Optimal Control Course | IIT Roorkee | Prof. Barjeev Tyagi | Postgraduate Engineering

Course Details

Unlock Advanced System Design with Optimal Control

In the realm of advanced engineering, the ability to design systems that not only function but perform at their absolute best is paramount. Optimal Control provides the mathematical framework and practical tools to achieve this goal. This sophisticated branch of control theory is dedicated to determining control signals that cause a process to satisfy physical constraints while simultaneously extremizing—maximizing or minimizing—a chosen performance criterion, known as a cost function or performance index.

Whether the approach is algebraic or geometric, the interest is in single or multiple objectives, or the signals are deterministic or stochastic, optimization techniques are fundamental. For postgraduate students, research engineers, and scientists aiming to push the boundaries in fields like aerospace, robotics, power systems, and automation, a deep understanding of optimal control is indispensable.

Course Instructor: Expertise from IIT Roorkee

This intensive course is led by Prof. (Dr.) Barjeev Tyagi, an esteemed Associate Professor in the Electrical Engineering Department at IIT Roorkee. Prof. Tyagi brings a wealth of knowledge and experience, with an academic journey spanning India's premier institutions:

• Ph.D. in Electrical Engineering from IIT Kanpur (2005)
• M.Tech in Control Systems from IIT Kharagpur (2000)
• B.E. in Electrical Engineering from IIT Roorkee (1987)

His research interests encompass Control System Analysis and Design, with specific applications in Power Systems and Distributed Generation. Under his guidance, students will gain insights from both rigorous theoretical foundations and practical research perspectives.

Who Should Enroll?

This course is meticulously designed as an elective for:

• Postgraduate (PG) students in Electrical, Electronics, and Communications Engineering.
• Research Engineers and Scientists in R&D sectors.
• Non-Ph.D. faculty members seeking to enhance their curriculum.

Prerequisite: A solid foundation in Advanced Control System theory is required to fully engage with the course material.

Industries That Value This Knowledge

Proficiency in Optimal Control is highly sought after by premier organizations and institutions, including:

• DRDO (Defence Research and Development Organisation)
• ISRO (Indian Space Research Organisation)
• Various Engineering Institutions and Industrial R&D divisions.

Detailed 8-Week Course Layout

The course is structured to build your knowledge from fundamental principles to advanced applications over eight weeks.

Week 1-2: Foundations of Calculus of Variations

The journey begins with the mathematical bedrock of optimal control. You will delve into the Calculus of Variations, learning to find functions that optimize functionals (functions of functions). Topics include:

• Basic concepts and the fundamental variational problem.
• Fixed end-point and free end-point problems.
• The Lagrange Multiplier method for optimizing functions and functionals under constraints.

Week 3-5: The Linear Quadratic Regulator (LQR) Framework

The core of modern optimal control for linear systems. This section covers the variational approach leading to the powerful LQR solution.

• Formulation and solution of the Linear Quadratic Optimal Control problem.
• The Infinite Horizon Regulator Problem for steady-state optimization.
• Analytical solutions to the critical Matrix Differential Riccati Equation using State Transition and Similarity Transformation approaches.
• Frequency domain interpretations of LQR design.

Week 6: Advanced Topics and Tracking Systems

Building on LQR, this week explores extended concepts and different problem formulations.

• LQR with a specified degree of stability.
• Inverse Riccati Equations.
• Linear Quadratic Tracking (LQT) systems for following desired trajectories.
• Introduction to Discrete-Time Optimal Control.

Week 7: Discrete-Time Systems Deep Dive

Focusing on digital implementation and computer-controlled systems.

• Detailed analysis of Discrete-Time Optimal Control.
• The Matrix Difference Riccati Equation and its analytical solutions.

Week 8: Dynamic Programming and Time-Optimal Control

The course concludes with powerful alternative methods and handling control constraints.

• Optimal Control Using Dynamic Programming, a recursive optimization strategy.
• The Hamilton-Jacobi-Bellman (HJB) Equation and its application to LQR.
• Time-Optimal Control (Bang-Bang Control) for systems with constrained control inputs, focusing on achieving the desired state in minimum time.

Essential Reference Materials

The course curriculum is supported by seminal textbooks in the field, providing students with comprehensive resources for deep study:

Why This Course is a Career Catalyst

Mastering Optimal Control equips you with the skills to design smarter, more efficient, and high-performance systems. From guiding satellites and missiles to stabilizing power grids and optimizing industrial processes, the applications are vast and critical. This 8-week course with Prof. Barjeev Tyagi offers a unique opportunity to learn these advanced concepts from an IIT expert, structuring your learning to transition seamlessly from theory to application. Enroll to take a significant step towards becoming a specialist capable of solving the most challenging control problems in modern engineering.

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