Optimal control system of state space is a conservative system, whose approximate method should be symplectic conservation. Based on the precise integration method, an algorithm of symplectic conservative perturbation...Optimal control system of state space is a conservative system, whose approximate method should be symplectic conservation. Based on the precise integration method, an algorithm of symplectic conservative perturbation is presented. It gives a uniform way to solve the linear quadratic control （LQ control） problems for linear timevarying systems accurately and efficiently, whose key points are solutions of differential Riccati equation （DRE） with variable coefficients and the state feedback equation. The method is symplectic conservative and has a good numerical stability and high precision. Numerical examples demonstrate the effectiveness of the proposed method.展开更多
To solve the different time delays that exist in the control device installed on spatial structures, in this study, discrete analysis using a 2N precise algorithm was selected to solve the multi-time-delay issue for l...To solve the different time delays that exist in the control device installed on spatial structures, in this study, discrete analysis using a 2N precise algorithm was selected to solve the multi-time-delay issue for long-span structures based on the market-based control （MBC） method. The concept of interval mixed energy was introduced from computational structural mechanics and optimal control research areas, and it translates the design of the MBC multi-time-delay controller into a solution for the segment matrix. This approach transforms the serial algorithm in time to parallel computing in space, greatly improving the solving efficiency and numerical stability. The designed controller is able to consider the issue of time delay with a linear controlling force combination and is especially effective for large time-delay conditions. A numerical example of a long-span structure was selected to demonstrate the effectiveness of the presented controller, and the time delay was found to have a significant impact on the results.展开更多
基金Project supported by the National Natural Science Foundation of China (No.10202004)
文摘Optimal control system of state space is a conservative system, whose approximate method should be symplectic conservation. Based on the precise integration method, an algorithm of symplectic conservative perturbation is presented. It gives a uniform way to solve the linear quadratic control （LQ control） problems for linear timevarying systems accurately and efficiently, whose key points are solutions of differential Riccati equation （DRE） with variable coefficients and the state feedback equation. The method is symplectic conservative and has a good numerical stability and high precision. Numerical examples demonstrate the effectiveness of the proposed method.
基金provided by the Science Fund for Creative Research Groups of the National Natural Science Foundation of China under Grant Nos.51261120375 and 51421064
文摘To solve the different time delays that exist in the control device installed on spatial structures, in this study, discrete analysis using a 2N precise algorithm was selected to solve the multi-time-delay issue for long-span structures based on the market-based control （MBC） method. The concept of interval mixed energy was introduced from computational structural mechanics and optimal control research areas, and it translates the design of the MBC multi-time-delay controller into a solution for the segment matrix. This approach transforms the serial algorithm in time to parallel computing in space, greatly improving the solving efficiency and numerical stability. The designed controller is able to consider the issue of time delay with a linear controlling force combination and is especially effective for large time-delay conditions. A numerical example of a long-span structure was selected to demonstrate the effectiveness of the presented controller, and the time delay was found to have a significant impact on the results.
