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
A stochastic optimal control strategy for a slightly sagged cable using support motion in the cable axial direction is proposed. The nonlinear equation of cable motion in plane is derived and reduced to the equations ...A stochastic optimal control strategy for a slightly sagged cable using support motion in the cable axial direction is proposed. The nonlinear equation of cable motion in plane is derived and reduced to the equations for the first two modes of cable vibration by using the Galerkin method. The partially averaged Ito equation for controlled system energy is further derived by applying the stochastic averaging method for quasi-non-integrable Hamiltonian systems. The dynamical programming equation for the controlled system energy with a performance index is established by applying the stochastic dynamical programming principle and a stochastic optimal control law is obtained through solving the dynamical programming equation. A bilinear controller by using the direct method of Lyapunov is introduced. The comparison between the two controllers shows that the proposed stochastic optimal control strategy is superior to the bilinear control strategy in terms of higher control effectiveness and efficiency.展开更多
Steering control for an autonomous underwater glider （AUG） is very challenging due to its changing dynamic char- acteristics such as payload and shape. A good choice to solve this problem is online system identifica...Steering control for an autonomous underwater glider （AUG） is very challenging due to its changing dynamic char- acteristics such as payload and shape. A good choice to solve this problem is online system identification via in-field trials to capture current dynamic characteristics for control law reconfiguration. Hence, an online polynomial estimator is designed to update the yaw dynamic model of the AUG, and an adaptive model predictive control （MPC） controller is used to calculate the optimal control command based on updated estimated parameters. The MPC controller uses a quadratic program （QP） to compute the optimal control command based on a user-defined cost function. The cost function has two terms, focusing on output reference tracking and move suppression of input, respectively. Move-suppression performance can, at some level, represent energy-saving performance of the MPC controller. Users can balance these two competitive control performances by tuning weights. We have compared the control performance using the second-order polynomial model to that using the filth-order polynomial model, and found that the tbrmer cannot capture the main characteristics of yaw dynamics and may result in vibration during the flight. Both processor-in-loop （PIL） simulations and in-lake tests are presented to validate our steering control performance.展开更多
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 National Natural Science Foundation of China (11072212,10932009)the Zhejiang Natural Science Foundation of China (7080070)
文摘A stochastic optimal control strategy for a slightly sagged cable using support motion in the cable axial direction is proposed. The nonlinear equation of cable motion in plane is derived and reduced to the equations for the first two modes of cable vibration by using the Galerkin method. The partially averaged Ito equation for controlled system energy is further derived by applying the stochastic averaging method for quasi-non-integrable Hamiltonian systems. The dynamical programming equation for the controlled system energy with a performance index is established by applying the stochastic dynamical programming principle and a stochastic optimal control law is obtained through solving the dynamical programming equation. A bilinear controller by using the direct method of Lyapunov is introduced. The comparison between the two controllers shows that the proposed stochastic optimal control strategy is superior to the bilinear control strategy in terms of higher control effectiveness and efficiency.
基金supported by Beihang University and Institution of China Academy of Aerospace Aerodynamics
文摘Steering control for an autonomous underwater glider （AUG） is very challenging due to its changing dynamic char- acteristics such as payload and shape. A good choice to solve this problem is online system identification via in-field trials to capture current dynamic characteristics for control law reconfiguration. Hence, an online polynomial estimator is designed to update the yaw dynamic model of the AUG, and an adaptive model predictive control （MPC） controller is used to calculate the optimal control command based on updated estimated parameters. The MPC controller uses a quadratic program （QP） to compute the optimal control command based on a user-defined cost function. The cost function has two terms, focusing on output reference tracking and move suppression of input, respectively. Move-suppression performance can, at some level, represent energy-saving performance of the MPC controller. Users can balance these two competitive control performances by tuning weights. We have compared the control performance using the second-order polynomial model to that using the filth-order polynomial model, and found that the tbrmer cannot capture the main characteristics of yaw dynamics and may result in vibration during the flight. Both processor-in-loop （PIL） simulations and in-lake tests are presented to validate our steering control performance.
