Solver‐free optimal control for linear dynamical switched system by means of geometric algebra

An algorithm for finding a control of linear switched system by means Geometric Algebra is designed. More precisely, we develop switching path searching two-dimensional dynamical with non-singular matrix whose integral curves are formed two sets centralized ellipses. It natural to represent them as elements Conics and construct the calculating points, i.e., intersections contact points. For this, use symbolic algebra operations or, more wedge inner products that realizable sums in coordinate form. Therefore, no numerical solver equations needed. Indeed, only operation may bring an inaccuracy vector normalization, square root calculation. The resulting pieces ellipses chosen, respectively, from curves. points either first or final step our algorithm, This choice guarantees optimality respect number switches. Two examples provided demonstrate search conics and, consequently, description presented construction both cases.