Uncertain MIMO Nonlinear Systems Research Articles

Asymptotic Tracking Control for Uncertain MIMO Nonlinear Systems With Guaranteed Performance and Enhanced Controllability

Asymptotic Tracking Control for Uncertain MIMO Nonlinear Systems With Guaranteed Performance and Enhanced Controllability

Asymptotic tracking control of uncertain MIMO nonlinear systems with extended condition for controllability

AbstractFor uncertain multiple‐inputs multi‐outputs nonlinear systems, it is nontrivial to achieve asymptotic tracking due to the intrinsic coupling among inputs, while the controllability conditions in most existing methods are rather restrictive or even impractical especially when unexpected actuator faults are involved. In this article, we focus on extending such controllability condition by resorting to the existence (instead of a priori knowledge) of some feasible auxiliary matrix, upon which a robust adaptive control scheme is first presented in the absence of actuator faults that is not only able to achieve asymptotic tracking even in the presence of non‐parametric uncertainties with all the closed‐loop signals globally ultimately uniformly bounded, but also able to deal with a larger class of system models. Furthermore, for the case with intermittent actuator faults, we develop a fault‐tolerant control scheme with extended condition for controllability that is able to accommodate such faults automatically without using any fault detection or fault diagnosis unit. The effectiveness and benefits of the proposed method are verified via simulation on robotic systems.

Self-Triggered Synchronized Path Maneuvering of Constrained Uncertain MIMO Nonlinear Systems Based on Command Optimization

Self-Triggered Synchronized Path Maneuvering of Constrained Uncertain MIMO Nonlinear Systems Based on Command Optimization

Prescribed fixed-time adaptive fuzzy control for uncertain MIMO nonlinear systems with Preisach operators

Prescribed fixed-time adaptive fuzzy control for uncertain MIMO nonlinear systems with Preisach operators

High-order disturbance observer-based safe tracking control for a class of uncertain MIMO nonlinear systems with time-varying full state constraints

This paper investigates a high-order disturbance observer-based safe tracking control scheme for a class of uncertain multiple-input and multiple-output systems under time-varying full state constraints and disturbances. To achieve the safe tracking objective, a boundary protection algorithm is introduced to generate new safe desired signals which are within corresponding state constraints. An improved second-order dynamic surface control technology is developed to deal with the piecewise differentiability of safe desired signals and the phenomenon of repeatedly differentiation, simultaneously. To handle the negative effects of system uncertainties and obtain better estimation effect of high order time-varying disturbances, the radial basis function neural networks and high-order disturbance observer methods are developed. The safety and performance of the closed-loop nonlinear system under the proposed control scheme have been rigorous proved and discussed by Lyapunov stability analysis. Finally, a two-link manipulator model has been given as an example, and the numerical simulations are given to express the availability of the proposed controller.

Distributed and Performance Guaranteed Robust Control for Uncertain MIMO Nonlinear Systems With Controllability Relaxation

In this paper, we investigate the distributed output tracking problem for networked uncertain nonlinear strict-feedback systems with intermittent actuator faults under a directed protocol. By embedding some performance functions into the control design, a distributed control scheme is developed that exhibits several salient features: 1)relaxing the system controllability conditions by inserting some differentiable compensation terms into the controllers; 2)dealing with mismatched uncertainties and accommodating actuation ineffectiveness automatically while achieving prescribed transient and steady-state tracking performance; 3)lowering structural and computational complexity by avoiding the derivatives of virtual controllers and desired trajectory, eluding the usage of extra observers to estimate the states of the neighbors, and demanding little prior information on system nonlinearities; and 4) reducing the communication burden by requiring only the output information from the neighbors for control design. All the closed-loop signals are ensured to be semi-globally ultimately uniformly bounded. Finally, the benefits of this method are verified via numerical simu

Disturbance-Compensation-Based Multilayer Neuroadaptive Control of MIMO Uncertain Nonlinear Systems

Committed to further enhancing the achievable tracking performance, a novel disturbance-compensation-based composite multilayer neural network adaptive control algorithm is developed for a class of multiple input multiple output nonlinear systems with modeling uncertainties. Specially, an extended state observer is utilized to estimate the exogenous disturbance and meanwhile predict the system state. Moreover, the nonlinear function uncertainties are approximated by the multilayer neural networks. Furthermore, the modeling uncertainties can be compensated in a feedforward manner. Notably, the multilayer neural network weights are updated via the composite adaption laws driven by the output tracking error and the prediction errors of the system state and control input, which brings improved function approximation performance. Finally, the application results demonstrate the efficacy of the integrated intelligent controller.

Anti-Disturbance Compensation-Based Nonlinear Control for a Class of MIMO Uncertain Nonlinear Systems.

Multi-Inputs-Multi-Outputs (MIMO) systems are recognized mainly in industrial applications with both input and state couplings, and uncertainties. The essential principle to deal with such difficulties is to eliminate the input couplings, then estimate the remaining issues in real-time, followed by an elimination process from the input channels. These difficulties are resolved in this research paper, where a decentralized control scheme is suggested using an Improved Active Disturbance Rejection Control (IADRC) configuration. A theoretical analysis using a state-space eigenvalue test followed by numerical simulations on a general uncertain nonlinear highly coupled MIMO system validated the effectiveness of the proposed control scheme in controlling such MIMO systems. Time-domain comparisons with the Conventional Active Disturbance Rejection Control (CADRC)-based decentralizing control scheme are also included.

Fixed-time output tracking control for a class of uncertain nonlinear MIMO systems

This article proposed a new fixed-time output tracking control scheme for a class of high-order MIMO nonlinear systems with unknown nonlinearities, parameter uncertainties and external disturbances. Firstly, a novel nonsingular recursive integral terminal sliding mode (ITSM) surface is designed by employing appropriate integral function and integer orders. Then the lumped system matched and mismatched uncertainties are estimated by developing a new adaptive fixed-time disturbance observer (AFTDO) based on super-twisting technique. The chattering problem existed in traditional disturbance observer (DO) can be reduced with the proposed AFTDO allowing the gains to adapt the changed derivative of lumped disturbances, effectively. Furthermore, semi-global fixed-time stability analysis is presented by means of Lyapunov stability theorem and it is proved that the system convergence time is independent of the system initial states and allowed to be arbitrarily adjusted based on practical demands. Finally, theoretical results are supported by numerical simulation and experimental results.

Adaptive Tracking for Uncertain MIMO Nonlinear Systems With Time-Varying Parameters and Bounded Disturbance

In this article, tracking control is considered for a class of uncertain multi-input-multi-output (MIMO) nonlinear systems, where the time-varying parameters, the time-varying control coefficient and the time-varying disturbance are assumed to be unknown but to be bounded. Three stable adaptive tracking schemes for a given reference signal are proposed by devising different control algorithms. In the first scheme, bounded-error tracking is achieved in the sense that the tracking error converges exponentially to an adjustable region around the origin, where the σ-modification adaptive laws are used to ensure the boundedness of all closed-loop signals. In the second scheme, asymptotic tracking is obtained in the sense that the tracking error converges to zero asymptotically, where the strictly positive and integral functions are employed in the control law to ensure the signal boundedness and zero-error tracking. In the third scheme, exponential tracking is gotten in the sense that the tracking error exponentially converges to zero with a given convergence speed, where exponential functions are incorporated into control law and adaptive laws to ensure system stability and the faster convergence. Three adaptive tracking schemes are, respectively, applied to nonlinear chaotic Chua's circuit with control inputs. The parametric model is developed for Chua's circuit with uncertain parameters and external disturbances. The effectiveness of the proposed control algorithms is demonstrated by comparative simulation studies.

Reduced Adaptive Fuzzy Decoupling Control for Lower Limb Exoskeleton.

This article reports our study on a reduced adaptive fuzzy decoupling control for our lower limb exoskeleton system which typically is a multi-input-multi-output (MIMO) uncertain nonlinear system. To show the applicability and generality of the proposed control methods, a more general MIMO uncertain nonlinear system model is considered. By decoupling control, the entire MIMO system is separated into several MISO subsystems. In our experiments, such a system may have problems (even unstable) if a traditional fuzzy approximator is used to estimate the complicated coupling terms. In this article, to overcome this problem, a reduced adaptive fuzzy system together with a compensation term is proposed. Compared to traditional approaches, the proposed fuzzy control approach can reduce possible chattering phenomena and achieve better control performance. By employing the proposed control scheme to an actual 2-DOF lower limb exoskeleton rehabilitation robot system, it can be seen from the experimental results that, as expected, it has good performance to track the model trajectory of a human walking gait. Therefore, it can be concluded that the developed approach is effective for the control of a lower limb exoskeleton system.

Robust adaptive dynamic surface back-stepping tracking control of high-order strict-feedback nonlinear systems via disturbance observer approach

In this study, we propose an adaptive tracking dynamic surface back-stepping control based on Nussbaum disturbance observer for uncertain high-order strict-feedback MIMO nonlinear systems with external disturbances, unknown parameters and modelling uncertainties. It is assumed that the control action is affected by input saturation; so to compensate the resulted undesirable effects, the tanh(.) function is used as an approximation to the saturation function. To tackle the unknown external disturbances and uncertainties, a Nussbaum disturbance observer is proposed. Moreover, an appropriate adaptive law is presented to deal with the unknown parameters. Then, the dynamic surface control method is used to overcome the inherent problem ‘explosion of complexity’ that appeared in the conventional back-stepping method. The Lyapunov stability analysis proves that the closed-loop system is semi-globally uniformly bounded. At last, reasonable effectiveness and applicability of the adaptive tracking dynamic surface control are illustrated by simulation results.

Adaptive neural fault-tolerant control for uncertain MIMO nonlinear systems with actuator faults and coupled interconnections

Handling both intermittent actuator faults and coupled interconnections in uncertain multiple-input–multiple-output nonlinear system is still a challenge in the control community. In this paper, to address this issue, an adaptive neural fault-tolerant control scheme is developed. Firstly, neural networks with random hidden nodes are used to approximate unknown functions, and an inequality is introduced to construct controllers such that the singularity problem of the controllers can be circumvented. Secondly, a projection algorithm is adopted to update online the estimated parameters in the controllers such that the boundedness of estimated parameters is ensured. In particular, the boundedness of estimate of unknown fault parameters with intermittent jumps can be definitely guaranteed. Due to the effects of intermittency jumps of unknown parameters on the system stability during operation, a modified Lyapunov function is developed to prove the system stability. It is proved that the system stability only depends on the jumping amplitude of Lyapunov function and the minimum fault time interval and is not affected by the total number of faults. Thirdly, a root mean square type of bound for the tracking error is established by using iterative calculation to illustrate that the system transient performance in the sense of the tracking error is adjustable by proper choice of design parameters. Finally, simulation studies are carried out to verify the effectiveness of the theoretical results.

Adaptive Fuzzy Control for Multivariable Nonlinear Systems with Indefinite Control Gain Matrix and Unknown Control Direction

Abstract In this paper, we focus on the direct adaptive fuzzy control design for a class of uncertain MIMO nonlinear systems with indefinite control gain matrix and unknown control direction. The control design is based on the approximation of an unknown ideal control law that can meet the control objective by using fuzzy systems. The adjustable parameters of the used fuzzy systems are adjusted online using the error between the unknown ideal controller and the fuzzy controller. In this paper, unlike most existing works, the Nussbaum gain technique is not used to overcome the obstacle of the unknown control direction. In fact, with the help of a matrix decomposition technique, the unknown control direction is redefined as an unknown constant vector, which is estimated online by a suitable update law. The stability of the closed-loop system is studied using the Lyapunov direct approach. Numerical simulation results are provided to illustrate the effectiveness of the proposed control design approach.

Adaptive high‐order sliding mode controller‐observer for MIMO uncertain nonlinear systems

AbstractIn this paper, an adaptive high‐order sliding mode controller‐observer is proposed for multi input–multi output uncertain systems with application to robotic manipulators. Firstly, a type‐2 Takagi‐Sugeno fuzzy system is used to model the original system. Next, with the unavailability of velocity measurement, a fuzzy high‐order sliding mode observer is designed to estimate both the joint velocities and uncertainties. Moreover, based on a super twisting second‐order sliding mode, the proposed robust controller generates smooth control and guarantees finite‐time convergence to the third‐order sliding set with respect to the sliding variable by keeping second‐order sliding mode constraint. The controller gains are generated based on an adaptive estimation scheme without overestimation. The finite‐time stability of the suggested controller is proved by using an homogeneous and strict Lyapunov function. Finally, the obtained simulation results for two‐link robot manipulators demonstrate the effectiveness of the proposed controller.

Distributed optimization for a class of uncertain MIMO nonlinear multi-agent systems with arbitrary relative degree

The paper is concerned with the distributed optimization problem (DOP) for a class of uncertain multi-input-multi-output (MIMO) nonlinear multi-agent systems with arbitrary relative degree. The target is to design distributed control laws such that the outputs of the agent systems converge to a consensus value and on which the sum of the local cost functions is minimized. By introducing pseudo gradient technique, internal model technique and adaptive control technique, a novel state based distributed control law is firstly constructed. An incremental type Lyapunov function based approach is presented to show that the proposed DOP is solved by the state based control law without requiring the eigenvalue information of Laplacian matrix. By further introducing distributed high-gain observer technique, an output based distributed control law is constructed and by which the DOP is solved under some mild assumption. The proposed control laws are validated on a group of Euler-Lagrange systems, a group of robot manipulators with flexible joints and a group of Chua circuit systems. The simulation results illustrate the effectiveness of the proposed methods.

Robust adaptive NN tracking control for MIMO uncertain nonlinear systems with completely unknown control gains under input saturations

This paper focuses on the study of tracking control problem for a class of multiple-input-multiple-output (MIMO) uncertain nonlinear systems with completely unknown control gains under input saturations. A hyperbolic tangent function is introduced to approximate the input saturation nonlinearity. Based on the above, a novel robust adaptive neural network (NN) tracking control scheme is proposed combining finite-time nonlinear tracking differentiator (FTNTD), Nussbaum-type function and adaptive NN with backstepping design tool. Within our scheme, a constructed novel nonlinear function featured by “small-error large-gain and large-error small-gain” is inset into virtual and actual control laws to achieve a balance between the feedback control gain and the system control performance and prevent the over-learning of parameter adaptive laws caused by the input saturation. By means of a newly constructed non-quadratic Lyapunov function, it is theoretically shown that all the signals in the closed-loop control system are semi-globally uniformly ultimately bounded. Finally, the effectiveness of our proposed scheme is verified by the simulations of two simulation examples.

Adaptive neural dynamic surface control of MIMO uncertain nonlinear systems with time-varying full state constraints and disturbances

In order to stabilize multiple-input–multiple-output uncertain strict feedback nonlinear systems with time-varying full-state constraints and external disturbances, an adaptive neural dynamic surface control method is investigated in this paper. A new compensator is proposed, which combines approximation error based adaptive radial basis function neural networks (RBFNNs) and nonlinear disturbance observer (NDOB) to improve the compensate performance of unmodeled dynamics and external disturbances. To prevent that the time-varying full state constraints are violated, the controller is designed via asymmetric time-varying barrier Lyapunov function (ATBLF). Meanwhile, the dynamic surface control is established to avoid the problem of “explosion of complexity” in traditional backstepping design. All closed-loop signals are proved to be semiglobally uniformly ultimate bounded through stability analysis. Finally, the simulation for six degrees of freedom (6-DOF) model unmanned airship are given to illustrate the effectiveness of the proposed control method.

Adaptive high order sliding mode controller/observer based terminal sliding mode for MIMO uncertain nonlinear system

ABSTRACT In this paper, an adaptive super twisting high order sliding mode controller observer is investigated for multi input–multi output uncertain system, with application to robotic manipulator based only on position measurement. First, a type-2 Takagi–Sugeno fuzzy system is used to model the original system. Next, by combining thefuzzy model with third order sliding mode observer, a novel fuzzy observer is designed to estimate both the joint velocities and uncertainties. Moreover, based on super twisting algorithm the proposed controller generates a smooth control signal and guarantees the finite time stabilisation of second order sliding mode. The controller gains are generated based on adaptive estimation scheme, in which the gains overestimation problem and the prior knowledge of the upper boundaries of uncertainties can be avoided. The stability of proposed controller/ observer scheme is discussed using Lyapunov approach. Finally, the obtained simulation results for two link robot manipulator demonstrate the effectiveness of the proposed controller.

Combining Prescribed Tracking Performance and Controller Simplicity for a Class of Uncertain MIMO Nonlinear Systems With Input Quantization

For the class of multi-input multi-output nonlinear systems, comprised of fully interconnected strict-feedback subsystems, having uncertain, though locally Lipschitz nonlinearities and input quantization equipped with a hysteretic property, the objective is to construct a closed-loop system that combines prescribed, output trajectory tracking performance attributes (maximum overshoot, minimum convergence rate, maximum steady-state error), and a low-complexity control solution. In this paper, the task is succeeded by designing a state-feedback controller that is not only structurally and computationally simple, but additionally it is decentralized and requires knowledge of the desired output trajectories only at each time instant. Further, no time derivatives of the output references are utilized. The aforementioned functionalities are achieved irrespectively of the quantization parameters, which besides being unknown, are considered as piecewise constant functions of time. Simulations are provided to verify and clarify the theoretical findings.