Neighboring Extremal Solution for Nonlinear Discrete-Time Optimal Control Problems With State Inequality Constraints

• Published in: IEEE transactions on automatic control Vol. 54; no. 11; pp. 2674 - 2679
• Main Authors: Ghaemi, R., Jing Sun, Kolmanovsky, I.V.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.11.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Automatic control; Automatic programming; Computer science; control theory; systems; Control systems; Control theory. Systems; Convergence; Cost function; Dynamic programming; Exact sciences and technology; Exact solutions; Inequalities; Linear programming; Mathematical analysis; Model predictive control (MPC); neighboring extremal (NE); Nonlinearity; Optimal control; Riccati equations; Switched systems; Model predictive control; Model predictive control (MPC); Extremum; Optimal control; Inequality constraint; Discrete time; Non linear control; Time optimal control; neighboring extremal (NE); State constraint; Exact solution
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2009.2031576

A neighboring extremal control method is proposed for discrete-time optimal control problems subject to a general class of inequality constraints. The approach is applicable to a broad class of systems with input and state constraints, including two special cases where the constraints depend only on states but not inputs and the constraints are over determined. A closed form solution for the neighboring extremal control is provided and a sufficient condition for existence of the neighboring extremal solution is specified.