Adaptive MPC for Uncertain Discrete-Time LTI MIMO Systems with Incremental Input Constraints

In this study, an adaptive model predictive control (MPC) strategy is proposed for a class of discrete-time linear systems with parametric uncertainty. In the presented adaptive MPC, an updating law is firstly designed to update the estimated parameters online. By utilizing the estimated parameters, a standard MPC optimization problem for unconstrained systems is established. Then, to deal with constrained systems, the min-max MPC technique is developed under the set-based approach for the estimated parameters. Furthermore, it is shown theoretically that the recursive feasibility and closed-loop stability can be rigorously proved, respectively. Finally, numerical simulations and comparative analysis are presented to illustrate the superiority of the proposed algorithms in control performance.

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“…where a s (k + 1) is defined in (28). Analogously, after a finite time, a s (k + 1) is almost close to zero.…”

Section: Feasibility and Stability Analysismentioning

confidence: 97%

“…Indeed, some research efforts are made to reshape the proposed control framework to make it applicable to constrained systems. 28 Nonetheless, rigorous proof of recursive feasibility is missing in this work. In 2020, Zhu et al 29 proposed a new adaptive MPC based on his previous work, which can directly address constraints.…”

Section: Introductionmentioning

confidence: 99%

An adaptive model predictive control strategy for a class of discrete‐time linear systems with parametric uncertainty

Gou

Ding

et al. 2021

Adaptive Control & Signal

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“…Then, in order to make the self‐tuning Equation () hold true. The input

u (k)

must satisfy the following conditions [32, 33]:

Γ {(k)}^{T} Γ (k) \leq \frac{2 - α}{λ}

where

0 < α < 2

. Moreover, to make the cost function (11) feasible,

λ

must also satisfy:

λ < \frac{2 - α}{U_{m a x}^{2} + {normalΓ}_{m a x}}

where

U_{m a x}

is the bound of the input;

{normalΓ}_{m a x}

is the bound of

Γ (k)

;…”

Section: Self‐tuning Predictive Control For Unit Module Of Magnetic L...mentioning

confidence: 99%

Self‐tuning predictive control applicable to ship magnetic levitation damping device

Zhang¹,

Yan

Wang

et al. 2021

IET Collab Intel Manufact

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In the ship design, there are strict vibration-proof requirements for precision instruments. Therefore, a ship repulsive magnetic levitation damping device is designed to achieve vibration reduction. And one self-tuning predictive control method is proposed to achieve the stable levitation of this device. Firstly, a predictive control (MPC) method with state constraints and input constraints is adopted to realise the stable suspension of the floater. The MPC can solve the problem of position imbalance of the magnetic levitation system under the external complex disturbances. Secondly, a self-tuning MPC method based on recursive least square is proposed to solve the problem caused by the fixed parameters of the traditional predictive controller. At the beginning of each control cycle, the recursive least-squares (RLS) method is used to estimate the parameters of the system. Thus, the optimal control model could be obtained for the current situation. Then, this model is applied to the predictive controller to solve the problem of parameter fixation in the traditional predictive control. Finally, the simulation results show that it can improve the accuracy, dynamic response and anti-interference performance obviously.

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“…An adaptive MPC is a viable option for solutions to nonlinear problems [41,42]. The work reported here takes advantage of the low computational cost of the adaptive MPC to minimize 𝐶𝑂 emissions and fuel consumption while respecting the system constraints.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Model Predictive Control Including Battery Thermal Limitations for Fuel Consumption Reduction in P2 Hybrid Electric Vehicles

Ezemobi

Yakhshilikova

Ruzimov

et al. 2022

WEVJ

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The primary objective of a hybrid electric vehicle (HEV) is to optimize the energy consumption of the automotive powertrain. This optimization has to be applied while respecting the operating conditions of the battery. Otherwise, there is a risk of compromising the battery life and thermal runaway that may result from excessive power transfer across the battery. Such considerations are critical if factoring in the low battery capacity and the passive battery cooling technology that is commonly associated with HEVs. The literature has proposed many solutions to HEV energy optimization. However, only a few of the solutions have addressed this optimization in the presence of thermal constraints. In this paper, a strategy for energy optimization in the presence of thermal constraints is developed for P2 HEVs based on battery sizing and the application of model predictive control (MPC) strategy. To analyse this approach, an electro-thermal battery pack model is integrated with an off-axis P2 HEV powertrain. The battery pack is properly sized to prevent thermal runaway while improving the energy consumption. The power splitting, thermal enhancement and energy optimization of the complex and nonlinear system are handled in this work with an adaptive MPC operated within a moving finite prediction horizon. The simulation results of the HEV SUV demonstrate that, by applying thermal constraints, energy consumption for a 0.9 kWh battery capacity can be reduced by 11.3% relative to the conventional vehicle. This corresponds to about a 1.5% energy increase when there is no thermal constraint. However, by increasing the battery capacity to 1.5 kWh (14s10p), it is possible to reduce the energy consumption by 15.7%. Additional benefits associated with the predictive capability of MPC are reported in terms of energy minimization and thermal improvement.

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Adaptive MPC for Uncertain Discrete-Time LTI MIMO Systems with Incremental Input Constraints

Cited by 12 publications

References 10 publications

An adaptive model predictive control strategy for a class of discrete‐time linear systems with parametric uncertainty

An adaptive model predictive control strategy for a class of discrete‐time linear systems with parametric uncertainty

Self‐tuning predictive control applicable to ship magnetic levitation damping device

Adaptive Model Predictive Control Including Battery Thermal Limitations for Fuel Consumption Reduction in P2 Hybrid Electric Vehicles

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