• MATH 4315: Introduction to partial differential equations, Fall 2006
• MATH 6370: Differential Calculus for Teachers, Summer 2006.
• MATH 1592: Calculus II, Spring 2006.
• MATH 1591: Calculus I, Fall 2005, Fall 2006.
• MATH 3331: Differential Equations,  Summer 2007.
• MATH 1191: Math Software (Matlab), Fall 2005, Spring 2006.
• Finite Element Method, 2005 Winter, University of Western Ontario.
• GE127 College Mathematics I, Online teaching, ITT Technical Institute, 2004, Summer.
• Math3110 (Teaching Slides, pptfile), Differential Equations I (Dalhousie University, Spring 2001)
• Math251, Calculus I (University of Cincinnati, Autumn 2001)

In general terms, control theory is a separate branch of mathematics and can be described as the study of how to design the process of influencing the behavior of a physical system to achieve a desired goal. Control theory consists of three main components: feedback control, controllability, and optimal control. My research interest  focuses on feedback control because, in comparison with controllability and optimal control, it is mathematically simpler and physically more applicable in solving control problems in engineering and sciences.

Feedback control  refers to an operation that, in the presence of disturbance, tends to reduce the difference between the output of a system and some reference output and does so on the basis of this difference.

Feedback control theory has developed an extensive literature covering its various concepts, theories, and applications. Significant works in the early stage of feedback control were due to Watt, Minorsky, Hazen, and Nyquist, among many others. The first significant work in automatic control was James Watt's centrifugal governor for the speed control of a steam engine in the eighteenth century.

In the 1930s, automatic control was still an engineer's dominion. Feedback controllers were designed and used by process engineers to regulate temperatures and pressures, by mechanical engineers to control the speed of engines, and by telephone engineers to build linear amplifiers. Despite their wide use, a large fraction of feedback control design consisted of ``trial and error" methods with little analysis involved if any at all. In 1934, Ivanoff  stated that ``the science of the automatic regulation of temperature is at present in the anomalous position of having erected a vast practical edifice on negligible theoretical foundations."

While feedback controllers were generally specialized mechanisms designed to solve immediate industrial problems, there were also a small number of researchers examining the theory behind these controllers. In the 1920s, while studying the automatic steering of ships at sea, Nicolas Minorsky used differential equations to model the dynamics of the ship and proportional-integral-derivative (PID) controllers and then investigated their stability. In the 1930s, using open-loop responses to steady-state sinusoidal inputs, Harry Nyquist developed a theory about the stability of closed-loop systems. Harold Hazen introduced the term servomechanisms for position control systems with a changing input and designed relay servomechanisms to track the changing input. During the decade of the 1940s, frequency-response methods represented by the Bode diagram method due to Hendrick Bode were developed. From the end of the 1940s to the early 1950s, the root-locus method due to Walter R. Evans was established. The frequency-response and root-locus methods made it possible for engineers to design linear single-input-single-output closed-loop control systems that satisfy a set of performance requirements. These early development of control theory constitutes classical control theory with the frequency-response and root-locus
methods as its core.

Modern feedback control systems have becomes more and more complex. These systems have many inputs and outputs. The stringent requirements on accuracy lead to distributed parameter systems in which partial differential equations is required to model the physical systems. Therefore classical control theory, which deals only with single-input-single-output control systems, becomes powerless for the modern complex control systems. Since about 1960, modern control theory has been developed to cope with the increasing complexity of multiple-inputs-multiple-outputs control systems. Unlike classical control theory that is based on frequency-domain analysis, modern control theory is based on time-domain analysis and synthesis using state variables.

Since the 1960s, control theory of distributed parameter systems has followed right on the heels of that of finite dimensional dynamical systems, but with slower and heavier tread. Many control concepts and theories in finite dimensional systems have been transplanted to distributed parameter systems. Control theory for many distributed parameter systems, such as the wave equation, reaction-convection-diffusion equations, elastic equations, thermoelastic equations, viscoelastic equations, Schrödinger's equations,  and Navier-Stokes equations, has been well developed.

Recently it has become appreciated that control theory can be used to analyze non-engineering systems, such as biological systems and control theory has been inspired by these biological systems.