Robust model predictive control with ℓ1-gain performance for positive systems

Zhang, Junfeng; Cai, Xiushan; Zhang, Wei; Han, Zhengzhi

doi:10.1016/j.jfranklin.2015.05.007

Cited by 25 publications

(20 citation statements)

References 47 publications

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“…Thus, the following constraint conditions are introduced for the system (5) :

where δ > 0 and η > 0 are given constants. Some similar constraint conditions have also been used in [29] and [30] .…”

Section: Dmpc Of Pmjssmentioning

confidence: 99%

“…MPC is a step-by-step optimization technique, in which an optimal control input is obtained at each time instant by solving an optimization problem. To deal with the optimal control of positive systems, a linear centralized MPC framework was established in [29] , [30] , [31] . As described in above positive systems literature, linear Lyapunov functions and linear programming are used in the linear MPC framework.…”

Section: Introductionmentioning

confidence: 99%

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Distributed model predictive control of positive Markov jump systems

Zhang

Deng

Zhang

et al. 2020

Journal of the Franklin Institute

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This paper proposes a new distributed model predictive control (DMPC) for positive Markov jump systems subject to uncertainties and constraints. The uncertainties refer to interval and polytopic types, and the constraints are described in the form of 1-norm inequalities. A linear DMPC framework containing a linear performance index, linear robust stability conditions, a stochastic linear co-positive Lyapunov function, a cone invariant set, and a linear programming based DMPC algorithm is introduced. A global positive Markov jump system is decomposed into several subsystems. These subsystems can exchange information with each other and each subsystem has its own controller. Using a matrix decomposition technique, the DMPC controller gain matrix is divided into nonnegative and non-positive components and thus the corresponding stochastic stability conditions are transformed into linear programming. By virtue of a stochastic linear co-positive Lyapunov function, the positivity and stochastic stability of the systems are achieved under the DMPC controller. A lower computation burden DMPC algorithm is presented for solving the min-max optimization problem of performance index. The proposed DMPC design approach is extended for general systems. Finally, an example is given to verify the effectiveness of the DMPC design.

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“…Thus, the following constraint conditions are introduced for the system (5) :

where δ > 0 and η > 0 are given constants. Some similar constraint conditions have also been used in [29] and [30] .…”

Section: Dmpc Of Pmjssmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Distributed model predictive control of positive Markov jump systems

Zhang

Deng

Zhang

et al. 2020

Journal of the Franklin Institute

Self Cite

View full text Add to dashboard Cite

show abstract

“…Then, the gain of the feedback controller is so designed that the closed‐loop system is stable, a cost function is minimised and the constraints of the system and actuator are handled. Although this method for nominal general systems has been largely investigated [11–13], there are just few studies regarding MPC method in the field of positive systems [14–17]. In [14], a robust MPC with

l_{1} - gain

performance is designed for discrete‐time systems with the constraint on the state variables in the presence of an exogenous input.…”

Section: Introductionmentioning

confidence: 99%

“…Although this method for nominal general systems has been largely investigated [11–13], there are just few studies regarding MPC method in the field of positive systems [14–17]. In [14], a robust MPC with

l_{1} - gain

performance is designed for discrete‐time systems with the constraint on the state variables in the presence of an exogenous input. MPC method with mixed performances has been considered for discrete‐time positive systems with interval and polytope uncertainties in [15], in which the disturbance attenuation level is minimised and the output of the system is 1‐norm bounded.…”

Section: Introductionmentioning

confidence: 99%

“…MPC method with mixed performances has been considered for discrete‐time positive systems with interval and polytope uncertainties in [15], in which the disturbance attenuation level is minimised and the output of the system is 1‐norm bounded. The adopted control strategy in both references [14, 15] is multi‐step. In the multi‐step control strategy, a sequence of inputs is designed.…”

Section: Introductionmentioning

confidence: 99%

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