonlinear non-minimum phase systems

In this paper, an output-feedback tracking controller is proposed for a class of nonlinear non-minimum phase systems. To keep the unstable internal dynamics bounded, the method of output redefinition is applied to let the stability of the internal dynamics depend on that of redefined output, thus we only need to consider the new external dynamics rather than internal dynamics in the process of designing control law. To overcome the explosion of complexity problem in traditional backstepping design, the dynamic surface control (DSC) method is firstly used to deal with the problem of tracking control for the nonlinear non-minimum phase systems. The proposed output-feedback DSC controller not only forces the system output to asymptotically track the desired trajectory, but also drives the unstable internal dynamics to follow its corresponding bounded and causal ideal internal dynamics, which is solved via stable system center method. Simulation results illustrate the validity of the proposed output-feedback DSC controller.

Adaptive fuzzy output-feedback dynamic surface control of MIMO switched nonlinear systems with unknown gain signs

This paper investigates the problem of adaptive fuzzy tracking control for a class of multi-input–multi-output (MIMO) switched uncertain nonlinear systems with unknown gain signs and unmeasurable states. Fuzzy logic systems are used to approximate the unknown nonlinear functions, a fuzzy MIMO switched observer is designed to estimate the unmeasurable states. The Nussbaum-type functions are utilized to handle the unknown gain signs of the system under study. A switched-dynamic-surface-based adaptive fuzzy control approach is then established by exploiting the average dwell time method and backstepping and the dynamic surface control technique, which constructs multiple switched first-order filters to overcome the multiple “explosion of complexity” problem when applying the backstepping recursive design scheme. Also, the proposed approach extends the classical dynamic surface control technique from its original non-switched nonlinear version to a switched nonlinear version. It is proved that all the signals in the closed-loop system are semiglobal uniformly ultimately boundedness under a class of switching signals with average dwell time, and the tracking errors converge to a small neighborhood of the origin. A mass–spring–damper system with controller switching as a practical example is provided to demonstrate the effectiveness of the proposed design method.

Adaptive output feedback dynamic surface control of stochastic nonlinear systems with state and input unmodeled dynamics

SummaryIn this paper, an adaptive neural output feedback control scheme is investigated for a class of stochastic nonlinear systems with unmeasured states and four kinds of uncertainties including uncertain nonlinear function, dynamic disturbance, input unmodeled dynamics, and stochastic inverse dynamics. The unmeasured states are estimated by K‐filters, and stochastic inverse dynamics is dealt with by constructing a changing supply function. The considered input unmodeled dynamic subsystem possesses nonlinear feature, and a dynamic normalization signal is introduced to counteract the unstable effect produced by the input unmodeled dynamics. Combining dynamic surface control technique with stochastic input‐to‐state stability, small‐gain condition, and Chebyshev's inequality, the designed robust adaptive controller can guarantee that all the signals in the closed‐loop system are bounded in probability, and the error signals are semi‐globally uniformly ultimately bounded in mean square or the sense of four‐moment. Simulation results are provided to verify the effectiveness of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.

Composite adaptive fuzzy output feedback dynamic surface control design for stochastic large-scale nonlinear systems with unknown dead zone

In this paper, a composite adaptive fuzzy output feedback decentralized control problem is investigated for a class of nonlinear stochastic large-scale systems. The nonlinear large-scale systems under study have unknown nonlinear functions, unknown dead-zone and immeasurable states. Fuzzy logic systems are used to approximate the unknown nonlinear functions, a fuzzy adaptive state observer is designed to estimate the unmeasured states. By utilizing the designed fuzzy state observer, a serial-parallel estimation model is established. Based on adaptive backstepping dynamic surface control technique and the prediction error between the system states observer model and the serial-parallel estimation model, an adaptive output feedback controller is constructed. The designed fuzzy controller with the composite parameters adaptive laws ensures that all the variables of closed-loop system are bounded in probability, and tracking error converges to a small neighborhood of zero. A numerical example is provided to verify the effectiveness of the proposed approach.

Fuzzy Adaptive Output Feedback Control of MIMO Nonlinear Systems With Partial Tracking Errors Constrained

In this paper, a partial tracking error constrained fuzzy output-feedback dynamic surface control (DSC) scheme is proposed for a class of uncertain multi-input and multi-output (MIMO) nonlinear systems. The considered MIMO nonlinear systems contain unknown functions and without the requirement of their states being available for the controller design. With the help of fuzzy logic systems identifying the MIMO unknown nonlinear systems, a fuzzy adaptive observer is established to estimate the unmeasured states. By transforming the tracking errors into new virtual error variables and based on the DSC backstepping recursive design technique, a new adaptive fuzzy output-feedback control method is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are bounded and the partial state tracking errors are confined all times within the prescribed bounds. The simulation results and comparisons with the previous control approaches confirm the effectiveness and utility of the proposed scheme.