Robust set stabilization of Boolean control networks with impulsive effects

This paper addresses the robust set stabilization problem of Boolean control networks (BCNs) with impulsive effects via the semi-tensor product method. Firstly, the closed-loop system consisting of a BCN with impulsive effects and a given state feedback control is converted into an algebraic form. Secondly, based on the algebraic form, some necessary and sufficient conditions are presented for the robust set stabilization of BCNs with impulsive effects under a given state feedback control and a free-form control sequence, respectively. Thirdly, as applications, some necessary and sufficient conditions are presented for robust partial stabilization and robust output tracking of BCNs with impulsive effects, respectively. The study of two illustrative examples shows that the obtained new results are effective

Why Inflation Rose and Fell: Policymakers' Beliefs and US Postwar Stabilization Policy

This paper provides an explanation for the run-up of U.S. inflation in the 1960s and 1970s and the sharp disinflation in the early 1980s, which standard macroeconomic models have difficulties in addressing. I present a model in which rational policymakers learn about the behavior of the economy in real time and set stabilization policy optimally, conditional on their current beliefs. The steady state associated with the self-confirming equilibrium of the model is characterized by low inflation. However, prolonged episodes of high inflation ending with rapid disinflations can occur when policymakers underestimate both the natural rate of unemployment and the persistence of inflation in the Phillips curve. I estimate the model using likelihood methods. The estimation results show that the model accounts remarkably well for the evolution of policymakers' beliefs, stabilization policy and the postwar behavior of inflation and unemployment in the United States.

Opportunistic Wireless Control Over State-Dependent Fading Channels

The heterogeneous system consisting of the wireless control system (WCS) and mobile agent system (MAS) is ubiquitous in Industrial Internet of Things (IIoT) systems. Within this system, the positions of mobile agents may lead to shadow fading on the wireless channel that the WCS is controlled over and can significantly compromise the WCS's performance. This paper focuses on the controller design for the MAS to ensure the performance of WCS in the presence of WCS and MAS coupling. Firstly, the constrained finite field network (FFN) with profile-dependent switching topology is adopted to proceed the operational control for the MAS. By virtue of the algebraic state space representation (ASSR) method, an equivalent form is obtained for the WCS and MAS coupling. A necessary and sufficient condition in terms of constrained set stabilization is then established to ensure the Lyapunov-like performance with expected decay rate. Finally, a graphical method together with the breath-first searching is provided to design state feedback controllers for the MAS. With this method, it is easy to check the constrained set stabilization of MAS and to ensure the performance requirements of WCS in the presence of WCS and MAS coupling. The study of an illustrative example shows the effectiveness of the proposed method

Observer-based Synchronization of Multi-agent Systems Using Intermittent Output Measurements

The problem of synchronizing multiple continuous-time linear time-invariant systems connected over a complex network, with intermittently available measurements of their outputs, is considered. To solve this problem, we propose a distributed observer-based feedback controller that utilizes a local hybrid observer to estimate neighboring states only from output measurements at such potentially nonperiodic isolated event times. Due to the inherent continuous and discrete dynamics emerging from coupling the impulsive measurement updates and the interconnected networked systems, we use hybrid systems to model and analyze the resulting closed-loop system. The problem of synchronization and state estimation is then recast as a set stabilization problem, and, utilizing a Lyapunov-based analysis for hybrid systems, we provide sufficient conditions for global exponential stability of the synchronization and zero estimation error set. A numerical example is provided to illustrate the results

The Design, Construction, and Performance of a Magnetic Focusing, Semi-Circular, Low Energy Beta-Ray Spectrometer

A semi-circular beta-ray spectrometer (Fig. 1) has been constructed for operation between 2 and 120 kev electron energy. This instrument was designed to supplement the ring- focusing beta-ray spectrometer whose lower limit is approximately 25 kev. The 180° spectrometer has an electron trajectory radius of 12 cm. The field is produced by two iron free coils spaced to give a nearly homogeneous field (with some second order focusing) in the region of the electron trajectories . The field current is supplied by a one kw motor- generator set. Stabilization is obtained to 2 parts in 10, 000 with a rotating electro- mechanical unit and an electronic servo system. Source and Geiger counter window dimensions for a standard resolution of 0 .8% are 0.1 cm x 4 cm. With a 10 μ.g/cm^2 formvar window, transmission is assured down to 2 kev electron energy. A recording potentiometer traces the counting rate vs. electron energy. Several examples of chart recordings are reproduced to illustrate the performance of the semi- circular beta-ray spectrometer

On Robust Stability of Limit Cycles for Hybrid Systems with Multiple Jumps

In this paper, we address stability and robustness properties of hybrid limit cycles for a class of hybrid systems with multiple jumps in one period. The main results entail equivalent characterizations of stability of hybrid limit cycles for hybrid systems. The hybrid limit cycles may have multiple jumps in one period and the jumps are allowed to occur on sets. Conditions guaranteeing robustness of hybrid limit cycles are also presented