Model predictive control of non-linear discrete time systems: a linear matrix inequality approach

Poursafar, Noushin; Taghirad, Hamid D.; Haeri, ءMohammad

doi:10.1049/iet-cta.2009.0650

Cited by 74 publications

(81 citation statements)

References 15 publications

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“…The first example shows a direct current and alternating current (DC/AC) converter model [28] [29], while the second example gives a model of an isothermal series/parallel Van de Vussue reaction in a continuous stirred-tank reactor [30] [31]. In these models, the real plants are in nonlinear structure and the single output is measured.…”

Section: Illustrative Examplesmentioning

confidence: 99%

See 1 more Smart Citation

A Gauss-Newton Approach for Nonlinear Optimal Control Problem with Model-Reality Differences

Kek¹,

Li²,

Leong³

et al. 2017

OJOp

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Output measurement for nonlinear optimal control problems is an interesting issue. Because the structure of the real plant is complex, the output channel could give a significant response corresponding to the real plant. In this paper, a least squares scheme, which is based on the Gauss-Newton algorithm, is proposed. The aim is to approximate the output that is measured from the real plant. In doing so, an appropriate output measurement from the model used is suggested. During the computation procedure, the control trajectory is updated iteratively by using the Gauss-Newton recursion scheme. Consequently, the output residual between the original output and the suggested output is minimized. Here, the linear model-based optimal control model is considered, so as the optimal control law is constructed. By feed backing the updated control trajectory into the dynamic system, the iterative solution of the model used could approximate to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, current converted and isothermal reaction rector problems are studied and the results are demonstrated. In conclusion, the efficiency of the approach proposed is highly presented.

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Section: Illustrative Examplesmentioning

confidence: 99%

“…Consider the state space representation of a direct current/alternating current (DC/AC) converter model [28] [29] given by ( ) shows that the model output is very close to the real output. Hence, the approach proposed is efficient to obtain the optimal solution of Problem (P).…”

Section: Examplementioning

confidence: 99%

A Gauss-Newton Approach for Nonlinear Optimal Control Problem with Model-Reality Differences

Kek¹,

Li²,

Leong³

et al. 2017

OJOp

View full text Add to dashboard Cite

show abstract

“…Additionally, the response of the system can also be shaped using weighting matrices, applied on the system outputs, the control action and the control rates respectively. Each MPC V ,j MPC (k), corresponding to the , j th PWA model of the quadrotor's motion at time k, is being obtained by solving the following optimisation problem, defined by the cost min u J (k) (25) subject to the , j th PWA system dynamics and their associated constraints, where J (k) is (see (26)) where → x η , x ExEy , x Ez indicates that all parameters refer either to the attitude, altitude or horizontal motion PWA…”

Section: H Exeymentioning

confidence: 99%

“…The proposed novel control strategy is based on a piecewise affine (PWA) dynamic modelling approach, and on a switching model predictive control (SMPC) [24][25][26] design scheme. More specifically, the contributions of this paper include: (a) the PWA modelling of the attitude and translational dynamics of the quadrotor that enable the development of switching control actions for a larger part of the helicopter's flight envelope, (b) the modelling of the effects induced by wind gusts as affine output disturbances, (c) the development of an SMPC that accounts for the state and actuation constraints of the quadrotor, and (d) the application of the proposed control scheme in an indoor environment, where there is lack of absolute localisation data (i.e.…”

Section: Introductionmentioning

confidence: 99%

Model predictive quadrotor control: attitude, altitude and position experimental studies

Alexis

Nikolakopoulos

Tzes

2012

IET Control Theory Appl.

320

115

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This study addresses the control problem of an unmanned quadrotor in an indoor environment where there is lack of absolute localisation data. Based on an attached inertia measurement unit, a sonar and an optic-flow sensor, the state vector is estimated using sensor fusion algorithms. A novel switching model predictive controller is designed in order to achieve precise trajectory control, under the presence of forcible wind gusts. The quadrotor's attitude, altitude and horizontal linearised dynamics result in a set of piecewise affine models, enabling the controller to account for a larger part of the quadrotor's flight envelope while modelling the effects of atmospheric disturbances as additive-affine terms in the system. The proposed controller algorithm accounts for the state and actuation constraints of the system. The controller is implemented on a quadrotor prototype in indoor position tracking, hovering and attitude manoeuvres experiments. The experimental results indicate the overall system's efficiency in position/altitude/attitude set-point manoeuvres.

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“…However, in many systems, the nonlinear effects cannot be ignored. In these conditions, the system can be approximated by a linear model and be considered on the scope approximation error [15,16,17]. Predictive control has a strong advantage: it can consider constraints explicitly in the problem, but it cannot explicitly calculate the model uncertainty in the formulation.…”

Section: Introductionmentioning

confidence: 99%

Tube-MPC for a class of uncertain continuous nonlinear systems with application to surge problem

Ziabari¹,

Jahed‐Motlagh²,

Salahshoor³

et al. 2017

Kybernetika

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Model predictive control of non-linear discrete time systems: a linear matrix inequality approach

Cited by 74 publications

References 15 publications

A Gauss-Newton Approach for Nonlinear Optimal Control Problem with Model-Reality Differences

A Gauss-Newton Approach for Nonlinear Optimal Control Problem with Model-Reality Differences

Model predictive quadrotor control: attitude, altitude and position experimental studies

Tube-MPC for a class of uncertain continuous nonlinear systems with application to surge problem

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