Synthesis of minimum-time feedback laws for dynamic systems using neural networks

Lee, Allan Y.; Smyth, Padhraic

doi:10.2514/3.21280

Cited by 5 publications

(5 citation statements)

References 3 publications

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“…The open-loop results show that there is a good agreement between the investigated results and the analytical results of minimum-time feedback laws achieved for dynamic systems [3] . Then by, the closed-loop optimal control is computed using NOC law in the exact solution.…”

Section: Resultssupporting

confidence: 60%

“…In this way, the following algebraic equations are derived as: It should be noted that the investigated results are identical with the analytical results of reference [3]. By regarding this fact that the solution parameters , , u v y and x have been expressed in the terms of β , and β is related to τ , so that the solution parameters could be expressed respect to τ .…”

Section: T Y T U T T U V T T Y T T Hmentioning

confidence: 77%

“…This law is an exact solution to the two-point boundary value problem associated with the first variation necessary conditions [2] . The results of minimum-time Feedback Laws [3] are used to validate the results of an analytical open-loop strategy proposed in this paper. Jardin and Bryson used the technique of NOC to develop an algorithm for optimizing aircraft trajectories in general wind fields computing time-varying linear feedback gains [4] .…”

Section: Introductionmentioning

confidence: 99%

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Determination of Nonlinear Optimal Feedback Law for Satellite Injection Problem Using Neighboring Optimal Control

Afshari¹,

Novinzadeh²,

Roshanian³

2009

American Journal of Applied Sciences

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An optimal trajectory design of a nonlinear satellite injection problem for transfer to a final target orbit by minimizing the time was investigated. Indeed, this design was an exact solution to the nonlinear two-point boundary value problem which determined optimal control history as well as optimal state trajectories in the open-loop form. Furthermore, the obtained optimal guidance strategy was exerted in the closed-loop form against the environment disturbances using neighboring optimal control method in the exact solution. Neighboring Optimal Control (NOC) law could produce timevariant feedback gains minimizing the performance measure to second order for perturbations from a nominal optimal path. Generally, this law was a function of perturbations appeared in the states and constraints and could be computed utilizing the backward sweep method. The simulation results indicated that the presented methodology was successfully utilized in the real world applications with good robustness to each noise or disturbance produced in each state variable.

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Section: Resultssupporting

confidence: 60%

Section: T Y T U T T U V T T Y T T Hmentioning

confidence: 77%

Section: Introductionmentioning

confidence: 99%

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Determination of Nonlinear Optimal Feedback Law for Satellite Injection Problem Using Neighboring Optimal Control

Afshari¹,

Novinzadeh²,

Roshanian³

2009

American Journal of Applied Sciences

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“…Note that the results are identical with the analytical results of reference (Lee and Smyth, 1993) and that the solution parameters u; v; y and x have been expressed in terms of b, where b is related to t. This control law is of course in openloop form.…”

Section: Analytical Open-loop Solution Of the Orbital Transfer Problemsupporting

confidence: 71%

Non‐linear feedback optimal control law for minimum‐time injection problem using fuzzy system

Pourtakdoust

Rahbar²,

Novinzadeh³

2005

Aircraft Eng & Aerospace Tech

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Purpose -To devise a new technique to synthesise optimal feedback control law for non-linear dynamic systems through fuzzy logic. Design/methodology/approach -The proposed methodology utilizes the open-loop optimal control solutions (OCSs) of the non-linear systems for the training of the fuzzy system in the process of developing closed-loop fuzzy logic guidance (FLG). This is achieved through defining a set of nondimensionalised variables related to the system states. Findings -FLG is capable of generating closed-loop control law for the non-linear problem investigated. Since the proposed fuzzy structure is independent of the system equations, the approach is potentially applicable to other non-linear system. Introduction of the non-dimensional variables in place of the regular states has effectively increased the fuzzy training performance and greatly reduced the number of fuzzy rule bases required to produce accurate solutions for other untrained scenarios. Originality/value -There exist many complex non-linear problems in guidance and control of aerospace vehicles. Determination of optimal control laws for such systems is usually a difficult task even in an open-loop form and in a noise-free off-line environment. On the other hand, closed-loop OCSs are highly desirable for their robust characteristics in actual operating environments, so are more suitable for online applications, but can seldom be realized for complex non-linear systems. Even though a few researchers have worked in the area of non-linear optimal control and application of fuzzy logic on such systems, non-have dealt with closed-loop optimal fuzzy controllers. This research proposes a new strategy for the determination of optimal feedback control laws for non-linear systems, which can be utilized in many spacecraft mission applications.

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“…Lewis and Abu‐Khalaf (2004) have proposed nearly optimal state feedback control for constrained non‐linear systems through HJB equation using neural networks. Lee and Symth (1993) and Goh et al (1996) have also used neural networks in the solution of minimum time optimal control problem. Pourtakdoust et al (2005a) have developed a time optimal closed‐loop control for non‐linear lunar‐lander problem using fuzzy networks.…”

Section: Introductionmentioning

confidence: 99%

A neuro‐optimal approach for thrust‐insensitive trajectory planning

Pourtakdoust

Pazooki

Noushabadi

2009

Aircraft Engineering and Aerospace Technology

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PurposeThe purpose of this paper is to devise a new approach to synthesize closed‐loop feedback guidance law for online thrust‐insensitive optimal trajectory generation utilizing neural networks.Design/methodology/approachThe proposed methodology utilizes an open‐loop variational formulation that initially determines optimal launch/ascent trajectories for various scenarios of known uncertainties in the thrust profile of typical solid propellant engines. These open‐loop optimized trajectories will then provide the knowledge base needed for the subsequent training of a neural network. The trained network could eventually produce thrust‐insensitive closed‐loop optimal guidance laws and trajectories in flight.FindingsThe proposed neuro‐optimal guidance scheme is effective for online closed‐loop optimal path planning through some measurable and computable engine and flight parameters.Originality/valueDetermination of closed‐loop optimal guidance law for non‐linear dynamic systems with uncertainties in system and environment has been a challenge for researchers and engineers for many years. The problem of steering a solid propellant driven vehicle is one of these challenges. Even though a few researchers have worked in the area of non‐linear optimal control and thrust‐insensitive guidance, this paper proposes a new strategy for the determination of closed‐loop online thrust insensitive guidance laws leading to optimal flight trajectories for solid propellant launch and ascent vehicles.

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Synthesis of minimum-time feedback laws for dynamic systems using neural networks

Cited by 5 publications

References 3 publications

Determination of Nonlinear Optimal Feedback Law for Satellite Injection Problem Using Neighboring Optimal Control

Determination of Nonlinear Optimal Feedback Law for Satellite Injection Problem Using Neighboring Optimal Control

Non‐linear feedback optimal control law for minimum‐time injection problem using fuzzy system

A neuro‐optimal approach for thrust‐insensitive trajectory planning

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