OPTIMAL BOUNDED CONTROL OF LINEAR SAMPLED-DATA SYSTEMS USING QUADRATIC PERFORMANCE CRITERIA
STANFORD UNIV CA
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This investigation studies optimal control of linear sampled-data systems where the control is subject to saturation. The system is described by the state-space method. The control is con sidered to be optimal when it minimizes a per formance index which is defined as a sum over the sampling instants of a quadratic function of the states and controls. Both one- and two input control are considered. The two-input case requires a third set of recurrence rela tions for use when one input is saturated and the other is not. More inputs can be handled using the same methods, but the complexity in creases rapidly with the number of inputs. A detailed discussion of a simple method for find ing the minimum of a positive definite quadratic function in two variables subject to the con straint that the minimum be on or within a rec tangle is presented. Four examples showing the optimal control of second-order systems deter mined by the computing method given in this report are presented and discussed.
- Operations Research