Recent Trends in Stabilization and Control of Distributed Parameter Dynamic Systems

The field of control and stabilization of distributed parameter systems described by partial differential equations has recently seen an increasing number of results published by very respected researchers in excellent control engineering and applied mathematics journals. This paper presents a survey of control and stabilization results with emphasis on controls. Various distributed parameter dynamic control and stabilization problems have been studied corresponding to heat conduction, wave propagation, Schrodinger equation, crowd (swarm) dynamics, magneto-hydro-dynamic channel flow, string and beam equations, viscous Burger equation, and general diffusion equations. Various techniques have been used for control and stabilization of such systems: Lyapunov stabilization, backstepping, gain scheduling, singular perturbations, sliding mode control, observer driven controller, tracking control, sampled-data control, neural networks. The field still remains widely open for future research. Applications of surveyed results to various areas including robots, aircraft, networks, transmission lines, electrochemical processes in energy systems are indicated.