A novel recurrent nonlinear neural network for solving quadratic programming problems

Effati, Sohrab; Ranjbar, Mahdi

doi:10.1016/j.apm.2010.10.001

Cited by 24 publications

(8 citation statements)

References 9 publications

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“…To solve the above optimisation problem effectively, (23) is formulated in terms of the Lagrangian dual problem form [38] and is given as

\begin{matrix} right leftthickmathspace.5em \\ inf_{α} (\frac{1}{2} normalΔ U_{k}^{T} {bold-italicQ}_{1} normalΔ U_{k} + Q_{2} normalΔ U_{k} + α ()(, H_{k} normalΔ U_{k} - G_{k})) \\ normalsubjected normalto : α \geq 0 \end{matrix}

The objective function in (24) is strictly convex for given

normalΔ U

. Thus, the minimum value is obtained by finding the derivation of (24) with respect to

normalΔ U

and is given by

{bold-italicQ}_{1} normalΔ U_{k} + Q_{2} + H^{normalT} α = 0

A unique solution to (25) is thus given as

normalΔ U_{k} = - {bold-italicQ}_{1}^{- 1} false(Q_{2} + H^{normalT} α false)

Using the expression

normalΔ U

from (26) in (24), one obtains

\underset{α}{truemax} ()(, \frac{1}{2} α^{T} λ_{1} α + α λ_{2} - \frac{1}{2} Q_{2}^{normalT} {bold-italicQ}_{1}^{- 1} Q_{2})

…”

Section: Control Law Formulationmentioning

confidence: 99%

Extreme learning‐based non‐linear model predictive controller for an autonomous underwater vehicle: simulation and experimental results

Rath

Subudhi

2019

IET cyber-systems robotics

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“…To solve the above optimisation problem effectively, (23) is formulated in terms of the Lagrangian dual problem form [38] and is given as

\begin{matrix} right leftthickmathspace.5em \\ inf_{α} (\frac{1}{2} normalΔ U_{k}^{T} {bold-italicQ}_{1} normalΔ U_{k} + Q_{2} normalΔ U_{k} + α ()(, H_{k} normalΔ U_{k} - G_{k})) \\ normalsubjected normalto : α \geq 0 \end{matrix}

The objective function in (24) is strictly convex for given

normalΔ U

. Thus, the minimum value is obtained by finding the derivation of (24) with respect to

normalΔ U

and is given by

{bold-italicQ}_{1} normalΔ U_{k} + Q_{2} + H^{normalT} α = 0

A unique solution to (25) is thus given as

normalΔ U_{k} = - {bold-italicQ}_{1}^{- 1} false(Q_{2} + H^{normalT} α false)

Using the expression

normalΔ U

from (26) in (24), one obtains

\underset{α}{truemax} ()(, \frac{1}{2} α^{T} λ_{1} α + α λ_{2} - \frac{1}{2} Q_{2}^{normalT} {bold-italicQ}_{1}^{- 1} Q_{2})

…”

Section: Control Law Formulationmentioning

confidence: 99%

Extreme learning‐based non‐linear model predictive controller for an autonomous underwater vehicle: simulation and experimental results

Rath

Subudhi

2019

IET cyber-systems robotics

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“…However, if the system is mildly nonlinear, a linearized model (such as the one proposed in this paper) can be used to obtain suboptimal control laws in real-time using quadratic programming. Also, when the quadratic programming (QP) subproblem (22) is strictly convex, a more efficient and fast QP algorithm can be used (Effati and Ranjbar, 2011). The fast QP algorithm is derived as follows.…”

Section: Mpc Optimization Problemmentioning

confidence: 99%

An ELM based predictive control method for HCCI engines

Janakiraman

Nguyen

Assanis

2016

Engineering Applications of Artificial Intelligence

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We formulate and develop a control method for homogeneous charge compression ignition (HCCI) engines using model predictive control (MPC) and models learned from operational data. An HCCI engine is a highly efficient but complex combustion system that operates with a high fuel efficiency and reduced emissions compared to the present technology. HCCI control is a nonlinear, multi-input multi-output problem with state and actuator constraints which makes controller design a challenging task. In this paper, we propose an MPC approach where the constraints are elegantly included in the control problem along with optimality in control. We develop the engine models using experimental data so that the complexity and time involved in the modeling process can be reduced. An extreme learning machine (ELM) is used to capture the engine dynamic behavior and is used by the MPC controller to evaluate control actions. We also used a simplified quadratic programming making use of the convexity of the MPC problem so that the algorithm can be implemented on the engine control unit that is limited in memory. The working and effectiveness of the proposed MPC methodology has been analyzed in simulation using a nonlinear HCCI engine model. The controller tracks several reference signals taking into account the constraints defined by HCCI states, actuators and operational limits.

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“…Thereafter, the neural networks for solving different kinds of quadratic programming problems have been studied extensively and significant research results have been achieved [11][12][13][14][15][16]. For example, Kennedy and Chua [11] presented a neural network which contains finite penalty parameters and generates approximate solution for solving nonlinear programming problems.…”

Section: Introductionmentioning

confidence: 99%

“…Based on projection methods, several projection neural networks [17,18] were used for solving linear and quadratic programming problems, their approaches which deal with inequality constraints indirectly convert the inequality constraints into equality constraints by adding slack or surplus variables. By utilizing the Lagrangian coefficients, Effati and Ranjbar [14] proposed a new neural network model with a simple form and a less number calculation operation.…”

Section: Introductionmentioning

confidence: 99%

A new delayed projection neural network for solving quadratic programming problems with equality and inequality constraints

2015

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A novel recurrent nonlinear neural network for solving quadratic programming problems

Cited by 24 publications

References 9 publications

Extreme learning‐based non‐linear model predictive controller for an autonomous underwater vehicle: simulation and experimental results

Extreme learning‐based non‐linear model predictive controller for an autonomous underwater vehicle: simulation and experimental results

An ELM based predictive control method for HCCI engines

A new delayed projection neural network for solving quadratic programming problems with equality and inequality constraints

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