Output regulation by postprocessing internal models for a class of multivariable nonlinear systems

Abstract

In this paper we propose a new design paradigm, which employing a post-processing internal model unit, to approach the problem of output regulation for a class of multivariable minimum-phase nonlinear systems possessing a partial normal form. Contrary to previous approaches, the proposed regulator handles control inputs of dimension larger than the number of regulated variables, provided that a controllability assumption holds, and can employ additional measurements that need not to vanish at the ideal error-zeroing steady state, but that can be useful for stabilization purposes or to fulfill the minimum-phase requirement. Conditions for practical and asymptotic output regulation are given, underlying how in post-processing schemes the design of internal models is necessarily intertwined to that of the stabilizer.

Global robust output regulation of a class of MIMO nonlinear systems by nonlinear internal model control

“…Third, the nonlinear internal model (7) is quite general and can include the linear internal model as well as Luenberger internal model of the form proposed in the works of Nikiforov 32 and Marconi et al, 18 respectively, and the nonlinear internal model of the form proposed in the work of Huang and Chen 30 as a special case. Finally, although the nonlinear internal model (7) seems not constructive as the internal models proposed in the works of Byrnes and Isidori, 16,17 McGregor et al 23 and Bin and Marconi, 27 our method offers a much greater degree of flexibility to synthesize an internal model candidate without assuming some restrictive conditions on the steady‐state signals.…”

“…However, Byrnes and Isidori 17 only considered a semi‐global output regulation problem while we deal with the global robust output regulation problem. Moreover, the nonlinear internal model (7) does not employ high‐gain technique which means that L i does not have to be large enough as in the works of Byrnes and Isidori, 17 McGregor et al 23 and Bin and Marconi 27 and only needs to be selected such that the transformed internal model dynamics satisfy certain input‐to‐state stable property which will be clarified shortly. Third, the nonlinear internal model (7) is quite general and can include the linear internal model as well as Luenberger internal model of the form proposed in the works of Nikiforov 32 and Marconi et al, 18 respectively, and the nonlinear internal model of the form proposed in the work of Huang and Chen 30 as a special case.…”

“…Note that the key for solving the output regulation problem is to design an appropriate internal model, which can reproduce the necessary steady‐state signals of the plant and guarantee that the stabilization problem of the augmented system is solvable 16‐21 . Although excellent research outcomes on output regulation theory for SISO nonlinear systems have been achieved, the extension of the theory to MIMO nonlinear systems is still a challenging problem despite a few representative research outcomes 1,2,22‐27 . In particular, Chen and Huang 22 proposed a constructive nonlinear internal model design approach to achieve local robust output regulation of generic MIMO nonlinear systems.…”

“…Wang et al 25,26 solved robust output regulation problem of invertible and input–output linearizable MIMO square nonlinear systems which can be transformed into a system having unitary vector relative degree by output redesign (see the works of Wang et al 28,29 for the stabilization results of the invertible MIMO nonlinear systems). Bin and Marconi 27 proposed a postprocessing internal model approach to solve the semi‐global output regulation problem of a class of multivariable nonsquare nonlinear systems possessing a partial normal form. For system (1), Ping and Huang 1 proposed a linear internal model based state feedback control law to solve its global robust output regulation problem subject to a linear exosystem.…”

“…This control problem is challenging for the following two reasons. First, system (1) not only may not have well‐defined relative degree and cannot be put into a normal form considered in the works of McGregor et al 23 and Astolfi et al, 24 but also may not possess a linear input–output behavior rendered by a state‐dependent feedback law considered in the works of Wang et al 25,26 and Bin and Marconi 27 . Second, when unmeasurable disturbance is taken into account and is assumed to be generated by a nonlinear exosystem, the constructive nonlinear internal model design in the works of Chen and Huang, 22 Yang and Huang, 20 and Ping et al 2 becomes invalid because the proposed nonlinear internal models rely on the exogenous signal.…”