An ecologically inspired direct search method for solving optimal control problems with Bézier parameterization

Ghosh, Arnob; Das, Swagatam; Chowdhury, Aritra; Giri, Ritwik

doi:10.1016/j.engappai.2011.04.005

Cited by 26 publications

(16 citation statements)

References 14 publications

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“…Taking into account the key phases described above, the steps of implementing the IWO algorithm can be summarized as follows (Ghosh et al 2011;Roy et al 2013;Li et al 2011;Kundu et al 2012;Mehrabian and Lucas 2006) • Step 1: Initialize randomly generated weeds in the entire search space.…”

Section: Biological Invasionmentioning

confidence: 99%

Invasive Weed Optimization Algorithm

Xing

Gao²

2013

Intelligent Systems Reference Library

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Section: Biological Invasionmentioning

confidence: 99%

Invasive Weed Optimization Algorithm

Xing

Gao²

2013

Intelligent Systems Reference Library

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“…Minimization of the quadratic cost given in (17) leads to the solution of the Discrete Algebraic Riccati Equation (DARE) given by (18) ( )…”

Section: Discrete Time Quadratic Regulator Theory Applied To Optimal mentioning

confidence: 99%

“…Thus, for a specific sampling time s T , the optimal controller needs to be derived using the discrete version of the LQR formulation i.e. DARE given by (18). Fig.…”

Section: Discrete Time Quadratic Regulator Theory Applied To Optimal mentioning

confidence: 99%

“…The mixed H 2 /H ∞ optimal PID controller tuning of Chen et al [14] has been improved with GA as a single objective disturbance rejection PID controller in Krohling and Rey [15] and as multi-objective loop-shaping based design in Lin et al [16]. A wide class of standard optimal control problems has been solved using evolutionary and swarm intelligence based global optimization techniques in Ghosh et al [17], [18].…”

Section: Introductionmentioning

confidence: 99%

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LQR based improved discrete PID controller design via optimum selection of weighting matrices using fractional order integral performance index

Das

Pan

Halder

et al. 2013

Applied Mathematical Modelling

120

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The continuous and discrete time Linear Quadratic Regulator (LQR) theory has been used in this paper for the design of optimal analog and discrete PID controllers respectively. The PID controller gains are formulated as the optimal state-feedback gains, corresponding to the standard quadratic cost function involving the state variables and the controller effort. A real coded Genetic Algorithm (GA) has been used next to optimally find out the weighting matrices, associated with the respective optimal state-feedback regulator design while minimizing another time domain integral performance index, comprising of a weighted sum of Integral of Time multiplied Squared Error (ITSE) and the controller effort. The proposed methodology is extended for a new kind of fractional order (FO) integral performance indices. The impact of fractional order (as any arbitrary real order) cost function on the LQR tuned PID control loops is highlighted in the present work, along with the achievable cost of control. Guidelines for the choice of integral order of the performance index are given depending on the characteristics of the process, to be controlled.

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“…Shi et al [23] presented an improved GA with variable population-size inspired by the natural features of the variable size of the population used to continuous optimization problems. Ghosh et al [13] used an ecologically inspired optimization technique for solving NOCPs. They used Bézier curves to parameterize the control functions.…”

Section: Introductionmentioning

confidence: 99%

Integrating PSO with modified hybrid GA for solving nonlinear optimal control problems

Ghanbari

Nezhadhosein

Heidari

2014

IJAMR

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Here, a two-phase algorithm based on integrating particle swarm optimization (PSO) with modified hybrid genetic algorithm (MHGA) is proposed for solving the associated nonlinear programming problem of a nonlinear optimal control problem. In the first phase, PSO starts with a completely random initial swarm of particles, where each of them contains two random matrices in time nodes. After phase 1, to achieve more accurate solutions, the number of time nodes is increased. The values of the associated new control inputs are estimated by linear or spline interpolations using the curves computed in the phase 1. In addition, to maintain the diversity in the population, some additional individuals are added randomly. Next, in the second phase, MHGA, starts by the new population constructed by the above procedure and tries to improve the obtained solutions at the end of phase 1. MHGA combines a GA with a successive quadratic programming, SQP, as a local search. Finally, we implement the proposed algorithm on some well-known nonlinear optimal control problems. The numerical results show that the proposed algorithm can find almost better solution than other proposed algorithms.

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An ecologically inspired direct search method for solving optimal control problems with Bézier parameterization

Cited by 26 publications

References 14 publications

Invasive Weed Optimization Algorithm

Invasive Weed Optimization Algorithm

LQR based improved discrete PID controller design via optimum selection of weighting matrices using fractional order integral performance index

Integrating PSO with modified hybrid GA for solving nonlinear optimal control problems

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