Iterative Learning-Based Trajectory Optimization Using Fourier Series Basis Functions

Drallmeier, Joseph A.; Siegel, Jason B.; Stefanopoulou, Anna G.

doi:10.1109/lcsys.2021.3139986

Cited by 3 publications

(3 citation statements)

References 16 publications

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“…Besides, the direction of the updating process is obtained from the partial derivative of the cost function with respect to the coefficient according to (20) and (24). It should be noted that to avoid getting a complex number, the expression underneath the radical sign is used as the search direction.…”

Section: Optimal Gains Design Based On the Steepest Descentmentioning

confidence: 99%

“…Rather than taking only the numerator coefficients into consideration, the denominator coefficients are now added to compute the gradient direction. Since the partial derivative of the cost function with respect to the denominator coefficient in (24) is nonzero, the nonzero gradient forces a jump to the next step where the cost is higher. Since the steepest descent attempts to reduce the cost in the next iteration, the graphs swing back and forth with the growing trend in all cases.…”

Section: Comparison Between the Finite Impulse Response Compensator A...mentioning

confidence: 99%

“…An equality constraint of the plant equation and an inequality constraint of the control input difference can be added 21 to balance the tracking accuracy and size of the control input signal. Modern designs include the spatial repetitive controller, 22 two-dimensional based approach, 23 real-time algorithm to optimize the parameterized trajectory of a system, 24 and output-feedback RC. 25 Cost functions in the aforementioned algorithms are formulated in the time domain.…”

Section: Introductionmentioning

confidence: 99%

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The optimal design of repetitive controllers based on inverse frequency response

Panomruttanarug

2023

Optim Control Appl Methods

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This article presents a complete design of non-causal finite impulse response (FIR) and infinite impulse response (IIR) compensators for repetitive control.The concept of repetitive controllers involves imitating the inverse frequency response of the feedback control system by minimizing the amplitude of error propagation from one period to the next in the frequency domain. The FIR compensator design has already been presented in our previous work. However, it was not complete since some parameters, such as the number of causal gains and total number of gains were still left open for the designers to select. This work provides a reasonable suggestion on how to choose parameters based on the steepest descent method. In addition, an IIR compensator is further developed based on the designed FIR design. The gains of the IIR compensator are adjusted by aiming to minimize the cost function using the steepest descent. As can be observed from the results, the IIR compensator developed from the FIR compensator cannot overcome the original FIR compensator since its learning performance is relatively slow and the extra gains added to the denominator increase memory usage when executing.

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Section: Optimal Gains Design Based On the Steepest Descentmentioning

confidence: 99%

Section: Comparison Between the Finite Impulse Response Compensator A...mentioning

confidence: 99%