Robust control of set-valued discrete-time dynamical systems

• Published in: IEEE transactions on automatic control Vol. 43; no. 1; pp. 61 - 75
• Main Authors: Baras, J.S., Patel, N.S.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.1998; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Computer science; control theory; systems; Control system synthesis; Control systems; Control theory. Systems; Exact sciences and technology; Linear systems; Nonlinear control systems; Nonlinear dynamical systems; Nonlinear systems; Output feedback; Robust control; Shape control; State estimation; Sufficient conditions; Robust control; Dynamic game; Control synthesis; Certainty equivalence principle; Discrete system; Dynamic programming; Non linear system; Output feedback; Convergence
• ISSN: 0018-9286
• DOI: 10.1109/9.654887

This paper presents results obtained for the control of set-valued discrete-time dynamical systems. Such systems model nonlinear systems subject to persistent bounded noise. A robust control problem for such systems is introduced. The problem is formulated as a dynamic game, wherein the controller plays against the set-valued system. Both necessary and sufficient conditions in terms of (stationary) dynamic programming equalities are presented. The output feedback problem is solved using the concept of an information state, where a decoupling between estimation and control is obtained. The methods yield a conceptual approach for constructing controlled-invariant sets and stabilizing controllers for uncertain nonlinear systems.