Using a modified Modal Series to analyse weakly nonlinear circuits

Khatibi, Mahmood; Shanechi, H.M.

doi:10.1080/00207217.2014.982212

Cited by 7 publications

(7 citation statements)

References 13 publications

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“…• Step 3. Set N = k. By using expressions (32)- (33), compute x N (t) and u N (t). Then, calculate J N according to expression (35).…”

Section: Algorithm 1 (Designing the Suboptimal Trajectory And Control)mentioning

confidence: 99%

“…The modal series method is a series expansion approach developed for the analysis of nonlinear dynamical systems. () Recently, the authors have extended this method for the optimal control and model predictive control of nonlinear dynamical systems. () In this manuscript, the modal series method together with the eigenvalue decomposition approach are employed to transform the coupled nonlinear TPBVP appeared in the nonlinear OCPs into a sequence of linear TPBVPs.…”

Section: Introductionmentioning

confidence: 99%

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Optimal control of nonlinear dynamical systems based on a new parallel eigenvalue decomposition approach

Jajarmi

Băleanu

2018

Optim Control Appl Methods

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Summary This manuscript aims to investigate a new approach based on the modal series method and eigenvalue decomposition technique to solve a class of nonlinear optimal control problems. For this purpose, a sequence of decoupled linear two‐point boundary value problems is solved iteratively instead of solving the coupled nonlinear two‐point boundary value problem derived from the maximum principle. The convergence analysis of the suggested technique is also investigated. In addition, the problem that needs to be solved at each iteration is composed of lower‐order decoupled subproblems; hence, they can be solved in parallel. Thus, the new scheme has a parallel computing property improving its computational effectiveness. Numerical simulations and comparative results show that the proposed approach is efficient and provides satisfactory results.

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“…• Step 3. Set N = k. By using expressions (32)- (33), compute x N (t) and u N (t). Then, calculate J N according to expression (35).…”

Section: Algorithm 1 (Designing the Suboptimal Trajectory And Control)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal control of nonlinear dynamical systems based on a new parallel eigenvalue decomposition approach

Jajarmi

Băleanu

2018

Optim Control Appl Methods

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“…The fundamental principle of this method is based on the Taylor series expansion and the linear transformation of the state space to obtain the second order approximate analytical solution of the nonlinear system [9][10][11]. This method is characterized by easy derivation, simple calculation and obtaining the analytical solutions without solving high-dimensional nonlinear equations, and it is widely used to analyze the interaction effect of power systems with faults or disturbances [12][13][14]. For example, Khatibi et al utilized a modified modal series to investigate weakly nonlinear circuits using a modified modal series [12].…”

Section: Introductionmentioning

confidence: 99%

“…This method is characterized by easy derivation, simple calculation and obtaining the analytical solutions without solving high-dimensional nonlinear equations, and it is widely used to analyze the interaction effect of power systems with faults or disturbances [12][13][14]. For example, Khatibi et al utilized a modified modal series to investigate weakly nonlinear circuits using a modified modal series [12]. Sajjadi et al…”

Section: Introductionmentioning

confidence: 99%

Nonlinear modal interaction analysis and vibration characteristics of a francis hydro-turbine generator unit

Luo

Egusquiza

et al. 2021

Renewable Energy

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“…[21], gives a good view of nonlinear systems' dynamical behaviours [22][23]. This method was firstly developed for the analysis of dynamical systems with nonlinear terms [24][25][26], and recently it was extended for the optimal control and MPC of nonlinear dynamical systems [27][28][29]. Motivated by the remarkable advantages of the model series method, we aim to extend this technique in this paper to solve a class of discrete nonlinear OCPs.…”

Section: Introductionmentioning

confidence: 99%

On a New and Efficient Numerical Technique to Solve a Class of Discrete-time Nonlinear Optimal Control Problems

Abadi¹,

Vaziri²,

Jajarmi³

2019

JESA

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This article proposes a new and efficient iterative procedure to solve a class of discrete-time nonlinear optimal control problems. Based on the Pontryagin's maximum principle, the necessary optimality conditions are formulated in the form of a nonlinear discrete boundary value problem (BVP). This problem is then reduced into a sequence of linear discrete BVPs by applying a series expansion approach called the modal series method. Solving the aforementioned sequence by using the techniques of solving linear difference equations, the optimal control law is derived in the form of a uniformly convergent series. In order to demonstrate the efficiency of the proposed method in practice, an iterative algorithm with a fast rate of convergence is provided. In a recursive manner, only a few iterations are needed to find a suboptimal control law with enough accuracy. The effectiveness of this new technique is verified by solving some numerical examples.

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Using a modified Modal Series to analyse weakly nonlinear circuits

Cited by 7 publications

References 13 publications

Optimal control of nonlinear dynamical systems based on a new parallel eigenvalue decomposition approach

Optimal control of nonlinear dynamical systems based on a new parallel eigenvalue decomposition approach

Nonlinear modal interaction analysis and vibration characteristics of a francis hydro-turbine generator unit

On a New and Efficient Numerical Technique to Solve a Class of Discrete-time Nonlinear Optimal Control Problems

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