Closed-form solutions for a class of optimal quadratic regulator problems with terminal constraints. (English) Zbl 0596.49002

Juang, Jer-Nan; Turner, James D.; Chun, Hon M.

J. Dyn. Syst. Meas. Control 108, 44-48 (1986).

The paper describes three new developments related to a class of optimal finite-time quadratic regulator problems with terminal constraints instead of penalizing the terminal states. First, analytical solutions are obtained for the feedback gains by means of three coupled Riccati- like matrix differential equations and then a closed form expression for the closed-loop system state trajectory is derived. A new way of implementing these solutions is also developed, leading to considerably simplified computational procedures, based on matrix transformations.
Examples including a first-order system and a simple spacecraft are used to demonstrate the validity of all the analytical solutions presented in the paper.

Reviewer: O.Pastravanu

MSC:

49J15	Existence theories for optimal control problems involving ordinary differential equations
34A05	Explicit solutions, first integrals of ordinary differential equations
34B30	Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
34H05	Control problems involving ordinary differential equations
93B17	Transformations
93C15	Control/observation systems governed by ordinary differential equations
93D15	Stabilization of systems by feedback
93B40	Computational methods in systems theory (MSC2010)
65K10	Numerical optimization and variational techniques

Keywords:

optimal finite-time quadratic regulator problems; terminal constraints; analytical solutions; coupled Riccati-like matrix differential equations