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CONTROL OF DYNAMICAL SYSTEMS WITH CONSTRAINTS

By ΗΛΙΑΝΑ ΓΡΑΒΑΛΟΥ

Abstract

THE BASIC AIM OF THE THESIS IS TO PROPOSE SOLUTIONS TO THE PROBLEM OF THE CONTROL OF DISCRETE TIME SYSTEMS UNDER LINEAR STATE AND CONTROL CONSTRAINTS. THE PRESENT APPROACH IS BASED ON THE THEORY OF POSITIVE INVARIANCE OF POLYHEDRAL SETS OF STATES. THE THEORY IS BEING GENERALIZED AND EXTENED IN THE CASE WHERE THE SETS OF STATES ARE DESCRIBED BY THEIR VERTICES. SOLUTIONS TO THE LINEAR CONSTRAINED REGULATION PROBLEM ARE OBTAINED USING A GENERALIZED CRITERION AND AN ITERATIVE ALGORITHM FOR THE DERIVATION (BY LINEAR PROGRAMMING) OF ADMISSIBLE STATE FEEDBACK CONTROL LAWS. THEN THE ROBUST LINEAR CONSTRAINED REGULATIONPROBLEM IN THE PRESENCE OF PARAMETER UNCERTAINTY OR EXTERNAL DISTURBACES IS ANALYZED. IN THE CASE OF NONLINEAR SYSTEMS, THE POSITIVE INVARIANCE IS RELATED TO THE EXISTENCE OF CERTAIN COMPARISON SYSTEMS AND SOLUTIONS FOR THE CONTROL OF A CLASS OF NONLINEAR SYSTEMS ARE PROPOSED. FINALLY, ALGORITHMS FOR ON-LINE CONTROL OF LINEAR AND NONLINEAR SYSTEMS OF GENERAL FORM ARE PROPOSED, WHEREAN OPTIMIZATION PROBLEM TAKING INTO ACCOUNT THE CONSTRAINTS IS SOLVED AT EACH SAMPLING INSTANT. THE POSITIVE INVARIANCE IN THE THEORETICAL LEVEL AND LINEAR PROGRAMMING IN THE PRACTICAL LEVEL ARE PROVED TO BE EXTREMELY USEFUL TOOLSFOR THE MANIPULATION OF LINEAR CONSTRAINTS AND THE DERIVATION OF ADMISSIBLECONTROL LAWS.

Topics: Automatic control, Constraints, Control algorithms, Discrete time systems, POSITIVE INVARIANCE, Stability, Αλγόριθμοι ελέγχου, Αυτόματος έλεγχος, Ευστάθεια, ΘΕΤΙΚΟΙ ΑΜΕΤΑΒΛΗΤΟΤΗΤΑ, Περιορισμοί, Συστήματα διακριτού χρόνου
Publisher: University of Patras
Year: 1995
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