Introduction to matrix analysis (2nd ed.)
Introduction to matrix analysis (2nd ed.)
Paper: A solution of nonlinear TPBVP's occuring in optimal control
Automatica (Journal of IFAC)
Suboptimal control for the nonlinear quadratic regulator problem
Automatica (Journal of IFAC)
Paper: Design of nonlinear automatic flight control systems
Automatica (Journal of IFAC)
| Hi-index | 22.15 |
An approximation method is presented to construct an optimal state regulator for a nonlinear system with quadratic performance index. The nonlinearity is taken to be a perturbation to the system, and a parameter @e is introduced to stand for it. By making use of a power-series expansion in @e, a sequence of partial differential equations is derived whose solutions form a suboptimal feedback law. Given a polynomial nonlinearity, the partial differential equations are reduced to ordinary differential equations by separation of variables. The zero-order terms yield a well known Riccati equation. Higher-order equations are transformed into conventional type linear equations, owing to a lemma regarding an extended Liapunov equation. It is demonstrated that the l-th order approximation for the feedback law results in the (2l+1)th order approximation to the optimal performance. The procedure developed has a wide variety of applications. As one of the straightforward applications, the synthesis of a suboptimal control is discussed for a large-scale system as composed of several subsystems of lower dimensions. Three examples attached illustrate several features of the method.