L2-gain Design Research Articles

Disturbance suppression and NN compensation based trajectory tracking of underactuated AUV

For the trajectory tracking of underactuated autonomous underwater vehicle (AUV) subject to disturbances, a disturbance suppression and neural network (NN) compensation based control strategy is proposed. Lyapunov method is used to guide the overall design of control system. To deal with the underactuation, Light of sight (LOS) guidance is used to establish the relationship between heading angle and cross-track error. To suppress the external disturbance, L2-gain design is employed to guarantee the controller robustness. To improve the tracking accuracy, on-line neural networks with guaranteed stability are designed to identify unknown dynamics including the derivatives of virtual controls and errors induced by input saturation. Numerical simulation is performed to verify the effectiveness of the proposed control strategy. Compared with sliding mode controller (SMC) and disturbance observer approaches, the proposed controller performs better in terms of robustness and the input saturation is alleviated.

L2-Gain-Based Practical Stabilization of an Underactuated Surface Vessel

To obtain a stabilizer for an underactuated surface vessel with disturbances, an L2-gain design is proposed. Surge, sway, and yaw motions are considered in the dynamics of a surface ship. To ob-tain a robust adaptive controller, a diffeomorphism transformation and the Lyapunov function are employed in controller design. Two auxiliary controllers are introduced for an equivalent sys-tem after the diffeomorphism transformation. Different from the commonly used disturbance ob-server-based approach, the L2-gain design is used to suppress random uncertain disturbances in ship dynamics. To evaluate the controller performance in suppressing disturbances, two error sig-nals are defined in which the variables to be stabilized are incorporated. Both time-invariant dis-continuous and continuous feedback laws are proposed to obtain the control system. Stability analysis and simulation results demonstrate the validity of the controllers proposed. A comparison with a sliding mode controller is performed, and the results prove the advantage of the proposed controller in terms of faster convergence rate and chattering avoidance.

A unified approach to output synchronization of heterogeneous multi-agent systems via L2-gain design

In this paper, a unified design procedure is given for output synchronization of heterogeneous multi-agent systems (MAS) on communication graph topologies, using relative output measurements from neighbors. Three different control protocols, namely, full-state feedback, static output-feedback, and dynamic output-feedback, are designed for output synchronization. It is seen that a unified design procedure for heterogeneous MAS can be given by formulation and solution of a suitable local L2-gain design problem. Sufficient conditions are developed in terms of stabilizing the local agents’ dynamics, satisfying a certain small-gain criterion, and solving the output regulator equations. Local design procedures are presented for each agent to guarantee that these sufficient conditions are satisfied. The proposed control protocols require only one copy of the leader’s dynamics in the compensator, regardless of the dimensions of the outputs. This results in lower-dimensional compensators for systems with high-order outputs, compared to the p-copy internal model approach. All three proposed control protocols are verified using numerical simulations.

Identification Recurrent Type 2 Fuzzy Wavelet Neural Network and L2‐Gain Adaptive Variable Sliding Mode Robust Control of Electro‐Hydraulic Servo System (EHSS)

AbstractAn electro‐hydraulic servo system (EHSS) is a kind of system with the characteristics of time‐variant, serious nonlinearity, parameter and structural uncertainty, and uncertain load disturbance in most cases. These characteristics make it very difficult to realize highly accurate control by conventional methods. In order to solve the above problems, this paper introduces a recurrent type 2 fuzzy wavelet neural network to approximate the unknown nonlinear functions of the dynamic systems through tuning by the desired adaptive law. Based on the identification by recurrent type 2 fuzzy wavelet neural network, a L2 gain design method, combining gain adaptive variable sliding mode control with H infinity control, is proposed for load disturbance, thereby accommodating uncertainties that are the main factors affecting system stability and accuracy in EHSS. In this algorithm, a recurrent type 2 fuzzy wavelet neural network is employed to evaluate the unknown dynamic characteristics of the system and gain adaptive variable sliding mode control to compensate for evaluating errors, and H infinity control to suppress the effect on system by load disturbance. The experiment results show that the proposed system L2 gain design method can make the system exhibit strong robustness to parameter variation and load disturbance.

Control for Ship Course-Keeping Using Optimized Support Vector Machines

Support vector machines (SVM) are proposed in order to obtain a robust controller for ship course-keeping. A cascaded system is constructed by combining the dynamics of the rudder actuator with the dynamics of ship motion. Modeling errors and disturbances are taken into account in the plant. A controller with a simple structure is produced by applying an SVM and L2-gain design. The SVM is used to identify the complicated nonlinear functions and the modeling errors in the plant. The Lagrangian factors in the SVM are obtained using on-line tuning algorithms. L2-gain design is applied to suppress the disturbances. To obtain the optimal parameters in the SVM, then particle swarm optimization (PSO) method is incorporated. The stability and robustness of the close-loop system are confirmed by Lyapunov stability analysis. Numerical simulation is performed to demonstrate the validity of the proposed hybrid controller and its superior performance over a conventional PD controller.

Adaptive H∞ Consensus Control of Multi-Agent Systems on Directed Graph by Utilizing Neural Network Approximators

Design methods of adaptive H∞ consensus control of multi-agent systems composed of the first-order and the second-order regression models on directed network graphs and with nonlinear terms by utilizing neural network approximators, are presented in this paper. The proposed control schemes are derived as solutions of certain H∞ control problems, where estimation errors of tuning parameters and approximate and algorithmic errors in neural network estimation schemes are regarded as external disturbances to the process. It is shown that the resulting control systems are robust to uncertain system parameters and that the desirable consensus tracking is achieved approximately via adaptation schemes and L2-gain design parameters.

Robust fin control for ship roll stabilization based on L2-gain design

A robust fin controller based on L2 gain design is proposed, in order to reduce the roll motion of surface ships. The plant consists of the ship roll dynamics and that of the fin actuator. The uncertainties including the modelling errors and the environmental disturbances induced by waves are considered in the cascaded roll system. A state feedback control is adopted to compensate the modelling errors and the derivative of desired fin angle. The disturbance is suppressed by L2 gain design. The Lyapunov function is employed in the controller design, which guarantees the stability of the fin stabilizer. Simulation results are reported and the superior performance of the fin controller with L2-gain design is illustrated when compared to a PD controller.

Neural-Network- and L2-Gain-Based Cascaded Control of Underwater Robot Thrust

This paper presents a robust cascaded control strategy to underwater robot thrust. The dynamics of surge motion, of propeller axial flow, of propeller shaft, and of electrically driven circuit in the motor constitute a cascaded system with respect to propeller thrust. Instead of the usual parameter perturbation, generalized modeling errors are considered in the plant, which may be parametric errors, ignored high-order modes, or some unmodeled dynamics in the underwater thrust system. External disturbances are also taken into account, which may be the random noises from mechanical or electrical equipment, or the environmental forces possibly induced by nonuniform currents, ocean internal wave, or cable tension. Combined with state feedback control, an online neural network (NN) compensator is introduced to identify the modeling errors, while L2-gain design is used to suppress the externally continuous or instantaneous disturbances. The Lyapunov's second method is applied to instruct the controller design, which guarantees the uniformly ultimately bounded (UUB) stability of the error system. By analyzing the tracking errors, it is recommended how to properly select the controller parameters. Good tracking performance and reasonable control inputs are illustrated by numerical simulations.

Adaptive H∞ Consensus Control of Multi-Agent Systems

Design methods of adaptive H∞ consensus control of multi-agent systems composed of the first-order and the second-order regression models are presented in this paper. The proposed control schemes are derived as solutions of certain H∞ control problems, where estimation errors of tuning parameters and imperfect knowledge of the leader are regarded as external disturbances to the processes. It is shown that the resulting control systems are robust to uncertain system parameters and that the desirable consensus tracking is achieved approximately via adaptation schemes and L2-gain design parameters.

Global L2-gain design for a class of nonlinear systems

It is known that the so-called H ∞ control problem of a nonlinear system is locally solvable if the corresponding problem for the linearized system can be solved by linear feedback. In this paper we prove that this condition suffices to solve also a global H ∞ control problem, for a fairly large class of nonlinear systems, if one is free to choose a state-dependent weight of the control input. Using a two-way (backward and forward) recursive induction argument, we simultaneously construct, starting from a solution of the Riccati algebraic equation, a global solution of the Hamilton–Jacobi–Isaacs partial differential equation arising in the nonlinear H ∞ control, as well as a state feedback control law that achieves global disturbance attenuation with internal stability for the nonlinear systems.