Lectures related to Linear Quadratic (LQ) Optimal Control: Proof of Theorem

Linear Quadratic Optimal Control: Analysis and Solution

Explores Linear Quadratic optimal control, analyzing cost, and presenting the solution to the FH-LQ problem.

Infinite-Horizon LQ Control: Solution & Example

Explores Infinite-Horizon Linear Quadratic (LQ) optimal control, emphasizing solution methods and practical examples.

Multivariable Control: Weight Design and Stability Analysis

Explores weight design and stability analysis in multivariable control systems, emphasizing Lyapunov theory and LQR stability.

Linear Quadratic Optimal Control: Theory and Applications

Explores Linear Quadratic optimal control theory, covering FH-LQ and IH-LQ problems and the importance of observability in control systems.

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Nonlinear Model Predictive Control

Explores Nonlinear Model Predictive Control, covering stability, optimality, pitfalls, and examples.

Multivariable Control: System Theory and Applications

Covers system theory, classic feedback control, and applications in green building and natural gas refrigeration plants.

Quadratic Forms and Symmetric Bilinear Forms

Explores quadratic forms, symmetric bilinear forms, and their properties.

Dynamics on Homogeneous Spaces and Interactions with Number Theory

Delves into Oppenheim's conjecture on quadratic forms and their connection to number theory.

State Representation and Controller Design

Covers state representation, controller design, LQR controllers, and optimal control criteria.

Dynamic Programming: Optimal Control

Explores Dynamic Programming for optimal control, covering machine replacement, Markov chains, control policies, and linear quadratic problems.

Introduction to Multivariable Control

Covers the basics of multivariable control, including system modeling, temperature control, and optimal strategies, emphasizing the importance of considering all inputs and outputs simultaneously.

Multivariable Control: Design and Analysis

Explores integral control, disturbance estimation, controller design, and observer design in multivariable control systems.

Equidistribution of CM Points

Covers the joint equidistribution of CM points in algebraic structures and quadratic forms.

Classification of Quadratic Forms

Explores the classification of quadratic forms based on eigenvalues and orthogonal diagonalization of symmetric matrices.

Multivariable Control: Eigenvalue Assignment and Disturbance Estimation

Discusses closed-loop eigenvalue selection and disturbance impact in multivariable control systems.

Pseudo-Euclidean Spaces: Isometries and Bases

Explores pseudo-Euclidean spaces, emphasizing isometries and bases in vector spaces with non-degenerate quadratic forms.

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, quadratic forms, and critical points in functions of two variables.

Finite Element Method: Higher Order Models

Explores precision of higher order finite element models and applications of quadratic finite elements in elastodynamics.

State Observers and Output-Feedback Controllers

Covers the design and implementation of state observers and output-feedback controllers in multivariable control systems.