Fixed point transformation-based adaptive optimal control using nonlinear programming

Khan, Hamza; Szeghegyi, Ágnes; Tar, J.K.

doi:10.1109/nc.2017.8263279

Cited by 6 publications

(2 citation statements)

References 12 publications

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“…Returning to the question of adaptive MPC or adaptive RHC in [11] a simple proposition was done. While in the original version of the RHC the problem of the modeling errors is tackled by the application of the available approximate system model for the calculation of the control signals, and normally only a small part of the calculated horizon is actually utilized, furthermore, the control is frequently redesigned by the introduction of novel horizons in the beginning of which the actually measured system variables are used as initial conditions, in [11] the following idea was suggested: instead using the control forces generated by the RHC controller, the controller can adaptively track the "optimized trajectory". In this approach the mathematical frameworks of the optimal and the adaptive controllers can be integrated without any technical difficulty.…”

Section: Delay1mentioning

confidence: 99%

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On the Implementation of Fixed Point Iteration-based Adaptive Receding Horizon Control for Multiple Degree of Freedom, Higher Order Dynamical Systems

Khan¹,

Tar²

2019

ACTA POLYTECH HUNG

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Based on the observation that it is very difficult to combine the mathematical frameworks of the prevailing Lyapunov function-based adaptive controllers and the traditional, optimal control-based "Model Predictive Controllers (MPC)", a novel adaptive solution was introduced to improve the operation of the "Receding Horizon Controllers (RHC)". Because at the local optima the gradient of the auxiliary function is zero, Lagrange's original "Reduced Gradient Method (RGM)" was replaced by a "Fixed Point Iteration (FPI)"-based algorithm that directly drove this gradient toward zero. According to "Banach's Fixed Point Theorem" the convergence of the method was guaranteed by a contractive function that generated the iterative sequence. The greatest modeling burden in this approach was the need for the calculation of the Jacobian of the problem, i.e. the gradient of the gradient of the auxiliary function. In the first simulations only a single "Degree of Freedom (DoF)" 2 nd order nonlinear system, a van der Pol oscillator was investigated. The attempts that were made to evade the calculation of the Jacobian were finished with the conclusion that at least a rough numerical approximation of this Jacobian generally must be utilized. Though the MPC approach allows the use a great variety of cost functions and dynamical models, mathematically well established results are available only for quadratic cost functions and "Linear Time-invariant (LTI)" models. For other cost functions and models careful numerical analysis is needed. In this paper the use of non-quadratic cost functions is numerically investigated in the FPI-based adaptive RHC control of 2 DoF 2 nd order nonlinear system that consists of two, nonlinearly coupled van der Pol oscillators, is considered. To guarantee lucid calculations simple functions are introduced that map the active parts of the horizon under consideration to the elements of the gradient of the auxiliary function that are calculated analytically. For the calculation of the Jacobian only a rough numerical estimation is applied. The simulation results reveal certain limitations of the suggested method.

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Section: Delay1mentioning

confidence: 99%

“…[10] also related to economic and educational issues). Based on these antecedents in [11] the dynamic control of a 1 st order single variable hypothetical system, and in [12] its possible use in the model-based treatment of the illness type 1 diabetes mellitus was investigated.…”

Section: Introductionmentioning

confidence: 99%

On the Implementation of Fixed Point Iteration-based Adaptive Receding Horizon Control for Multiple Degree of Freedom, Higher Order Dynamical Systems

Khan¹,

Tar²

2019

ACTA POLYTECH HUNG

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Studying Various Cost Functions by Nonlinear Programming for the Control of an Underactuated Mechanical System

Faitli

Tar

2018

Advances in Service and Industrial Robotics

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Novel Contradiction Resolution in Fixed Point Transformation-based Adaptive Control

Khan

Tar

2018

2018 IEEE 18th International Symposium on Computational Intelligence and Informatics (CINTI)

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Fixed point transformation-based adaptive optimal control using nonlinear programming

Cited by 6 publications

References 12 publications

On the Implementation of Fixed Point Iteration-based Adaptive Receding Horizon Control for Multiple Degree of Freedom, Higher Order Dynamical Systems

On the Implementation of Fixed Point Iteration-based Adaptive Receding Horizon Control for Multiple Degree of Freedom, Higher Order Dynamical Systems

Studying Various Cost Functions by Nonlinear Programming for the Control of an Underactuated Mechanical System

Novel Contradiction Resolution in Fixed Point Transformation-based Adaptive Control

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