Minimizing control energy in a class of bounded-control linear-quadratic regulator problems
- Costanza, Vicente
- Rivadeneira Paz, Pablo Santiago
- González, Alejandro Hernán
DOIAbstract
Minimal-control-energy strategies are substantiated and illustrated for linear-quadratic problems with penalized endpoints and no state-trajectory cost, when bounds in control values are imposed. The optimal solution for a given process with restricted controls, starting at a known initial state, is shown to coincide with the saturated solution to the unrestricted problem that has the same coefficients but starts at a generally different initial state. This result reduces the searching span for the solution: from the infinite-dimensional set of admissible control trajectories to the finite-dimensional Euclidean space of initial conditions. An efficient real-time scheme is proposed here to approximate (eventually to find) the optimal control...
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