標題: Convex Quadratic Equation
作者: Lin, Li-Gang
Liang, Yew-Wen
Hsieh, Wen-Yuan
電控工程研究所
Institute of Electrical and Control Engineering
關鍵字: Convex quadratic equation;Matrix algebra;Optimal control;Nonlinear system;Convex quadratic function
公開日期: 1-九月-2020
摘要: Two main results (A) and (B) are presented in algebraic closed forms. (A) Regarding the convex quadratic equation, an analytical equivalent solvability condition and parameterization of all solutions are formulated, for the first time in the literature and in a unified framework. The philosophy is based on the matrix algebra, while facilitated by a novel equivalence/coordinate transformation (with respect to the much more challenging case of rank-deficient Hessian matrix). In addition, the parameter-solution bijection is verified. From the perspective via (A), a major application is re-examined that accounts for the other main result (B), which deals with both the infinite and finite-time horizon nonlinear optimal control. By virtue of (A), the underlying convex quadratic equations associated with the Hamilton-Jacobi equation, Hamilton-Jacobi inequality, and Hamilton-Jacobi-Bellman equation are explicitly solved, respectively. Therefore, the long quest for the constituent of the optimal controller, gradient of the associated value function, can be captured in each solution set. Moving forward, a preliminary to exactly locate the optimality using the state-dependent (resp., differential) Riccati equation scheme is prepared for the remaining symmetry condition.
URI: http://dx.doi.org/10.1007/s10957-020-01727-5
http://hdl.handle.net/11536/155465
ISSN: 0022-3239
DOI: 10.1007/s10957-020-01727-5
期刊: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
Volume: 186
Issue: 3
起始頁: 1006
結束頁: 1028
顯示於類別:期刊論文