Introduction to matrix analysis (2nd ed.)
Introduction to matrix analysis (2nd ed.)
Correspondence item: Suboptimal feedback control for nonlinear systems
Automatica (Journal of IFAC)
A method for suboptimal design of nonlinear feedback systems
Automatica (Journal of IFAC)
Guaranteed cost control of affine nonlinear systems via partition of unity method
Automatica (Journal of IFAC)
| Hi-index | 22.15 |
In this paper a suboptimal solution to the nonlinear quadratic regulator and tracking problem with infinite final time is investigated. The plant may well be time-varying and nonlinear in state and control. The plant is represented by an apparent linearization and the suboptimal control at any given instant is determined by the optimal control law for the linear model valid at the particular instant. It is shown that with certain restrictions the suboptimal control law exists and is a continuous function of state and time. It is further shown that this suboptimal control law results in a closed-loop system which is asymptotically stable in a sufficiently small region. A computational method for obtaining the suboptimal control law is presented which reduces the amount of computations significantly. This suboptimal control law, based on the solution to the linear regulator problem, involves the steady-state solution to the Riccati differential equation. This matrix is expanded in a Taylor series. The terms of this series can be calculated recursively off-line and thus the problem of repeatedly solving the Riccati equation circumvented. It is shown that the control law obtained by using any finite number of terms in this series preserves the stability of the system.