Course

Optimal Control, Guidance and Estimation

Indian Institute of Science Bangalore

This course delves into optimal control, guidance, and state estimation techniques tailored for aerospace vehicles, particularly focusing on:

  • Aircrafts
  • Launch vehicles
  • Missiles

The study encompasses both linear and nonlinear systems theory frameworks, ensuring a well-rounded educational experience. Students from diverse engineering backgrounds will find the theoretical knowledge and practical examples beneficial.

Course Lectures
  • This introductory module sets the stage for the course, outlining its objectives and motivations. Students will gain insight into the importance of optimal control and guidance in aerospace applications.

  • This module provides an overview of the state-space approach and matrix theory, which are foundational for understanding optimal control systems. Key topics include:

    • State-space representation
    • Linear and nonlinear system matrices
    • Matrix operations and properties
  • This module reviews various numerical methods that are crucial for solving optimal control problems. Students will learn about:

    • Numerical integration techniques
    • Root-finding algorithms
    • Optimization algorithms

    Understanding these methods is vital for implementing control strategies effectively.

  • This module introduces static optimization concepts, focusing on the foundational principles and techniques. Key discussions include:

    • Definitions and applications of static optimization
    • Examples of static optimization in aerospace contexts
    • Comparison with dynamic optimization methods
  • This module continues the exploration of static optimization, delving deeper into techniques and applications. Students will examine:

    • Advanced static optimization techniques
    • Case studies illustrating real-world applications
    • Limitations and considerations in static optimization
  • This module provides a comprehensive review of the calculus of variations, a mathematical tool essential for optimal control theory. Topics include:

    • Fundamentals of the calculus of variations
    • Applications in optimal control problems
    • Variational principles and their significance
  • Continuing the exploration of calculus of variations, this module focuses on advanced techniques and problem-solving approaches, including:

    • Boundary conditions in variational problems
    • Applications in aerospace vehicle dynamics
    • Comparative analysis with other optimization techniques
  • This module focuses on the optimal control formulation using the calculus of variations. Key aspects include:

    • Formulating control problems as variational problems
    • Understanding the Euler-Lagrange equation
    • Applications in aircraft and missile guidance
  • This module introduces classical numerical methods used to solve optimal control problems. Students will learn about:

    • Dynamic programming techniques
    • Finite difference methods
    • Comparative effectiveness of various numerical approaches
  • This module delves into the Linear Quadratic Regulator (LQR), a critical method in control theory. Key discussions include:

    • Fundamentals of LQR design
    • Stability and performance analysis
    • Applications in aerospace vehicle control
  • This module continues the examination of the Linear Quadratic Regulator (LQR), focusing on advanced topics such as:

    • Multi-variable LQR systems
    • Robustness and sensitivity analysis
    • Real-world applications and case studies
  • This module concludes the study of the Linear Quadratic Regulator (LQR), addressing the following aspects:

    • Optimal control strategies using LQR
    • Performance metrics and evaluation
    • Integration with state feedback systems
  • This module continues with advanced LQR discussions, focusing on:

    • Implementation challenges in real systems
    • Trade-offs in control performance
    • Case studies highlighting LQR applications
  • This module introduces discrete-time optimal control techniques, emphasizing their relevance in modern control systems. Key topics include:

    • Discrete-time system modeling
    • Optimal control in discrete-time frameworks
    • Applications in digital control systems
  • This module provides an overview of flight dynamics, crucial for understanding aircraft behavior. It covers:

    • Basic principles of flight dynamics
    • Equations of motion
    • Stability and control in flight
  • Continuing the exploration of flight dynamics, this module addresses advanced topics such as:

    • Nonlinear flight dynamics
    • Dynamic stability analysis
    • Flight control systems
  • This module concludes the study of flight dynamics, focusing on:

    • Practical applications in aerospace vehicle design
    • Control strategies for flight stability
    • Case studies of real-world flight dynamics issues
  • This module focuses on linear optimal missile guidance using LQR techniques. Key topics include:

    • Guidance law formulation
    • Performance evaluation
    • Comparison with traditional guidance methods
  • This module introduces SDRE (State Dependent Riccati Equation) and θ-D designs, focusing on their applications in optimal control. Key discussions include:

    • Formulation of SDRE
    • Application examples in aerospace
    • Advantages and challenges of SDRE
  • Mod-10 Lec-20 Dynamic Programming
    Dr. Radhakant Padhi

    This module delves into dynamic programming, a critical method for solving complex control problems. Topics covered include:

    • Principles of dynamic programming
    • Applications in aerospace control problems
    • Comparative analysis with other methods
  • This module introduces approximate dynamic programming (ADP) and the adaptive critic method. Key discussions include:

    • Foundational principles of ADP
    • Implementation challenges
    • Case studies highlighting effectiveness
  • This module focuses on transcription methods for solving optimal control problems. Key topics include:

    • Formulation of transcription methods
    • Applications in aerospace control
    • Comparative analysis with other numerical methods
  • This module discusses model predictive static programming (MPSP) and its applications in optimal guidance of aerospace vehicles. Key discussions include:

    • Fundamentals of MPSP
    • Optimal guidance strategies
    • Case studies in aerospace applications
  • This module focuses on MPSP for optimal missile guidance, covering:

    • Guidance algorithms based on MPSP
    • Performance evaluation metrics
    • Comparative analysis with traditional methods
  • This module introduces model predictive spread control (MPSC) and generalized MPSP (G-MPSP) designs, emphasizing their applications in aerospace. Key topics include:

    • Principles of MPSC
    • Applications in optimal guidance
    • Comparative effectiveness of G-MPSP designs
  • This module provides an introduction to linear quadratic observers and offers an overview of state estimation techniques. Key discussions include:

    • Fundamentals of linear quadratic observers
    • Applications in state estimation
    • Comparison with traditional observer designs
  • This module reviews probability theory and random variables, which are integral to understanding stochastic processes in control. Key topics include:

    • Basic concepts of probability
    • Random variable definitions
    • Applications in control theory
  • This module focuses on the design of the Kalman filter, a key tool in state estimation. Topics covered include:

    • Kalman filter formulation
    • Applications in aerospace systems
    • Performance analysis of Kalman filters
  • This module continues the study of Kalman filter design, emphasizing:

    • Advanced filtering techniques
    • Real-time implementation challenges
    • Comparative analysis with other filters
  • This module concludes the Kalman filter design discussion, covering:

    • Performance evaluation metrics
    • Integration with control systems
    • Case studies demonstrating effectiveness
  • This module explores integrated estimation, guidance, and control techniques, emphasizing their importance in aerospace systems. Topics include:

    • Integration of estimation and control
    • Applications in aerospace vehicle guidance
    • Methodologies for effective integration
  • Continuing the discussion on integrated estimation, guidance, and control, this module examines advanced methods and applications:

    • Complex system integration challenges
    • Case studies highlighting effectiveness
    • Future directions in research and development
  • This module introduces Linear Quadratic Gaussian (LQG) design, focusing on:

    • Fundamentals of LQG control
    • Neighboring optimal control concepts
    • Sufficiency conditions for optimality
  • This module focuses on constrained optimal control methods, addressing key topics such as:

    • Formulating control problems with constraints
    • Applications in aerospace systems
    • Performance trade-offs in constrained environments
  • This module continues the exploration of constrained optimal control, focusing on:

    • Advanced constraint handling techniques
    • Case studies illustrating successes and challenges
    • Future trends in constrained control
  • This module concludes the study of constrained optimal control, emphasizing:

    • Integration of constraints in design
    • Applications in real-world aerospace scenarios
    • Evaluation of performance under constraints
  • This module introduces optimal control of distributed parameter systems, highlighting:

    • Fundamentals of distributed systems
    • Control strategies for distributed parameters
    • Applications in aerospace and engineering
  • This module continues the exploration of optimal control for distributed parameter systems, focusing on:

    • Advanced control methodologies
    • Case studies in aerospace applications
    • Future research directions
  • This module provides a summary of key concepts covered throughout the course, emphasizing:

    • Recap of optimal control principles
    • Applications in various aerospace contexts
    • Future learning and research opportunities
  • This concluding module provides additional take-home materials summarizing essential concepts and encouraging further study in optimal control, guidance, and estimation. Key points include:

    • Recap of critical topics
    • Suggestions for further reading
    • Encouragement for ongoing learning and research