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Lecture

Linear Quadratic Optimal Control: Theory and Applications

In course

ME-422: Multivariable control

This course covers methods for the analysis and control of systems with multiple inputs and outputs, which are ubiquitous in modern technology and industry. Special emphasis will be placed on discrete-time systems due to their relevance to digital and embe ...

Description

This lecture covers the theory and applications of Linear Quadratic (LQ) optimal control, focusing on the infinite-horizon LQ problem, convergence of the algebraic Riccati Equation, and computation of the optimal control law. The lecture discusses the LQ control over a finite horizon, the system under control, the optimal control cost, and the solution to the FH-LQ problem. It also explores the Difference Riccati Equation, the solution to the Infinite-Horizon (IH) LQ optimal control, and the importance of observability in control systems.

Instructor

Giancarlo Ferrari Trecate

Official source

Ontological neighbourhood

Information engineering

Control theory and engineering: Control theory

Related concepts (32)

Optimal control

Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the moon with minimum fuel expenditure.

Control theory

Control theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any delay, overshoot, or steady-state error and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller with the requisite corrective behavior is required.

Model predictive control

Model predictive control (MPC) is an advanced method of process control that is used to control a process while satisfying a set of constraints. It has been in use in the process industries in chemical plants and oil refineries since the 1980s. In recent years it has also been used in power system balancing models and in power electronics. Model predictive controllers rely on dynamic models of the process, most often linear empirical models obtained by system identification.

Linear–quadratic regulator

The theory of optimal control is concerned with operating a dynamic system at minimum cost. The case where the system dynamics are described by a set of linear differential equations and the cost is described by a quadratic function is called the LQ problem. One of the main results in the theory is that the solution is provided by the linear–quadratic regulator (LQR), a feedback controller whose equations are given below. LQR controllers possess inherent robustness with guaranteed gain and phase margin, and they also are part of the solution to the LQG (linear–quadratic–Gaussian) problem.

Adaptive control

Adaptive control is the control method used by a controller which must adapt to a controlled system with parameters which vary, or are initially uncertain.cite journal|author=Chengyu Cao, Lili Ma, Yunjun Xu|title="Adaptive Control Theory and Applications", Journal of Control Science and Engineering'|volume=2012|issue=1|year=2012|doi=10.1155/2012/827353|pages=1,2|doi-access=free For example, as an aircraft flies, its mass will slowly decrease as a result of fuel consumption; a control law is needed that adapts itself to such changing conditions.

Related lectures (35)

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 (LQ) Optimal Control: Proof of Theorem

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

Multivariable Control: System Theory and Applications

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

Multivariable Control: Design and Analysis