Nonstandard Linear Quadratic Optimal Control

Solve irregular, infinite-dimensional, and asymmetric LQ control problems

Standard LQ control theory breaks down when regularity assumptions fail, state dimensions become infinite, or controllers have asymmetric information or roles. Nonstandard Linear Quadratic Optimal Control identifies the root causes of these breakdowns and introduces decoupling-based methods for forward-backward difference/differential equations to resolve them across both discrete-time and continuous-time settings.

The book develops FBDEs decoupling techniques that enable optimal feedback controller design and feedback stabilization. Coverage extends to irregular LQ control of deterministic and stochastic systems with additive and multiplicative noise, stochastic LQ control with input delay and state delay, infinite-dimensional LQ control of partial differential systems, decentralized LQ control with various asymmetric information structures, open-loop and closed-loop Stackelberg game LQ control, and applications in networked control and multi-agent systems. Each topic connects theoretical results directly to engineering applications including autonomous driving.

Readers will also find:

• A proposed general method of decoupling FBDEs to address the difficulties encountered in analytical design
• Controller and stabilization conditions for different non-standard LQ control characterized by distinct self-developed Riccati-like equations

Designed for professionals and researchers in control theory, systems engineering, and autonomous driving, this book serves as both a theoretical reference and a practical toolkit. Graduate students with grounding in algebra, probability, and classical LQ regulation will find the structured progression from fundamentals to advanced applications accessible.