Lectures related to Introduction to Multivariable Control

Multivariable Control: System Theory and Applications

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

Controllability and Reachability

Explores reachability and controllability in multivariable control systems, discussing tests, proofs, and their implications.

Multivariable Control: System Theory and Linear Systems

Introduces multivariable control, covering system theory, linear systems, and time discretization.

Kalman Filter: Linearized vs Extended

Explores the linearized and extended Kalman Filters, illustrating their application in nonlinear systems and the estimation of unknown parameters.

Extended Kalman Predictor: Linearized KF

Explores the Extended Kalman Predictor algorithm and the linearized Kalman Filter for multivariable control systems, discussing the challenges and applications.

Multivariable Control: Weight Design and Stability Analysis

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

Multivariable Control: System Theory and Linear Systems

Introduces the basics of multivariable control, focusing on system theory and linear systems.

Linear Quadratic (LQ) Optimal Control: Proof of Theorem

Covers the proof of the recursive formula for the optimal gains in LQ control over a finite horizon.

Steady-state Kalman Predictor: Examples and Comparison

Discusses the steady-state Kalman predictor, provides examples, and compares Luenberger and Kalman filtering.

State Observers and Output-Feedback Controllers

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

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.

Infinite-Horizon LQ Control: Solution & Example

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

Multivariable Control

Covers Gaussian random variables, affine transformations, and linear systems driven by Gaussian noise in multivariable control.

Multivariable Control: Linear Quadratic Gaussian Control

Explores linear quadratic Gaussian control and the challenges of modeling errors in control systems.

Multivariable Control: Design and Analysis

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

Eigenvalue Assignment in Multivariable Control

Explores Eigenvalue Assignment in multivariable control, emphasizing the effects of discretization and the challenges in preserving system structure.

Multivariable Control: State Estimation and Kalman Filtering

Explores state estimation and Kalman filtering for multivariable control systems, with applications in communication channels and vehicle navigation.

Multivariable Control: Equilibria and Stability Analysis

Explores equilibria and stability analysis in multivariable control systems, focusing on eigenvalues and system modes.

Multivariable Control: Stability and Lyapunov Theorems

Explores multivariable control, optimal laws, and system stability theorems, emphasizing the importance of observability.

Luenberger Observers: Separation Principle

Explores Luenberger observers in multivariable control systems, emphasizing observer stability, separation principle, and filter design.