An output-feedback fuzzy approach to guaranteed cost control of vehicle lateral motion

This paper introduces a fuzzy guaranteed cost control approach for automated steering of a highway vehicle. The Takagi–Sugeno (T–S) fuzzy model is utilized to depict the dynamics of nonlinear time-varying lateral system. Based on the fuzzy model, an observer-based fuzzy controller is developed so that without knowing road’s curvature the vehicle can track center of the present lane on a curved highway section. Integrating H_∞ control and optimal control strategies, the fuzzy controller and observer are formulated by solving a minimization problem, which is to minimize a given quadratic performance function. Sufficient conditions to ensure minimum upper bound of the performance function are derived in terms of linear matrix inequalities (LMIs). Therefore, the designing work can be efficiently completed by applying the convex optimization techniques. Verified by computer simulation, the proposed method can perform well in driving safety and ride comfort.     

Further Results on H ∞ Filtering for a Class of Discrete-Time Singular Systems with Interval Time-Varying Delay

In this paper, the problem of delay-dependent robust H _∞ filtering for discrete-time singular systems with time-varying delay and polytopic uncertainties is investigated. Without introducing the free-weighting matrices to deal with the cross terms, a delay-dependent H _∞ performance analysis result is established for error singular system by considering the relationship between the time-varying delay and its bounds at first. Based on this result, a linear robust H _∞ filter is designed such that the filtering error singular system is regular, causal and asymptotically stable with a H _∞ norm bound. Numerical examples are given to show the advantages of the proposed results.     

Multi-objective control synthesis: an application to 4WS passenger vehicles

The vehicle dynamics and control play an important role in an automated highway system for passenger cars. This study addresses the problem of designing active controllers for four-wheel-steering (4WS) vehicles. We first obtain a set of linear maneuvering equations representing the four-wheel steering motions and independent wheel torques for lateral/directional plus roll dynamics. We then formulate simultaneous H₂ and H_∞ (sub)-optimal controls with a desired pole assignment via linear matrix inequalities (LMIs). The steering angles are actively controlled by steering wheel commands through the actuator mechanisms for the lateral/directional and roll motions. Further the wheel power and braking are directly controlled by independent torques. Numerical simulations are performed on a complex vehicle model in order to evaluate the vehicle performance (noise and disturbance attenuation), stability, and robustness under a given class of uncertainty. Finally, the presented autopilot controller provides greater maneuverability and improved directional stability for passenger vehicles.     

H ∞ Filtering for Systems with Delays and Time-varying Nonlinear Parameters

This paper is concerned with the gain-scheduled H _∞ filtering problem for a class of parameter-varying continuous systems with time delays. The systems under consideration are represented by nonlinear fractional transformation (NFT) which is a generalization of linear fractional transformation (LFT). Attention is focused on the design of a stable filter guaranteeing a prescribed disturbance attenuation level in an H _∞ sense. Sufficient solvability conditions of this problem are obtained based on Lyapunov function approach. A gain-scheduled filter can be constructed in terms of a set of linear matrix inequalities (LMIs). A numerical example is provided to demonstrate the applicability of the proposed approach.     

Exponential H ∞ Output Tracking Control for Switched Neutral System with Time-Varying Delay and Nonlinear Perturbations

In this paper, the problem of exponential H _∞ output tracking control is addressed for a class of switched neutral system with time-varying delay and nonlinear perturbations. The considered system consists of different neutral and discrete delays. By resorting to the average dwell time approach, a new Lyapunov–Krasovskii functional is proposed to establish sufficient conditions for the exponential stability and H _∞ performance of switched neutral systems. Then, the problem of exponential H _∞ output tracking control is investigated, an explicit expression for the desired exponential tracking controller is also given. Finally, a numerical example is provided to demonstrate the potential effectiveness of the proposed method.     

Delay-dependent H ∞ Control for Uncertain 2-D Discrete Systems with State Delay in the Roesser Model

This paper is concerned with the problem of H _∞ control for uncertain two-dimensional (2-D) state delay systems described by the Roesser model. Based on a summation inequality, a sufficient condition to have a delay-dependent H _∞ noise attenuation for this 2-D system is given in terms of linear matrix inequalities (LMIs). A delay-dependent optimal state feedback H _∞ controller is obtained by solving an LMI optimization problem. Finally, a simulation example of thermal processes is given to illustrate the effectiveness of the proposed results.     

H ∞ Filtering for Markovian Switching System with Mode-Dependent Time-Varying Delays

This paper deals with the problem of H _∞ filtering for Markovian switching systems. The system under consideration involves discrete and mode-dependent time-varying delays. The aim of this paper is to design a filter such that the filtering error system is stochastically stable with a prescribed H _∞ disturbance attenuation level. Sufficient conditions for the existence of H _∞ filters are expressed in terms of linear matrix inequalities (LMIs), which can be solved by using Matlab LMI control toolbox. Numerical examples are given by including a transmission control protocol (TCP) network model to illustrate the practical importance and effectiveness of the proposed main results.     

Robust H ∞ Control of a Class of Switching Nonlinear Systems with Time-Varying Delay Via T–S Fuzzy Model

This paper considers H _∞ control of a class of switching nonlinear systems with time-varying delays via T–S fuzzy model based on piecewise fuzzy weighting-dependent Lyapunov–Krasovskii functionals (PFLKFs). The systems are switching among several nonlinear systems. The Takagi and Sugeno (T–S) fuzzy model is employed to approximate the sub-nonlinear dynamic systems. Thus, with two level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce a continuous-time switched fuzzy systems, which inherently contain the features of the switched hybrid systems and T–S fuzzy systems. Average dwell-time approach and PFLKFs methods are utilized for the stability analysis and controller design, and with free fuzzy weighting matrix scheme. Switching and control laws are obtained such that the H _∞ performance is satisfied. The conditions of stability and the control laws are given in the form of LMIs which can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. A numerical example and the control of an uncertain radio-controlled (R/C) hovercraft with time-varying delay are given to demonstrate the efficiency of the proposed method.     

H ∞ Control of Piecewise-Linear Systems Under Unreliable Communication Links

This paper considers the problem of H _∞ control of piecewise-linear control systems under unreliable communication links. Due to the limited bandwidth of the channels, signal transmission delays and data packet losses can occur between the plant and the controller. In the presence of random signal transmission delays and data packet losses, a piecewise controller is designed to stabilize the piecewise-linear system in the sense of mean square and also achieve a prescribed H _∞ disturbance attenuation performance based on piecewise-quadratic Lyapunov–Krasovskii functionals. It is shown that the H _∞ controllers can be designed by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. Moreover, the controller design method is further extended to uncertain case where the system matrices’ uncertainties are represented in polytopic frameworks. Finally, an example is provided to illustrate the effectiveness of the developed theoretical results.     

H∞ loop shaping for the torque-vectoring control of electric vehicles: Theoretical design and experimental assessment

This paper presents an H_∞ torque-vectoring control formulation for a fully electric vehicle with four individually controlled electric motor drives. The design of the controller based on loop shaping and a state observer configuration is discussed, considering the effect of actuation dynamics. A gain scheduling of the controller parameters as a function of vehicle speed is implemented. The increased robustness of the H_∞ controller with respect to a Proportional Integral controller is analyzed, including simulations with different tire parameters and vehicle inertial properties. Experimental results on a four-wheel-drive electric vehicle demonstrator with on-board electric drivetrains show that this control formulation does not need a feedforward contribution for providing the required cornering response in steady-state and transient conditions.     

H ∞ Output Tracking Control for Discrete-Time Switched Systems Based on Switching Method

This paper addresses the H _∞ output tracking control problem for a class of discrete-time switched linear systems. We do not require that the H _∞ output tracking control problem for each individual subsystem to be solvable. Based on the multiple Lyapunov functions approach, a switching law depending on the system state is designed, which, together with the designed controllers, can guarantee that the output tracking error dynamics converges H _∞ asymptotically to zero. In sufficient conditions, we introduce an additional scalar matrix variable to realize the decoupling between the system matrices and Lyapunov matrices. The controller gains can be obtained by solving linear matrix inequalities (LMIs). A numerical example is provided to demonstrate the feasibility of the proposed design method.     

Robust Nonlinear H ∞ State Feedback Control of Polynomial Discrete-Time Systems: An Integrator Approach

This paper investigates the problem of designing a nonlinear H _∞ state feedback controller for polynomial discrete-time systems with norm-bounded uncertainties. In general, the problem of designing a controller for polynomial discrete-time systems is difficult, because it is a nonconvex problem. More precisely, in general, its Lyapunov function and control input are not jointly convex. Hence, it cannot be solved by semidefinite programming. In this paper, a novel approach is proposed, where an integrator is incorporated into the controller structure. In doing so, a convex formulation of the controller design problem can be rendered in a less conservative way than the available approaches. Furthermore, we establish the interconnection between robust H _∞ control of polynomial discrete-time systems with norm-bounded uncertainties and H _∞ control of scaled polynomial discrete-time systems. This establishment allows us to convert the robust H _∞ control problems to H _∞ control problems. Then, based on the sum of squares (SOS) approach, sufficient conditions for the existence of a nonlinear H _∞ state feedback controller are given in terms of solvability of polynomial matrix inequalities (PMIs), which can be solved by the recently developed SOS solvers. A tunnel diode circuit is used to demonstrate the validity of this integrator approach.     

H ∞ Filtering for Stochastic Systems with Markovian Switching and Partly Unknown Transition Probabilities

This paper considers the H _∞ filtering problem for stochastic systems. The systems under consideration involve Markovian switching, mode-dependent delays, Itô-type stochastic disturbance, distributed time-varying delays and partly unknown transition probabilities. Our aim is to design a full-order filter such that the corresponding filtering error system is stochastically stable and satisfies a prescribed H _∞ disturbance attenuation level. By using a new Lyapunov–Krasovskii functional, sufficient conditions are formulated in terms of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed main results.     

Position control of a pneumatic surgical robot using PSO based 2-DOF H∞ loop shaping structured controller

This research proposed novel development of a 2-DOF H_∞ loop shaping structured controller based on Particle Swarm Optimization (PSO) that considers the closed-loop dynamic response, robustness, stability, and minimal control input in design criteria to control position of 3-DOF pneumatic surgical robot. Unlike other conventional H_∞ controllers, the proposed controller offers robustness, high performance, but cost-effective simple structure, which has recently received attention from several researchers and preferred in industrial applications. The proposed technique is simulated and experimented on a nonlinear system of a pneumatic 3-DOF surgical robot for a Minimally Invasive Surgery (MIS). Mechanical design, dynamics modeling, and system identification of the surgical robot are conducted. The simulation results verify that the proposed controller can gain a better H_∞ sub-optimal solution than the conventional 2-DOF H_∞ loop shaping controller. Also, the experiments confirm that the proposed controller is capable to tolerate the perturbed conditions and can be alternative to the conventional controllers in pneumatic controlled system     

Mean-square H∞ filtering for stochastic systems: Application to a 2DOF helicopter

This paper designs the central finite-dimensional H_∞ filter for linear stochastic systems with integral-quadratically bounded deterministic disturbances, that is suboptimal for a given threshold γ with respect to a modified Bolza-Meyer quadratic criterion including the attenuation control term with the opposite sign. The original H_∞ filtering problem for a linear stochastic system is reduced to the corresponding mean-square H₂ filtering problem, using the technique proposed in Doyle (1989) [1]. In the example, the designed filter is applied to estimation of the pitch and yaw angles of a two degrees of freedom (2DOF) helicopter.     

Robust H ∞ Output Tracking Control for a Class of Nonlinear Systems with Time-Varying Delays

This paper addresses the H _∞ output tracking problem for a class of nonlinear systems subjected to model uncertainties and with interval time-varying delay. The stability of the nonlinear time-delay system is analyzed with a novel delay-interval-dependent Lyapunov–Krasovskii functional. Compared to state-of-the-art criteria for linear and nonlinear time-delay systems, less conservative stability conditions are derived with the introduction of new delay-interval-dependent terms and the exploitation of the delay subintervals size. The proposed analysis considers that the delay derivative is either upper and lower bounded, bounded above only, or unbounded, i.e., no restrictions are cast upon the derivative. Numerical examples are provided to enlighten the importance and advantages of the present criterion which outperforms previous criteria in time-delay systems literature. Also, an additional example is provided to highlight the effectiveness of the proposed H _∞ output tracking control design technique for complex nonlinear systems with time-varying delay.     

Relaxed H ∞ Controller Design for Continuous Markov Jump System with Incomplete Transition Probabilities

This paper studies the H _∞ state feedback control of continuous-time Markov jump linear systems (MJLSs) with incomplete transition probabilities (TPs) which are allowed to be known, uncertain with known lower and upper bounds, and completely unknown. Combining the TP property and a matrix transformation technique, a new method for the H _∞ controller synthesis is proposed in terms of linear matrix inequalities (LMIs). The dominant feature of the proposed method is that two sets of slack variables without coupling relationship are introduced. It is shown that the proposed method is less conservative than the existing result. The effectiveness of the proposed method is further illustrated by numerical examples.     

Robust H ∞ Control for a Class of 2-D Nonlinear Discrete Stochastic Systems

This paper is concerned with the problem of stability and robust H _∞ control for 2-D stochastic systems with parameter uncertainties and sector nonlinearities. The class of systems under investigation is described by the 2-D state-space Roesser model. Our attention is focused on the design of a state feedback controller for 2-D stochastic system with sector nonlinearity, such that the closed-loop 2-D stochastic system is asymptotically stable and has a prescribed H _∞ disturbance attenuation performance. First, a sufficient condition is established for the 2-D nonlinear stochastic systems to be asymptotically stable. Then, we extend the bounded real lemma for 2-D systems to 2-D stochastic systems with sector nonlinearities. Based on this lemma, solvability conditions for the H _∞ control of 2-D nonlinear stochastic systems in the form of LMIs (linear matrix inequalities) are derived. A numerical example illustrates the effectiveness of the proposed results.