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A PDE breach to the SDRE
Author(s) -
Rafee Nekoo Saeed
Publication year - 2020
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1961
Subject(s) - riccati equation , ode , mathematics , partial differential equation , ordinary differential equation , first order partial differential equation , nonlinear system , algebraic riccati equation , scalar (mathematics) , mathematical analysis , differential equation , control theory (sociology) , computer science , control (management) , physics , geometry , quantum mechanics , artificial intelligence
The state‐dependent Riccati equation (SDRE) is a nonlinear optimal controller derived from applying optimality conditions on a Hamiltonian equation. A co‐state vector is involved in the derivation process. This has been commonly considered a function of time only, despite the existence of states in the co‐state vector. This has resulted in a series of nonlinear coupled ordinary differential equations (ODEs) with a final boundary condition, known as the SDRE. In this work, for the first time, the co‐state vector is regarded as a function of time and states that results in a partial differential equation (PDE) instead of an ODE. The new governing equation is named partial differential state‐dependent Riccati equation (PDSDRE), and the PDE provides a tensor for gain over domains of time and states. Since the generated PDE is highly nonlinear, the solution to the PDSDRE is proposed based on the method of lines (MOL), which is an extension to the finite difference method (FDM). The proposed approach is implemented on both scalar and second order systems and is compared with an SDRE technique to validate the results and show the advantages of proposed structure.