Approximate solutions to the Hamilton-Jacobi equations for generating functions: The general cost function case

AEROSPACE TECHNOLOGY JAPAN

Fujimoto

2018

Self Cite

This paper studies rendezvous control of spacecraft via constrained optimal control using generating functions. The problem of minimum energy control of the spacecraft transiting between specified states with constraints is formalized into the constrained optimal control problem. The generating function approach is extended to such problems by equipping with penalties. Finally, the developed technique is summarized as algorithms to successfully realize optimal rendezvous control with velocity and thrust bounds.

Section: Numerical Implementationmentioning

confidence: 99%

Rendezvous Control of Spacecraft via Constrained Optimal Control Using Generating Functions

AEROSPACE TECHNOLOGY JAPAN

Fujimoto

2018

Self Cite

“…Generally, the Hamilton-Jacobi equation, that is a complicated partial differential equation with many calculations, needs to be solved for the H-infinity control method [33]. Moreover, only some special cases can obtain smoothly the closed-form solutions [34]. In this article, we use feedback linearized approach to the controller design of active driving suspension system.…”

Section: Introductionmentioning

confidence: 99%

Global optimization control for nonlinear full‐car active suspension system with multi‐performances

IET Control Theory & Appl

2021

In this article, based on feedback linearized approach and linear quadratic regulator optimization control approach using particle swarm optimization, the almost disturbance decoupling, input amplitude reduction, tuning parameter optimization, controllable convergence rate, improved suspension and globally exponential stability multi-performances of highly nonlinear multi-input multi-output full-car uncertain system are simultaneously achieved without applying any nonlinear function approximator including neural network approach and fuzzy logic approach. The article proposes a new method to achieve the optimal control matrices of LQR such that the composite controller can reduce the amplitudes of system control inputs. Determination of the LQR tuning parameters is conventionally determined via trial and error approach. In addition to being very troublesome, it is difficult to find the globally best tuning matrices with LQR method. This study has first proposed the convergence rate formula of the nonlinear system response as the fitness function of LQR approach by using PSO optimization algorithm to take the place of the conventional trial and error method and locally Jacobian linearized approach under the guarantee of globally exponential stability. The simulation results show how the full-car system can be controlled optimally and satisfactorily and confirm the superiority of the proposed method.

“…Designing sliding mode controllers for electrical systems is not easy because the chattering characteristics can damage the actuator. Nonlinear control methods usually have to solve the difficult Hamilton-Jacobi equation, which is a complex partial differential equation with many computational operations [16,46,58]. In addition, we can only obtain closed-form solutions for certain special systems [16].…”

Section: Introductionmentioning

confidence: 99%

“…Nonlinear control methods usually have to solve the difficult Hamilton-Jacobi equation, which is a complex partial differential equation with many computational operations [16,46,58]. In addition, we can only obtain closed-form solutions for certain special systems [16]. A lot of research has been conducted on the application of the feedback linearization method, which has been widely used to solve many industrial applications, including nonlinear spacecraft control [5,51], tracking control of nonholonomic mobile robots [60], three-phase grid-connected photovoltaic system [32] and compressor surge control based on passiveness [48].…”

Section: Introductionmentioning

confidence: 99%

New Method of Designing Controller for Uncertain Differential-Difference Systems and Application to Time-Delay Operational Amplifier System

Jin

J. Electr. Eng. Technol.

et al. 2020

This study combines the feedback linearization method and our recent researches of Chen electrical unifying approach to propose a global tracking controller design for nonlinear uncertain differential-difference systems with time delay. One example, which cannot be solved by the first paper on the almost disturbance decoupling problem, is presented in this study to show the essential points that the tracking performance is easily solved by the proposed approach. The study applies Chen electrical unifying approach to take the place of using the disorganized virtual ground technique and the Kirchhoff's law for those traditional approaches. In order to show its significant practicability, the study has firstly designed an easy-to-implement adder and a time-delay circuit, and an unstable time-delay operational amplifier control system based on the Chen electrical unifying approach, and then has proposed a stable controller.