Stability Analysis and Novel Control Concepts for Multiple Time-delay Systems

Systems with delays exist universally in engineering, such as manufacturing process, networked control systems, tele-operation of robots, multi-robot systems, internal combustion engines, and traffic dynamics. Delays are ubiquitously observed in these systems due to the unavoidable time, which is required to gather information needed for decision-making, to generate control decisions, and to execute these decisions. These delays are crucial factors that may deteriorate or even destabilize the performance of the controlled systems. A critical question is: How to design controllers so that these time-delayed control systems can tolerate larger delays? To answer this, we first explore the interplay between the stability and the performance features of the systems under the presence of multiple delays. This pathway leads to the ultimate objective of devising effective and efficient algorithms to analyze the stability of systems with multiple delays, and designing controllers for such systems, so that their stability can be guaranteed against larger delays and their performance can be optimized, in spite of the potential adverse effects of delays. As a result of this research, two control strategies were proposed for this class of systems: “Sign Inverting Control (SIC)” and “Delay Scheduling Control (DSC)”. Sign Inverting Control is a novel control strategy to increase the delay-robustness capability of the system against larger delays. It starts from an existing nominal control logic (such as linear-quadratic regulator, LQR) formulated for non-delayed dynamics and simply inverts the sign of the control gains. The selection option between the nominal and Sign Inverting control schemes render a more robust control performance against much larger delay variations than each of the schemes. The other control logic, Delay Scheduling Control, is an unusual and interesting control concept, which suggests to increase the existing delays intentionally to improve the control performance, such as recovering the lost stability and increasing the disturbance rejection speeds. Such a multi-faceted and paradoxical combination of control logics provides previously-unexplored tools to the controller designer