Adaptive parallel simultaneous stabilization of a set of uncertain port‐controlled hamiltonian systems subject to actuator saturation

Abstract

This paper investigates adaptive parallel simultaneous stabilization (APSS) of a set of uncertain nonlinear port-controlled Hamiltonian (PCH) systems subject to actuator saturation and proposes a number of results on the design of the APSS controllers. First, the case of two PCH systems is studied. Using both the dissipative Hamiltonian structural and saturated actuator properties, the two systems are combined to generate an augmented PCH system, with which, some results on the control designs are then obtained. When there are external disturbances in the two systems, an H 1 APSS controller is designed for the systems. Second, the case of more than two uncertain PCH systems subject to actuator saturation is investigated, and several new results are proposed for the APSS problem. Finally, an illustrative example is presented to show that the adaptive stabilization controllers obtained in this paper work very well.

A Family of Robust Simultaneous Controllers With Tuning Parameters Design for a Set of Port‐Controlled Hamiltonian Systems

“…Next, we apply Lemma 2.1 to investigate the RASS for systems (18) and (19), which are two PCH systems, obviously. To design a family of adaptive controller with parameters for a set of Hamiltonian systems, we assume as follows:…”

“…In most cases, we can find Ψ and θ such that (21) holds in [24]. (18) and (19), with the penalty function (2) and the given level γ > 0, assume that systems (18), (19) and penalty function (2) are generalized ZEG detectable (when u = 0).…”

“…is an L 2 disturbance attenuation controller such that both R1' and R2' hold for systems (18) and (19), where Φ(X 1 , X 2 , ν) is parameterized part of controller and ν are the tuning parameters,θ is an estimation of θ, Q = Diag {q 1 , ⋯, q n } > 0 is the adaptation gain matrix, which is constant.…”

“…Proof Substituting the controller (24) into systems (18) and (19), we obtain the following closed-loop systems: (25) The systems (18), (19) and penalty function (2) can be rewritten as augmented PCH systems…”

Simultaneous stabilization for singular systems with actuator saturation and nonlinear perturbation

“…The design is carried out by solving a pair of coupled linear simultaneous polynomial equations involving controller parameters via a generalized Sylvester matrix approach [1]. In [24], The paper investigates adaptive parallel simultaneous stabilization (APSS) of a set of uncertain nonlinear port-controlled Hamiltonian (PCH) systems subject to actuator saturation and proposes a number of results on the design of the APSS controllers. When there are external disturbances in the two systems, an H APSS controller is designed for the systems.…”