Hybrid almost output regulation of linear impulsive systems with average dwell-time

Self Cite

Summary For systems with switched linear dynamics and affected by persistent switched exosignals, we propose a new hybrid control approach to achieve not only closed‐loop stability but also tracking and/or rejection of persistent references/disturbances generated by multiple exosystems, namely, output regulation. It is assumed that both controlled plant and exosystem are described by switched linear models. The proposed hybrid controller/output regulator is specified as a switching impulsive system, where the controller states will undergo impulsive jumps at each switching instant. Based on the average dwell time switching technique, it has been shown how to completely reduce the synthesis problem of the hybrid controller to a set of linear matrix equations and linear matrix inequalities. Both continuous‐time and discrete‐time cases are discussed. To demonstrate its usefulness, the proposed hybrid control method has been applied to solve the output regulation problem for a mechanical system. Copyright © 2017 John Wiley & Sons, Ltd.

“…Our objective is to design a hybrid output‐feedback controller that stabilizes the switched plant with minimal weighted

{scriptL}_{2}

β \in scriptK scriptL

such that the error output e ( t ) satisfies ∥ e ( t )∥⩽ β (∥ ϕ (0)∥, t ) + ε ∥ d ( t )∥ with

ϕ (0) : = ([], \begin{matrix} array x_{p}^{T} (0) & array x_{c}^{T} (0) & array w^{T} (0) \end{matrix})

for all t ⩾0 and some ε > 0. In particular, e ( t ) is said to be asymptotically regulated if the aforementioned condition holds for d ( t ) ≡ 0.…”

Section: Resultsmentioning

confidence: 99%

x_{c} = ([], \begin{matrix} array x_{c 1} \\ array x_{c 2} \end{matrix})

with

x_{c 1} \in {double-struckR}^{n_{w}}, x_{c 2} \in {double-struckR}^{n_{c} - n_{w}}

and parameterize the controller coefficient and reset matrices for all i , j ∈ I [1, N p ] and i ≠ j as

…”

Section: Resultsmentioning

confidence: 99%

Almost output regulation of switched linear dynamics with switched exosignals

Yuan

2017

Self Cite

“…Classic control problems recently extended to linear impulsive systems are stabilization by state or output feedback, state estimation, linear quadratic control, disturbance decoupling, and output regulation . Less typical formulations of some of these problems have also been investigated for hybrid linear systems: see, eg, the work of Yuan and Wu on almost output regulation and the works of Amato et al on finite‐time stabilization and control.…”

Section: Introductionmentioning

confidence: 99%

“…Lastly, it is worth considering the work of Yuan and Wu . Indeed, the problem dealt with in the work of Yuan and Wu is an almost output regulation problem, since, in addition to output regulation, the minimization of a weighted

ℒ_{2}

‐norm from a pertubation input to the error is required. Moreover, global asymptotic stability of the closed‐loop hybrid dynamics is achieved under an average dwell time constraint, on the assumptions of stabilizability of the plant flow dynamics and of detectability of the extended system flow dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, global asymptotic stability of the closed‐loop hybrid dynamics is achieved under an average dwell time constraint, on the assumptions of stabilizability of the plant flow dynamics and of detectability of the extended system flow dynamics. Nonetheless, the problem tackled by Yuan and Wu reduces to exact output regulation when the

ℒ_{2}

‐requirement is dropped. Hence, the comparison between this work and that of Yuan and Wu makes sense only in this special case and points out a substantially different methodological approach.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Measurement dynamic feedback output regulation in hybrid linear systems with state jumps

Zattoni

Perdon

Conte

2017

Summary This work investigates the problem of designing a hybrid dynamic feedback regulator that forces the output of a hybrid linear system to asymptotically converge to the reference generated by a hybrid exogenous system, asymptotically rejects the exogenous disturbance, and attains global asymptotic stability of the compensated hybrid linear dynamics. The class of hybrid linear systems addressed exhibits a continuous‐time linear behavior except at isolated points of the time axis, where the state is subject to discontinuities that are caused by a jump behavior. In the presence of possibly unequally spaced state jumps, under the only constraint that the minimum time between any two consecutive jumps is no smaller than a given positive real constant, both implicit and explicit sufficient conditions for the existence of a solution to the stated problem are shown. The explicit condition is constructive, in the sense that it outlines the algorithmic procedure for the synthesis of the hybrid feedback regulator, provided that a certain output‐nulling hybrid controlled invariant subspace be known. Then, a necessary and sufficient condition for the existence of such subspace is proven, so that a computational means to derive it, if any exists, is given. Finally, the devised approach is applied to a numerical example borrowed from the literature, with the twofold aim of illustrating its implementation and making a comparison with the available method.

Almost output regulation for turbofan switched systems under multi‐source disturbances and time delay

Liu,

Chen,

Shi

et al. 2023

In allusion to the multi‐variable robust control for the turbofan engine with the large envelope, an almost output regulation (AOR) problem is discussed for a class of turbofan switched systems under multi‐source disturbances and time delay. The addressed disturbances include the regulated disturbance signal, the modeled disturbance from the input channel and the energy‐bounded disturbance. First of all, a disturbance observer is constructed to estimate the unknown disturbance in the system input. Then, by combining the output regulation method and the disturbance observer‐based control (DOBC) method, a switched composite regulation controller is developed to deal with the AOR problem of the turbofan switched systems and reject the adverse effects of disturbances. Through the multiple Lyapunov function method, a set of sufficient conditions are obtained to guarantee the AOR property with the performance and disturbance suppression ability. Finally, the validity of the proposed method is demonstrated by applying the composite anti‐disturbance regulator to the regulation of the speed and pressure ratio for the turbofan model.