This paper considers the optimal trajectory tracking control problem for near-surface autonomous underwater vehicles(AUVs) in the presence of wave disturbances. An approximate optimal tracking control(AOTC) approach i...This paper considers the optimal trajectory tracking control problem for near-surface autonomous underwater vehicles(AUVs) in the presence of wave disturbances. An approximate optimal tracking control(AOTC) approach is proposed. Firstly, a six-degrees-of-freedom(six-DOF) AUV model with its body-fixed coordinate system is decoupled and simplified and then a nonlinear control model of AUVs in the vertical plane is given. Also, an exosystem model of wave disturbances is constructed based on Hirom approximation formula. Secondly, the time-parameterized desired trajectory which is tracked by the AUV's system is represented by the exosystem. Then, the coupled two-point boundary value(TPBV) problem of optimal tracking control for AUVs is derived from the theory of quadratic optimal control. By using a recently developed successive approximation approach to construct sequences, the coupled TPBV problem is transformed into a problem of solving two decoupled linear differential sequences of state vectors and adjoint vectors. By iteratively solving the two equation sequences, the AOTC law is obtained, which consists of a nonlinear optimal feedback item, an expected output tracking item, a feedforward disturbances rejection item, and a nonlinear compensatory term. Furthermore, a wave disturbances observer model is designed in order to solve the physically realizable problem. Simulation is carried out by using the Remote Environmental Unit(REMUS) AUV model to demonstrate the effectiveness of the proposed algorithm.展开更多
The optimal control design for singularly perturbed time-delay systems affected by external distur-bances is considered.Based on the decomposition theory of singular perturbation,the system is decom-posed into a fast ...The optimal control design for singularly perturbed time-delay systems affected by external distur-bances is considered.Based on the decomposition theory of singular perturbation,the system is decom-posed into a fast subsystem without time-delay and a slow time-delay subsystem with disturbances.Theoptimal disturbances rejection control law of the slow subsystem is obtained by using the successive ap-proximation approach(SAA)and feedforward compensation method.Further,the feedforward and feed-back composite control(FFCC)law for the original problem is developed.The FFCC law consists of lin-ear analytic terms and a time-delay compensation term which is the limit of the solution sequence of theadjoint vector equations.A disturbance observer is introduced to make the FFCC law physically realiz-able.Numerical examples show that the proposed algorithm is effective.展开更多
A nonlinear synthesis problem of antennas according to the prescribed power (squared amplitude) radiation pattern (RP) is considered in the variational statement that yields in the possibility to take into account an ...A nonlinear synthesis problem of antennas according to the prescribed power (squared amplitude) radiation pattern (RP) is considered in the variational statement that yields in the possibility to take into account an additional restriction to the synthesized power RP. The problem of synthesis consists of finding such currents in antenna, which generates the RP with the best approximation to the given one. The respective Euler’s equation is reduced on the basis of used functional. This is nonlinear integral equation of Hammerstein’s type. The effective numerical methods are elaborated and applied for its solving. The computational results verify the effectiveness of approach proposed.展开更多
Successive approximate design of the optimal tracking controller for linear systems with time-delay is developed. By applying the successive approximation theory of differential equations, the two-point boundary value...Successive approximate design of the optimal tracking controller for linear systems with time-delay is developed. By applying the successive approximation theory of differential equations, the two-point boundary value (TPBV) problem with both time-delay and time-advance terms derived from the original optimal tracking control (OTC) problem is transformed into a sequence of linear TPBV prob- lems without delay and advance terms. The solution sequence of the linear TPBV problems uniformly converges to the solution of the original OTC problem The obtained OTC law consists of analytic state feedback terms and a compensation term which is the limit of the adjoint vector sequence. The com- pensation term can be obtained from an iteration formula of adjoint vectors. By using a finite term of the adjoint vector sequence, a suboptimal tracking control law is revealed. Numerical examples show the effectiveness of the algorithm.展开更多
基金supported in part by the National Natural Science Foundation of China (41276085)the Natural Science Foundation of Shandong Province (ZR2015FM004)
文摘This paper considers the optimal trajectory tracking control problem for near-surface autonomous underwater vehicles(AUVs) in the presence of wave disturbances. An approximate optimal tracking control(AOTC) approach is proposed. Firstly, a six-degrees-of-freedom(six-DOF) AUV model with its body-fixed coordinate system is decoupled and simplified and then a nonlinear control model of AUVs in the vertical plane is given. Also, an exosystem model of wave disturbances is constructed based on Hirom approximation formula. Secondly, the time-parameterized desired trajectory which is tracked by the AUV's system is represented by the exosystem. Then, the coupled two-point boundary value(TPBV) problem of optimal tracking control for AUVs is derived from the theory of quadratic optimal control. By using a recently developed successive approximation approach to construct sequences, the coupled TPBV problem is transformed into a problem of solving two decoupled linear differential sequences of state vectors and adjoint vectors. By iteratively solving the two equation sequences, the AOTC law is obtained, which consists of a nonlinear optimal feedback item, an expected output tracking item, a feedforward disturbances rejection item, and a nonlinear compensatory term. Furthermore, a wave disturbances observer model is designed in order to solve the physically realizable problem. Simulation is carried out by using the Remote Environmental Unit(REMUS) AUV model to demonstrate the effectiveness of the proposed algorithm.
基金the National Natural Science Foundation of China(No.60574023,40776051)the Natural Science Foundation of Zhejiang Province(No.Y107232)+1 种基金the Scientific Research Found of Zhejiang Provincial Education Department(No.Y200702660)the 123 Talent Funding Project of China Jiliang University(No.2006RC17)
文摘The optimal control design for singularly perturbed time-delay systems affected by external distur-bances is considered.Based on the decomposition theory of singular perturbation,the system is decom-posed into a fast subsystem without time-delay and a slow time-delay subsystem with disturbances.Theoptimal disturbances rejection control law of the slow subsystem is obtained by using the successive ap-proximation approach(SAA)and feedforward compensation method.Further,the feedforward and feed-back composite control(FFCC)law for the original problem is developed.The FFCC law consists of lin-ear analytic terms and a time-delay compensation term which is the limit of the solution sequence of theadjoint vector equations.A disturbance observer is introduced to make the FFCC law physically realiz-able.Numerical examples show that the proposed algorithm is effective.
文摘A nonlinear synthesis problem of antennas according to the prescribed power (squared amplitude) radiation pattern (RP) is considered in the variational statement that yields in the possibility to take into account an additional restriction to the synthesized power RP. The problem of synthesis consists of finding such currents in antenna, which generates the RP with the best approximation to the given one. The respective Euler’s equation is reduced on the basis of used functional. This is nonlinear integral equation of Hammerstein’s type. The effective numerical methods are elaborated and applied for its solving. The computational results verify the effectiveness of approach proposed.
基金This work was supported by the National Natural Science Foundation of China （Grant No. 60574023）the Natural Science Foundation of Shandong Province （Grant No. Z2005G01）the Natural Science Foundation of Qingdao City （Grant No. 05-1-JC-94）.
文摘Successive approximate design of the optimal tracking controller for linear systems with time-delay is developed. By applying the successive approximation theory of differential equations, the two-point boundary value (TPBV) problem with both time-delay and time-advance terms derived from the original optimal tracking control (OTC) problem is transformed into a sequence of linear TPBV prob- lems without delay and advance terms. The solution sequence of the linear TPBV problems uniformly converges to the solution of the original OTC problem The obtained OTC law consists of analytic state feedback terms and a compensation term which is the limit of the adjoint vector sequence. The com- pensation term can be obtained from an iteration formula of adjoint vectors. By using a finite term of the adjoint vector sequence, a suboptimal tracking control law is revealed. Numerical examples show the effectiveness of the algorithm.
