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Beam analogy for optimal control of linear dynamic systems. (English) Zbl 0976.74045
Summary: Optimal control problems for linear dynamic systems with quadratic performance index are solved using the beam analogy. The governing equations for optimal maneuver are derived in the form of coupled fourth-order differential equations in time domain. These equations are uncoupled using modal variables. Next, each independent equation is made analogous to the corresponding problem of a beam on elastic foundation. The beam problem in the spatial domain is solved using standard FEM software. Finally, the FEM results are transferred back to the time domain, where they represent optimal trajectories and controls for the dynamic system.
MSC:
74M05Control, switches and devices (“smart materials”)
70Q05Control of mechanical systems (general mechanics)
93C15Control systems governed by ODE
74S05Finite element methods in solid mechanics