Research

Robust Control Theory

Finite Frequency Analysis and Synthesis

Many design specifications can be transformed into certain performance in a finite frequency range. The generalized Kalman-Yakubovich-Popov (KYP) lemma provides an elegant tool for further transforming finite frequency specifications into a conven optimization problem in terms of linear matrix inequality (LMI). With the help of the general KYP lemma, not only can the tranditional robust control theory (e.g., H_∞ control) be generalized to deal with finite frequency specifications, but also new analysis methods can be devised for systems with complex dynamics.

The main problems in this direction include:

• Control synthesis with finite frequency specifications (e.g., static/dynamic output-feedback, repetitive control)
• Finite frequency characterization of complex systems (e.g., time-delay systems and multi-dimensional sytems)
• Frequency-partitioning approach to non-conservative analysis of complex systems
• Applied extensions in other engineering problems (e.g., filter design, Delta-Sigma modulator optimization, structural control)

Parameter-Dependent Lyapunov Function Approach

Uncertainties are ubiquitous in practical plants (e.g., unmodeled dynamics, model simplification or parameter drifting). The goals of robust control is to analyze the allowable uncertainty level under a given controller (robustness analysis) and to find a controller under a given uncertainty level (robustness synthesis). Parameter-dependent Lyapunov functions are more general than the traditional parameter-independent ones, and thus can provide less conservative analysis and synthesis results. However, to this end, the usual parameter-dependent approach will introduce many slack variables in the design conditions, thus sacrifacing the computational efficiency.

The main problems in this direction include:

• Robust analysis conditions with less conservatism but less loss of computional efficiency
• Robust H_∞ and H₂ control/filtering with less conservatism but less loss of computional efficiency
• Robust control/filtering for switching systems with uncertain transitions

Networked Multi-Agent Systems

Cost-Efficient Consensus of Networked Multi-Agent Systems

Multi-agent systems have potential applications in distributed optimization, unmanned vehicles, smart grids, sensor networks, animal flocking and swarming, etc., and thus have received considerable attention in the past years. Since each agent usually has limited energy storage and communication capacity, controllers for multi-agent systems (usually termed protocol) are expected to distributed (i.e., communicate between neighboring agents) and cost-efficient (i.e., easy to implement and less frequent communication). For the latter, there are basically two ways to achieve more cost-efficient: one is to increase spatial sparsity (e.g., reduce communication links and reduced-order protocols) and the other is to increase temporal sparsity (e.g., reduce sampling and communication frequencies).

The main problems in this direction include:

• Output-feedback protocols without controller interaction
• Robsut consensus for uncertain multi-agent systems
• Parameterization of reduced-order protocols with relative information sensing
• Event-/self-triggered protocols with improved sampling intervals
• Adaptive protocols with no need to compute the graph Laplacian