Title :
Least squares stationary optimal control and the algebraic Riccati equation
Author_Institution :
Massachusetts Institute of Technology, Cambridge, MA, USA
fDate :
12/1/1971 12:00:00 AM
Abstract :
The optimal control of linear systems with respect to quadratic performance criteria over an infinite time interval is treated. Both the case in which the terminal state is free and that in which the terminal state is constrained to be zero are treated. The integrand of the performance criterion is allowed to be fully quadratic in the control and the state without necessarily satisfying the definiteness conditions which are usually assumed in the standard regulator problem. Frequency-domain and time-domain conditions for the existence of solutions are derived. The algebraic Riccati equation is then examined, and a complete classification of all its solutions is presented. It is finally shown how the optimal control problems introduced in the beginning of the paper may be solved analytically via the algebraic Riccati equation.
Keywords :
Algebraic Riccati equation (ARE); Least-squares optimization; Linear systems, time-invariant continuous-time; Optimal control; Riccati equations, algebraic; Control systems; Feedback control; Frequency domain analysis; Least squares methods; Linear systems; Optimal control; Regulators; Riccati equations; Stability criteria; Time domain analysis;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.1971.1099831