What is the general idea of using Jacobian in control problems?

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Javad Azizabadi

سلام، جاکوبین در واقع ساده کننده روند حل مسئله است. به طور مثال برای یافتن پایداری یک سیستم غیر خطی سخت، که معادلات پیچیده ای دارد؛ باید با استفاده از قضیه پایداری لیاپانوف این عمل را انجام داد، که بعد پی به پایدار بودن آن سیستم برد. اما با استفاده از این ژاکوبین؛ میتوان یک مسیر میان بر را انتخاب نموده و براحتی با خطی کردن سیستم غیر خطی حول نقطه تعادل، تعیین کرد که آیا سیستم پایدار هست یا نیست. همین. که این به مراتب ساده تر و کم حجم تر از یافتن تابع لیاپانوف و پیاده سازی ان است.

Samira Eshghi

I see. Would you be so kind as to provide a reference for further reading

کتاب کنترل غیر خطی اسلوتین

مورد استفاده شما از ژاکوبین به چه مواردی محدود میشه؟

The Jacobian is frequently used in robotics, specially for arm control.