In this note we study robust consensus problems for continuous-time first-order multi-agent systems (MAS) with time delays. We assume that the agents input is subject to an uncertain constant delay, which may arise due to inter-agent communication or additionally, also by self-delay in the agent dynamics. We consider dynamic feedback control protocol in the form of PD control, and seek to determine the delay consensus margin (DCM) achievable by PD feedback protocols, whereas the DCM is a robustness measure that defines the maximal range of delay within which robust consensus can be achieved despite the uncertainty in the delay. With an undirected graph, we show that the DCM can be determined exactly by solving a unimodal concave optimization problem, which is one of univariate convex optimization and can be solved using convex optimization or gradient-based numerical methods. The results show how unstable agent dynamics and graph connectivity may limit the range of delay tolerable, so that consensus can or cannot be maintained in the presence of delay variations.

In this article, we study delay robustness of PID controllers in stabilizing systems containing uncertain delays. We consider second-order systems and seek analytical characterization and exact computation of the PID delay margin, where by PID delay margin we mean the maximal range of delay values within which the system can be robustly stabilized by a PID controller. Our primary contribution is threefold. First, we show that the delay margin achieved by PID control coincides with that by PD controllers. Second, we show that the PID delay margin can be computed efficiently by solving a pseudoconcave unimodal problem, i.e., a univariate optimization problem that admits a unique maximum and, hence, is a convex optimization problem in one variable. Finally, we demonstrate analytically the tradeoff between achieving delay margin and tracking performance, showing that for several canonical performance criteria, integral control reduces the delay margin. These results lend useful insights into the PID control of delay systems, and useful guidelines in the tuning and analytical design of PID controllers.

Proportional-Integral-Derivative (PID) control has been the workhorse of control technology for about a century. Yet to this day, designing and tuning PID controllers relies mostly on either tabulated rules (Ziegler-Nichols) or on classical graphical techniques (Bode). Our goal in this paper is to take a fresh look on PID control in the context of optimizing stability margins for low-order (first- and second-order) linear time-invariant systems. Specifically, we seek to derive explicit expressions for gain and phase margins that are achievable using PID control, and thereby gain insights on the role of unstable poles and nonminimum-phase zeros in attaining robust stability. In particular, stability margins attained by PID control for minimum-phase systems match those obtained by more general control, while for nonminimum-phase systems, PID control achieves margins that are no worse than those of general control modulo to a predetermined factor. Furthermore, integral action does not contribute to robust stabilization beyond what can be achieved by PD control alone.

Among various competing designs targeting similar functionality, the key differentiator typically consists of a small amount of custom Intellectual Property (IP). To protect this IP from reverse engineering, designers need effective solutions for hiding the unique aspects of their implementations. In this work, we introduce a general framework for partitioning the computation performed by a design into a part whose implementation is commonly known (and encountered across many designs), and a part which is unique to this design. The former can then be built using conventional techniques (including untrusted manufacturing facilities) while the latter needs to be protected using additional obfuscation techniques. The existence of several other known implementations of the (same or similar) target function serves as a decoy which deflects efforts seeking to reverse-engineer the unique implementation. We demonstrate our framework using a hardware accelerator case study where (a) partitioning is performed through High Level Synthesis (HLS), (b) the commonly known portion of the accelerator is implemented as an Application Specific Integrated Circuit (ASIC), and (c) the unique portion of the accelerator is implemented on an embedded Field-Programmable Gate Array (eFPGA).

In this paper we study delay robustness of multi-agent systems (MASs) connected via directed graphs. We consider first-order agents, and we assume that the agents' input is subject to an uncertain ...

This study first introduces the frequency- wise phases of $n$ -port linear time-invariant networks based on recently defined phases of complex matrices. Such a phase characterization can be utilized to quantify capacitive, inductive, and passive behaviors of $n$ -port networks, as well as to relate to the power factor of the networks. Further, a class of matrix operations induced by fairly common $n$ -port network connections is examined. The intrinsic phase properties of networks under such connections are preserved. Concretely, a scalable phase-preserving criterion is proposed, which involves only the phase properties of individual subnetworks, under the matrix operations featured by connections. This criterion ensures that the phase range of the integrated network can be verified effectively and that the scalability of the analyses can be maintained. In addition, the inverse operations of the considered connections, that is, network subtractions with correspondences are examined. With the known phase ranges of the integrated network and one of its subnetworks, the maximal allowable phase range of the remaining subnetwork can also be determined explicitly in a unified form for all types of subtractions. Finally, we extend the phase-preserving properties from the aforementioned connections to more general matrix operations defined using a certain indefinite inner product.