Robust adaptive control of uncertain nonlinear systems with unmodeled dynamics using command filter

In this work, a distributed cooperative control strategy is proposed for multiple high-speed trains (MHSTs) subject to input saturation and unmodeled dynamics. To facilitate the distributed controller design, the dynamics of trains are firstly modeled as a muti-agent system (MAS) with a state-dependent directed graph. Then, the distributed control laws that are equipped with a command filter and a robust adaptive neural network are developed to achieve the consensus task among the MHSTs with predefined displacement and speed trajectories. It should be highlighted that, to reduce the complexity of the control algorithms and computational burden, we propose adaptive estimation laws to estimate the upper bound of the norm of the neural network weight vectors, instead of the weights themselves. Further, an auxiliary dynamical system (ADS) is introduced to compensate the influence of the input saturation. The convergence of the proposed controllers are analyzed rigorously by applying Lyapunov theorem, and the effectiveness of the proposed control approach is demonstrated by numerical simulations.

Finite-time adaptive neural command filtered control for non-strict feedback uncertain multi-agent systems including prescribed performance and input nonlinearities

In this paper, a robust adaptive fuzzy control for a class of nonlinear uncertain systems preceded by an unknown dead-zone and with unknown upper bound of uncertainties is developed. The dead-zones are quite commonly encountered in many systems (e.g., DC servosystem, robot, and machine tools), are usually poorly known, and may severely limit the performance of control. In addition, the system uncertainties (e.g., parameter variations, or external load, unmodeled dynamics) often exist. Therefore, the controllers are required to deal with the robust stability and performance of the systems with unknown dead-zone and in the presence of uncertainties, whose upper bound is generally unknown. In the beginning, an adaptive dead-zone compensation is employed to improve system performance. Then the unknown system functions and the unknown upper bound of system uncertainties are respectively approximated by fuzzy logic systems with unknown weights. The unknown bounds caused by the learning error of the slope of dead-zone and the system functions are also tackled by an extra learning law. The above weights are all on-line learned to provide for the controller design. Moreover, the projection terms in these learning laws are designed such that the boundedness of the learning weight can be assured.

The finite‐time command filter tracking control for a class of nonstrictly feedback nonlinear systems with unmodeled dynamics and full‐state constraints is investigated in this paper. The hyperbolic tangent function is used as a nonlinear mapping technique to solve the obstacle of the full‐state constraints. A new adaptive finite time control method is proposed through command filtering reverse engineering, and the shortcomings of the dynamic surface control (DSC) method are overcome by the error compensation mechanism. Dynamic signal is designed to handle dynamical uncertain terms. Normalization signal is designed to handle input unmodeled dynamics. Unknown nonlinear functions are approximated by radial basis function neural networks. Based on the Lyapunov stability theory, it is proved that all signals in the closed‐loop system are semi‐globally consistent and finally bounded and the output tracking error converges in finite time. Two numerical examples are utilized to verify the effectiveness of the proposed control approach.

The problem of adaptive robust control for uncertain nonlinear systems with time-varying delay is considered in this paper. The upper bound of the uncertainty is assumed to be nonlinear functions with unknown coefficients. By using adaptive control method, a class of adaptive robust state feedback controller is proposed. Based on Lyapunov-Krasovskii method and Lyapunov stability theory, it is shown that the controller designed can render the uniform asymptotic stability of the system. Finally, a numerical example is given to show the controller is valid.

This paper develops a L1 adaptive output-feedback fault-tolerant controller for uncertain nonlinear systems in the presence of unmodeled actuator dynamics and actuator faults. The proposed controller consists of the output predictor, adaptive laws, and the control law. The output predictor is a dynamic system expressed as a linear system with adaptive parameters which mean the matched uncertainties and the unmatched uncertainties. Piecewise-constant adaptive laws are designed to update the adaptive parameters so that the estimation error is driven to zero at each integration time step. The control law with low-pass filters is introduced to compensate for the performance degradation because of system uncertainties, unmodeled actuator dynamics and faults, and to guarantee the uniform boundedness of the input and output signals of the system. Two simulation examples verify the effectiveness of the proposed controller.

Utilizing the feature of quick response of HVDC to improve the performance of AC/DC system has become the emphasis to be researched. This paper introduces firstly the principle of the robust adaptive control of nonlinear systems with unmodeled dynamics, then developed the robust adaptive additional control of HVDC with unmodeled dynamics of generator in order to improve stability of power system. The additional control of HVDC with unmodeled dynamics only uses the local signals and its design is simple, furthermore it can obviously improve the stability of power system in different operational conditions. Experimental results using the presented concepts obtained on single machine infinite bus model are also included. These results prove the efficiency of the control scheme. The design process of controller provided a new idea to design controller by use of simplified model.

This paper describes a hybrid approach to the problem of controlling a class of nonlinear systems in the face of both unknown nonlinearities and unmodeled dynamics. In the proposed methodology, neural networks and direct adaptive control compensate for unknown nonlinear mappings while dynamic nonlinear damping provides robustness to unmodeled dynamics. To illustrate the theoretical development, the authors design a longitudinal autopilot for a simplified nonlinear missile aerodynamic model with input unmodeled dynamics. Simulation results demonstrate robustness in the face of this type of uncertainty.

Adaptive neural tracking control of pure-feedback nonlinear systems with unknown gain signs and unmodeled dynamics

This paper explores adaptive fixed-time control for nonstrict-feedback nonlinear systems affected by input saturation and external disturbances, employing a command-filtered approach. To manage input saturation nonlinearity, a smooth non-affine function approximates the saturation effect. Radial basis function networks (RBFNN) estimate unknown nonlinear functions of the system, while adaptive techniques combined with backstepping design form a fixed-time control strategy. The “explosion of complexity” issue from derivatives of virtual controllers is reduced using command filters. To address filter errors and improve over conventional methods such as dynamic surface control, an error compensation mechanism is added. The proposed strategy ensures effective transient and steady-state tracking performance by applying a funnel constraint function. Using fixed-time stability theory, the tracking error convergence within fixed time and the boundedness of closed-loop signals are validated. Simulation results confirm the scheme’s effectiveness.

Neural network-based adaptive fault-tolerant control for nonlinear systems with unknown backlash-like hysteresis and unmodeled dynamics

Observer-based Adaptive Controller Design for Nonlinear Saturation Systems With Output Constraints

In this chapter, we present a new scheme to design adaptive controllers for uncertain nonlinear systems in the presence of input saturation. Similar to previous chapters, the developed controllers do not require uncertain parameters within a known compact set. Besides showing global stability, transient performance is also established and can be adjusted by tuning certain design parameters.

A nonlinear adaptive control algorithm is presented for a model helicopter to achieve the trajectory tracking in the presence of external disturbances. The design process is based on the backstepping technology with the simplified helicopter model. A command filter is utilized to avoid the complicated derivative computation of the virtual control. With the property of the hyperbolic tangent function, upper bounds of the disturbing terms composed by unmodeled dynamics, command filter errors and other external disturbances are estimated by adaptive algorithms and compensated for in control laws. It is proved that the proposed control algorithm guarantees uniform boundedness of the tracking error of the complete closed-loop system. Simulations verify the significant tracking performance of the proposed controller.

In this paper, the problem of adaptive neural control is considered for a class of strict-feedback nonlinear systems with unmodeled dynamics, dynamic disturbances and unknown input saturation. During the controller design, radial basis functions(RBF) neural networks are applied to model the unknown nonlinearities, and an adaptive neural control scheme is developed via backstepping, which guarantees that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded in mean square. A simulation example is provided to show the effectiveness of the proposed control scheme.