On a trajectory tracking problem for nonlinear control systems

An approach for studying typical point-to-point trajectory tracking problems for nonlinear control systems that possess a global linearization is proposed. The trajectory constraints include both the inequality and the equality (interpolatory) types. For purposes of theoretical analysis, system-behavior understanding, and controller design, a minimum control-energy criterion for the linearized system is used. Under this optimality criterion, a characterization result for describing all the possible solutions of such trajectory tracking problems is established. Moreover, the general structure is found in explicit closed-form for these solutions. The research is motivated by a specific example of robotic trajectory planning. Some computer simulation graphs on the robotic trajectory planning problem are included.