A Suboptimal Controller Design Methodology for Input-Output Feedback-Linearizable Systems

This paper addresses suboptimal control of nonlinear systems which can be feedbacklinearized from input to output. The case of input-to-state linearizable systems is also covered as a special case. The method is thus applicable to all nonlinear systems which can be partially linearized using the method of output-feedback linearization while having a stable internal (or zero) dynamics. The well-known LQR technique applied to the linearized system does not guarantee the suboptimality of the nonlinear system. This paper uses output feedback linearization technique to partially linearize the system and then designs an output-feedback for the feedback-linearized system in such a way that it ensures suboptimal performance of the original nonlinear system. The proposed method can optimize any arbitrary smooth function of states and input. The proposed controller is, however, suboptimal due to the facts that (1) the form of the controller is a linear static feedback of the linearized state, (2) the search algorithm may fall into a local extremum rather than a global, and (3) the calculated controller depends on the initial conditions. The method is successfully applied to control design of the longitudinal subsystem of a laboratory double-rotor helicopter and the results are discussed and compared with those of the LQR method.