Double cost function linear quadratic regulator (DLQR) is developed from LQR theory to solve an optimal control problem with a general nonlinear cost function. In addition to the traditional LQ cost function, anothe...Double cost function linear quadratic regulator (DLQR) is developed from LQR theory to solve an optimal control problem with a general nonlinear cost function. In addition to the traditional LQ cost function, another free form cost function was introduced to express the physical need plainly and optimize weights of LQ cost function using the search algorithms. As an instance, DLQR was applied in determining the control input in the front steering angle compensation control (FSAC) model for heavy duty vehicles. The brief simulations show that DLQR is powerful enough to specify the engineering requirements correctly and balance many factors effectively. The concept and applicable field of LQR are expanded by DLQR to optimize the system with a free form cost function.展开更多
To get better tracking performance of attitude command over the reentry phase of vehicles, the use of state-dependent Riccati equation (SDRE) method for attitude controller design of reentry vehicles was investigated....To get better tracking performance of attitude command over the reentry phase of vehicles, the use of state-dependent Riccati equation (SDRE) method for attitude controller design of reentry vehicles was investigated. Guidance commands are generated based on optimal guidance law. SDRE control method employs factorization of the nonlinear dynamics into a state vector and state dependent matrix valued function. State-dependent coefficients are derived based on reentry motion equations in pitch and yaw channels. Unlike constant weighting matrix Q, elements of Q are set as the functions of state error so as to get satisfactory feedback and eliminate state error rapidly, then formulation of SDRE is realized. Riccati equation is solved real-timely with Schur algorithm. State feedback control law u(x) is derived with linear quadratic regulator (LQR) method. Simulation results show that SDRE controller steadily tracks attitude command, and impact point error of reentry vehicle is acceptable. Compared with PID controller, tracking performance of attitude command using SDRE controller is better with smaller control surface deflection. The attitude tracking error with SDRE controller is within 5°, and the control deflection is within 30°.展开更多
The saturation problem is the one of the most common handicaps for applying to real applications, especially the actuator saturation. This paper focuses on the robustness of the sliding mode control （SMC） which inco...The saturation problem is the one of the most common handicaps for applying to real applications, especially the actuator saturation. This paper focuses on the robustness of the sliding mode control （SMC） which incorporates a saturation constraint technique compared to classical linear quadratic regulator （LQR） with saturation. In the first step, the authors present a design methodology of SMC of a class of linear saturated systems. The authors present the structure of the saturation, after that the synthesis of the sliding surface is formulate as a problem of root clustering, which leads to the development of a continuous and non-linear control law that ensures the reaching condition of the sliding mode. The second step is devoted to present briefly the LQR controller technique. Finally, to validate results, the authors demonstrate an example of a quarter of vehicle system.展开更多
In this paper,three optimal linear formation control algorithms are proposed for first-order linear multiagent systems from a linear quadratic regulator(LQR) perspective with cost functions consisting of both interact...In this paper,three optimal linear formation control algorithms are proposed for first-order linear multiagent systems from a linear quadratic regulator(LQR) perspective with cost functions consisting of both interaction energy cost and individual energy cost,because both the collective ob ject(such as formation or consensus) and the individual goal of each agent are very important for the overall system.First,we propose the optimal formation algorithm for first-order multi-agent systems without initial physical couplings.The optimal control parameter matrix of the algorithm is the solution to an algebraic Riccati equation(ARE).It is shown that the matrix is the sum of a Laplacian matrix and a positive definite diagonal matrix.Next,for physically interconnected multi-agent systems,the optimal formation algorithm is presented,and the corresponding parameter matrix is given from the solution to a group of quadratic equations with one unknown.Finally,if the communication topology between agents is fixed,the local feedback gain is obtained from the solution to a quadratic equation with one unknown.The equation is derived from the derivative of the cost function with respect to the local feedback gain.Numerical examples are provided to validate the effectiveness of the proposed approaches and to illustrate the geometrical performances of multi-agent systems.展开更多
To improve maneuverability and stability of articulated vehicles, we design an active steering controller, including tractor and trailer controllers, based on linear quadratic regulator(LQR) theory. First, a three-deg...To improve maneuverability and stability of articulated vehicles, we design an active steering controller, including tractor and trailer controllers, based on linear quadratic regulator(LQR) theory. First, a three-degree-of-freedom(3-DOF) model of the tractor-trailer with steered trailer axles is built. The simulated annealing particle swarm optimization(SAPSO) algorithm is applied to identify the key parameters of the model under specified vehicle speed and steering wheel angle. Thus, the key parameters of the simplified model can be obtained according to the vehicle conditions using an online look-up table and interpolation. Simulation results show that vehicle parameter outputs of the simplified model and Truck Sim agree well, thus providing the ideal reference yaw rate for the controller. Then the active steering controller of the tractor and trailer based on LQR is designed to follow the desired yaw rate and minimize their side-slip angle of the center of gravity(CG) at the same time. Finally, simulation tests at both low speed and high speed are conducted based on the Truck Sim-Simulink program. The results show significant effects on the active steering controller on improving maneuverability at low speed and lateral stability at high speed for the articulated vehicle. The control strategy is applicable for steering not only along gentle curves but also along sharp curves.展开更多
文摘Double cost function linear quadratic regulator (DLQR) is developed from LQR theory to solve an optimal control problem with a general nonlinear cost function. In addition to the traditional LQ cost function, another free form cost function was introduced to express the physical need plainly and optimize weights of LQ cost function using the search algorithms. As an instance, DLQR was applied in determining the control input in the front steering angle compensation control (FSAC) model for heavy duty vehicles. The brief simulations show that DLQR is powerful enough to specify the engineering requirements correctly and balance many factors effectively. The concept and applicable field of LQR are expanded by DLQR to optimize the system with a free form cost function.
基金Project(51105287)supported by the National Natural Science Foundation of China
文摘To get better tracking performance of attitude command over the reentry phase of vehicles, the use of state-dependent Riccati equation (SDRE) method for attitude controller design of reentry vehicles was investigated. Guidance commands are generated based on optimal guidance law. SDRE control method employs factorization of the nonlinear dynamics into a state vector and state dependent matrix valued function. State-dependent coefficients are derived based on reentry motion equations in pitch and yaw channels. Unlike constant weighting matrix Q, elements of Q are set as the functions of state error so as to get satisfactory feedback and eliminate state error rapidly, then formulation of SDRE is realized. Riccati equation is solved real-timely with Schur algorithm. State feedback control law u(x) is derived with linear quadratic regulator (LQR) method. Simulation results show that SDRE controller steadily tracks attitude command, and impact point error of reentry vehicle is acceptable. Compared with PID controller, tracking performance of attitude command using SDRE controller is better with smaller control surface deflection. The attitude tracking error with SDRE controller is within 5°, and the control deflection is within 30°.
文摘The saturation problem is the one of the most common handicaps for applying to real applications, especially the actuator saturation. This paper focuses on the robustness of the sliding mode control （SMC） which incorporates a saturation constraint technique compared to classical linear quadratic regulator （LQR） with saturation. In the first step, the authors present a design methodology of SMC of a class of linear saturated systems. The authors present the structure of the saturation, after that the synthesis of the sliding surface is formulate as a problem of root clustering, which leads to the development of a continuous and non-linear control law that ensures the reaching condition of the sliding mode. The second step is devoted to present briefly the LQR controller technique. Finally, to validate results, the authors demonstrate an example of a quarter of vehicle system.
基金supported by the National Natural Science Foundation of China(No.61375072)(50%)the Natural Science Foundation of Zhejiang Province,China(No.LQ16F030005)(50%)
文摘In this paper,three optimal linear formation control algorithms are proposed for first-order linear multiagent systems from a linear quadratic regulator(LQR) perspective with cost functions consisting of both interaction energy cost and individual energy cost,because both the collective ob ject(such as formation or consensus) and the individual goal of each agent are very important for the overall system.First,we propose the optimal formation algorithm for first-order multi-agent systems without initial physical couplings.The optimal control parameter matrix of the algorithm is the solution to an algebraic Riccati equation(ARE).It is shown that the matrix is the sum of a Laplacian matrix and a positive definite diagonal matrix.Next,for physically interconnected multi-agent systems,the optimal formation algorithm is presented,and the corresponding parameter matrix is given from the solution to a group of quadratic equations with one unknown.Finally,if the communication topology between agents is fixed,the local feedback gain is obtained from the solution to a quadratic equation with one unknown.The equation is derived from the derivative of the cost function with respect to the local feedback gain.Numerical examples are provided to validate the effectiveness of the proposed approaches and to illustrate the geometrical performances of multi-agent systems.
基金supported by the Program for Changjiang ScholarsInnovative Research Team in University,China(No.IRT0626)
文摘To improve maneuverability and stability of articulated vehicles, we design an active steering controller, including tractor and trailer controllers, based on linear quadratic regulator(LQR) theory. First, a three-degree-of-freedom(3-DOF) model of the tractor-trailer with steered trailer axles is built. The simulated annealing particle swarm optimization(SAPSO) algorithm is applied to identify the key parameters of the model under specified vehicle speed and steering wheel angle. Thus, the key parameters of the simplified model can be obtained according to the vehicle conditions using an online look-up table and interpolation. Simulation results show that vehicle parameter outputs of the simplified model and Truck Sim agree well, thus providing the ideal reference yaw rate for the controller. Then the active steering controller of the tractor and trailer based on LQR is designed to follow the desired yaw rate and minimize their side-slip angle of the center of gravity(CG) at the same time. Finally, simulation tests at both low speed and high speed are conducted based on the Truck Sim-Simulink program. The results show significant effects on the active steering controller on improving maneuverability at low speed and lateral stability at high speed for the articulated vehicle. The control strategy is applicable for steering not only along gentle curves but also along sharp curves.
