Sliding mode optimization in dynamic LTI systems

• Published in: Journal of optimization theory and applications Vol. 115; no. 3; pp. 727 - 740
• Main Authors: FERRARA, A, UTKIN, V. I
• Format: Journal Article
• Language: English
• Published: New York, NY Springer 01.12.2002; Springer Nature B.V
• Subjects: Applied sciences; Computer science; control theory; systems; Control system synthesis; Control theory. Systems; Convex analysis; Eigenvalues; Equilibrium; Exact sciences and technology; Inequality; Optimization; Linear time invariant system; Sliding mode; Variable structure system; Inequality constraint; Control synthesis; Linear programming; Dynamic programming; Convex programming; Constrained optimization
• ISSN: 0022-3239; 1573-2878
• DOI: 10.1023/A:1021267517097

This paper deals with the problem of constrained optimization in dynamic linear time-invariant (LTI) systems characterized by a control vector dimension less than that of the system state vector. The problem consists in designing a control signal capable of generating a system state evolution confined to the feasible region delimited by a number of inequality constraints less than or equal to the number of control vector components, as well as of steering the state trajectory to an equilibrium point where a prespecified cost function depending on the system state is being minimized. The finite-time convergence to a vicinity of order [straight epsilon] of the optimal equilibrium point is proved.