Hinfin State Feedback Controller Research Articles

基于H无穷状态反馈控制的插秧机曲线路径跟踪控制器研究

The accuracy of curved path-tracking for headland turning of transplanters is crucial to maintaining the row spacing precision required for rice planting. To address this issue, a method based on H-infinity state feedback control is proposed. In this method, the requirement of robustness is transformed into linear matrix inequalities (LMIs) to optimize the gain coefficients of the control law. The simulation test show that this method outperforms the Linear Quadratic Regulator (LQR) when facing uncertain parameters (longitudinal speed and cornering stiffness) and path curvature disturbance. In addition, the field test results show that when the transplanter tracks a 1/4 circular arc path with a radius of 2 meters, the mean value of the absolute lateral error and the absolute heading angle error using this controller are 0.029 m and 3.69°, respectively. The maximum absolute lateral error is 0.072 m, and 64% of the absolute lateral error are less than 0.04 m, meeting practical requirements. Compared with the LQR controller with feed forward control, the mean value of the absolute lateral error is reduced by 36%. This method meets the accuracy and robustness requirements for unmanned rice transplanter turning at the headland.

Comparative Study of Trajectory Tracking Control for Automated Vehicles via Model Predictive Control and Robust H-infinity State Feedback Control

A comparative study of model predictive control (MPC) schemes and robust H_{infty } state feedback control (RSC) method for trajectory tracking is proposed in this paper. The main objective of this paper is to compare MPC and RSC controllers’ performance in tracking predefined trajectory under different scenarios. MPC controller is designed based on the simple longitudinal-yaw-lateral motions of a single-track vehicle with a linear tire, which is an approximation of the more realistic model of a vehicle with double-track motion with a non-linear tire mode. RSC is designed on the basis of the same method as adopted for the MPC controller to achieve a fair comparison. Then, three test cases are built in CarSim-Simulink joint platform. Specifically, the verification test is used to test the tracking accuracy of MPC and RSC controller under well road conditions. Besides, the double lane change test with low road adhesion is designed to find the maximum velocity that both controllers can carry out while guaranteeing stability. Furthermore, an extreme curve test is built where the road adhesion changes suddenly, in order to test the performance of both controllers under extreme conditions. Finally, the advantages and disadvantages of MPC and RSC under different scenarios are also discussed.

Nonlinear H-Infinity Model Reference Controller Design

In this work, a nonlinear and robust controller is proposed for nonlinear uncertain systems by consolidating the H-infinity state feedback control with the model reference control approach. The proposed controller is motivated to achieve a satisfactory transient response by inserting a reference model. The upper and lower linear fractional transformations are constructed in order to extract the structured parametric uncertainties. The controller design procedure is performed based on the small gain theorem. Next, the proposed controller gain matrix is calculated by solving the H-infinity algebraic Riccati equation. The Lyapunov stability analysis is used to show the stability properties of the controlled system. To show the effectiveness of the proposed controller, two types of nonlinear uncertain systems are presented as case studies. Finally, the results demonstrate that the proposed controller is powerful and efficient in compensating the nonlinear uncertain systems and in imposing the asymptotic tracking between the system states and the reference model states.

A robust H-infinity controller design approach for neutral systems with time-varying delay and plant and controller uncertainties

This paper is concerned with a state feedback controller design method for neutral systems with a time-varying delay, considering uncertainties in the plant parameters, as well as in controller gain. The uncertainties are in additive form, affecting both the system matrices of the plant and the controller gain. The uncertainties that are assumed admissible are time-varying and norm-bounded. The neutral system is also subject to external disturbances. A robust stabilizing H-infinity state-feedback controller is synthesized under several conditions that are presented in the form of matrix inequalities. A new generalized type of Jensen integral inequality has been introduced for utilization in the derivation of the aforementioned results, which could thus have been relaxed via that approach. A feasible solution set is obtained using the well-known cone complementarity technique by solving a non-linear minimization problem subject to linear matrix inequalities. A numerical example with case studies concludes the present work. The results of the minimum achievable attenuation rate indicate considerable improvement in comparison with those reported in the literature.

Robust Control of Formation Dynamics for Autonomous Underwater Vehicles in Horizontal Plane

This paper presents a novel robust controller design for formation control of autonomous underwater vehicles (AUVs). We consider a nonlinear three-degree-of-freedom dynamic model for the horizontal motion of each AUV. By using the Jacobi transform, the horizontal dynamics of AUVs are explicitly expressed as dynamics for formation shape and formation center, and are further decoupled by feedback control. We treat the coupling terms as perturbations to the decoupled system. An H-infinity state feedback controller is designed to achieve robust stability of the closed loop formation and translation dynamics. By incorporating an orientation controller, the formation shape under control converges and the formation center tracks a desired trajectory simultaneously. Simulation results demonstrate the effectiveness of the controllers.

GA-based nonlinear predictive switching control for a boiler-turbine system

In this paper, the problem of designing a controller for a highly coupled constrained nonlinear boiler-turbine system is addressed with a predictive controller. First, a nonlinear predictive control is implemented by genetic algorithm. Second, to guarantee fast output stabilization, an H-infinity fuzzy state-feedback tracking control is applied with a designed switching principle. The success of such a control structure is based on taking advantage of the optimal input sequence derived from the nonlinear predictive control based on artificial intelligent while ensuring a fast decay of the steady state error. Simulation results of the proposed design are given to illustrate its effectiveness and compared to other control schemes.

Decentralized H-infinity state feedback control for discrete-time singular large-scale systems

The decentralized H-infinity control problem for discrete-time singular large-scale systems is considered. Based on the bounded real lemma of discrete-time singular systems, a sufficient condition for the existence of decentralized H-infinity controller for discrete-time singular large-scale systems is presented in terms of the solvability to a certain system of linear matrix inequalities by linear matrix inequality (LMI) approach, and the feasible solutions to the system of LMIs provide a parameterized representation of a set of decentralized H-infinity controller. The given example shows the application of the method.

H-Infinity State Feedback Control for a Class of Networked Cascade Control Systems With Uncertain Delay

Based on practical industrial process control, a typical configuration for networked cascade control systems (NCCSs) is analyzed. This kind of NCCSs with state feedback controllers, in which the network-induced delay is uncertain and less than a sampling period, is studied. The sufficient condition for the stabilizability of the NCCSs without disturbances is proposed, and the state feedback stabilization control laws are derived via Lyapunov stability theory and linear matrix inequality (LMI) approach. For the NCCSs with disturbances, the criterion of its robust asymptotically stability is derived and the ¿ -suboptimal state feedback <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">¿</sub> control laws are designed. The ¿-optimal state feedback <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">¿</sub> control laws are also put forward by optimizing a set of LMIs. A simulation example of a NCCS for the main steam temperature in a power plant is given to demonstrate the effectiveness of the proposed approaches.

Multi-Objective Robust $H_{\infty}$ Control of Spacecraft Rendezvous

Based on the relative motion dynamic model illustrated by C-W equations, the problem of robust Hinfin control for a class of spacecraft rendezvous systems is investigated, which contains parametric uncertainties, external disturbances and input constraints. An Hinfin state-feedback controller is designed via a Lyapunov approach, which guarantees the closed-loop system to meet the multi-objective design requirements. The existence conditions for admissible controllers are formulated in the form of linear matrix inequalities (LMIs), and the controller design is cast into a convex optimization problem subject to LMI constraints. An illustrative example is provided to show the effectiveness of the proposed control design method.

${\cal H}_{\infty}$ State-Feedback Control Design for Fuzzy Systems Using Lyapunov Functions With Quadratic Dependence on Fuzzy Weighting Functions

This paper proposes a method for designing an Hinfin state-feedback fuzzy controller for discrete-time Takagi-Sugeno (T-S) fuzzy systems. To derive less conservative Hinfin stabilization conditions, this paper enhances the interactions among the fuzzy subsystems using a multiple Lyapunov function with quadratic dependence on fuzzy weighting functions. Besides, for more allocation of the nonlinearity to the fuzzy control system, this paper introduces a slack variable that is quadratically dependent on the one-step-past fuzzy weighting functions as well as the current ones. In the derivation, the Hinfin stabilization conditions are formulated in terms of parameterized linear matrix inequalities (PLMIs), which are reconverted into LMI conditions with the help of an efficient relaxation technique.

Neural network solution for finite-horizon H-infinity constrained optimal control of nonlinear systems

In this paper, neural networks are used to approximately solve the finite-horizon constrained input H-infinity state feedback control problem. The method is based on solving a related Hamilton-Jacobi-Isaacs equation of the corresponding finite-horizon zero-sum game. The game value function is approximated by a neural network with time-varying weights. It is shown that the neural network approximation converges uniformly to the game-value function and the resulting almost optimal constrained feedback controller provides closed-loop stability and bounded L 2 gain. The result is an almost optimal H-infinity feedback controller with time-varying coefficients that is solved a priori off-line. The effectiveness of the method is shown on the Rotational/Translational Actuator benchmark nonlinear control problem.

$H_{\infty}$ Control of Discrete-Time Systems With Multiple Input Delays

This paper is concerned with the finite horizon Hinfin full-information control for discrete-time systems with multiple control and exogenous input delays. We first establish a duality between the Hinfin full-information control and the H2 smoothing of a stochastic backward system in Krein space. Like the duality between the linear quadratic regulation (LQR) of linear systems without delays and the Kalman filtering, the established duality allows us to address complicated multiple input delay problems in a simple way. Indeed, by applying innovation analysis and standard projection in Krein space, in this paper we derive conditions under which the Hinfin full-information control is solvable. An explicit controller is constructed in terms of two standard Riccati difference equations of the same order as the original plant (ignoring the delays). As special cases, solutions to the Hinfin state feedback control problem for systems with delays only in control inputs and the Hinfin control with preview are obtained. An example is given to demonstrate the effectiveness of the proposed Hinfin control design

H-infinity control for networked control systems (NCS) with time-varying delays

This paper discusses H-infinity state feedback control for a networked control system with time-varying delays. Based on the free-weighing matrix method, a delay-dependent stability criterion satisfying a prescribed H-infinity norm bound is presented for an NCS with unknown, time-varying and bounded delays. And then, the criterion is transformed into sufficient conditions based on linear matrix inequalities for H-infinity control. The conditions thus obtained are also used to design an H-infinity state feedback controller. This design method is further extended to solve the design problem of robust H-infinity state feedback control. A numerical example demonstrates the validity of die method.

Delay-dependent H-infinity control for linear descriptor systems with delay in state

A delay-dependent H-infinity control for descriptor systems with a state-delay is investigated. The purpose of the problem is to design a linear memoryless state-feedback controller such that the resulting closed-loop system is regular, impulse free and stable with an H-infinity norm bound. Firstly, a delay-dependent bounded real lemma(BRL) of the time-delay descriptor systems is presented in terms of linear matrix inequalities(LMIs) by using a descriptor model transformation of the system and by taking a new Lyapunov-Krasovsii functional. The introduced functional does not require bounding for cross terms, so it has less conservation.Secondly, with the help of the obtained bounded real lemma, a sufficient condition for the existence of a new delay-dependent H-infinity state-feedback controller is shown in terms of nonlinear matrix inequalities and the solvability of the problem can be obtained by using an iterative algorithm involving convex optimization. Finally, numerical examples are given to demonstrate the effectiveness of the new method presented.

Robust Hinfinity state feedback control of discrete time-delay linear systems with norm-bounded uncertainty

This paper studies, via a linear matrix inequality approach, the problem of Hinfinity control for discrete time-delay linear systems with parametric uncertainty. The system under consideration is subjected to both time-varying norm-bounded parameter uncertainty and time delay in the state. First, the problem of robust stability of the underlying system is investigated. Next, we address the problem of robust Hinfinity state feedback control in which both robust stability and a prescribed Hinfinity performance are required to be achieved irrespective of the uncertainty and time delay. It is shown that the above problem can be solved if a linear matrix inequality has a symmetric positive definite solution.