There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

1. Control Methodology 2. Dynamical Systems 3. Applications to Social and Environmental Problems

Dynamics and Control

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Introduction To Stochastic Control Theory

This paper presents a robust $H_{\infty}$ path following control strategy for autonomous ground vehicles with delays and data dropouts. The state measurements and signal transmissions usually suffer from inevitable delays and data packet dropouts, which may degrade the control performance or even deteriorate the system stability. A robust $H_{\infty}$ state-feedback controller is proposed to achieve the path following and vehicle lateral control simultaneously. A generalized delay representation is formulated to include the delays and data dropouts in the measurement and transmission. The uncertainties of the tire cornering stiffnesses and the external disturbances are also considered to enhance the robustness of the proposed controller. Two simulation cases are presented with a high-fidelity and full-car model based on the CarSim–Simulink joint platform, and the results verify the effectiveness and robustness of the proposed control approach.

Robust $H_{\infty}$ Path Following Control for Autonomous Ground Vehicles With Delay and Data Dropout

Operation optimization for modern subway trains usually requires the speed curve optimization and speed curve tracking simultaneously. For the speed curve optimization, a multi-objective seeking issue should be addressed by considering the requirements of energy saving, punctuality, accurate parking, and comfortableness at the same time. But most traditional searching methods lack in efficiency or tend to fall into the local optimum. For the speed curve tracking, the widely applied proportional integral differential (PID) and fuzzy controllers rely on complicated parameter tuning, whereas robust adaptive methods can hardly ensure the finite-time convergence strictly, and thus are not suitable for applications in fixed time intervals of trains. To address the above-mentioned two problems, this paper presents a novel approach for speed curve seeking and tracking control. First, we present the random reinforcement genetic algorithm (GA) algorithm to avoid the local optimum efficiently. Then, a sliding mode controller is developed for speed curve tracking with bounded disturbance. The Lyapunov theory is adopted to prove that the system can be stabilized in the finite time. Finally, using the real datasets of Yizhuang Line in Beijing Subway, the proposed approach is validated, demonstrating its effectiveness and superiorities for the operation optimization.

Bio-Inspired Speed Curve Optimization and Sliding Mode Tracking Control for Subway Trains

This paper presents a method for electronic stability control (ESC) based on model predictive control (MPC) using the bicycle model with lagged tire force to reflect the lagged characteristics of lateral tire forces on the prediction model of the MPC problem for better description of the vehicle behavior. To avoid the computational burden in finding the optimal solution of the MPC problem using the constrained optimal control theory, the desired states and inputs as references are generated since the solution of the MPC problem can be easily obtained in a closed form without using numeric solvers using these reference values. The suggested method controls the vehicle to follow the generated reference values to maintain the vehicle yaw stability while the vehicle turns as the driver intended. The superiority of the proposed method is verified through comparisons with an ESC method based on ordinary MPC in the simulation environments on both high- and low- μ surfaces using the vehicle dynamics software CarSim.

Model Predictive Control for Vehicle Yaw Stability With Practical Concerns

The tire-road friction coefficient is critical information for conventional vehicle safety control systems. Most previous studies on tire-road friction estimation have only considered either longitudinal or lateral vehicle dynamics, which tends to cause significant underestimation of the actual tire-road friction coefficient. In this paper, the parameters, including the tire-road friction coefficient, of the combined longitudinal and lateral brushed tire model are identified by linearized recursive least squares (LRLS) methods, which efficiently utilize measurements related to both vehicle lateral and longitudinal dynamics in real time. The simulation study indicates that by using the estimated vehicle states and the tire forces of the four wheels, the suggested algorithm not only quickly identifies the tire-road friction coefficient with great accuracy and robustness before tires reach their frictional limits but successfully estimates the two different tire-road friction coefficients of the two sides of a vehicle on a split- μ surface as well. The developed algorithm was verified through vehicle dynamics software Carsim and MATLAB/Simulink.

Linearized Recursive Least Squares Methods for Real-Time Identification of Tire–Road Friction Coefficient

It is well known that both the tire-road friction coefficient and the absolute vehicle velocity are crucial factors for vehicle safety control systems Therefore, numerous efforts have been made to resolve these problems, but none have presented satisfactory results in all cases In this paper, cost-effective observers are designed based on an adaptive scheme and a recursive least squares algorithm without the addition of extra sensors on a production vehicle or modification of the vehicle control system This paper has three major contributions First, the front biased braking characteristics of production vehicles such that the front wheel brake torques are saturated first are exploited when estimating the tire-road friction coefficient Second, the vehicle absolute speed is identified during the friction coefficient estimation process Third, unlike the conventional method, this paper proposes using already available excitation signals in production vehicles In order to verify the performance of the proposed observers, experiments based on real production vehicles are conducted, and the results reveal that the proposed algorithm can enhance the performance of any vehicle dynamics control systems

Adaptive Scheme for the Real-Time Estimation of Tire-Road Friction Coefficient and Vehicle Velocity

Using a special type of sliding mode controller, a new type of traction control system (TCS) for hybrid four-wheel drive vehicles is developed. This paper makes two major contributions. First, a new electric powertrain architecture with an in-wheel motor at the front wheels and a clutch on the rear of the transmission is proposed for maximum traction force. The in-wheel motors are controlled to cycle near the optimal slip point. Based on the cycling patterns of the front wheels, the desired wheel speed for rear wheel is defined. The rear wheels are controlled to track this defined speed by controlling the clutch torque. Unlike conventional TCS algorithms, the proposed method exploits clutch control instead of brake control. Second, a special type of sliding mode controller which uses a nonlinear characteristic of the tire is proposed. An important distinction between the proposed sliding mode control method and other conventional feedback controllers is that the former does not depend on feedback error but provides the same functionality. Therefore, the practical aspects are emphasized in this paper. The developed method is confirmed in simulations, and the results reveal that the proposed method opens up opportunities for new types of TCS.

Development of a Traction Control System Using a Special Type of Sliding Mode Controller for Hybrid 4WD Vehicles

This paper presents a control architecture that simultaneously utilizes active front steering (AFS) and differential braking for vehicle lateral stability while minimizing longitudinal perturbations. This control scheme is based on the model predictive control (MPC) using the extended bicycle model that captures the lagged characteristics of tire forces and actuators. The nonlinearities of tire force are also reflected on the extended bicycle model by linearizing the tire forces at the operating points. Instead of casting the MPC problem into a quadratic program with constraints that require numerical solvers, the proposed method is designed to follow the reference states with desired inputs since the solutions of MPC problems with affine models to track desired states can be easily obtained by matrix inversion. Simulation results, obtained by the vehicle dynamics software Carsim, demonstrate that the suggested method is able to control the vehicle to track the desired path while keeping the vehicle later...

Mooryong Choi

Papers

Model Predictive Control for Vehicle Yaw Stability With Practical Concerns

Linearized Recursive Least Squares Methods for Real-Time Identification of Tire–Road Friction Coefficient

Adaptive Scheme for the Real-Time Estimation of Tire-Road Friction Coefficient and Vehicle Velocity

Development of a Traction Control System Using a Special Type of Sliding Mode Controller for Hybrid 4WD Vehicles

MPC for vehicle lateral stability via differential braking and active front steering considering practical aspects