First-Order Continuous-Time Research Articles

Game-Based Consensus of Hybrid Multiagent Systems.

This article considers consensus of first-order/second-order hybrid multiagent systems (MASs) based on game modeling. In the first-order hybrid MAS (HMAS), a subset of agents select the Nash equilibrium of a multiplayer game as their states at each game time and the others update their states with first-order continuous-time (C-T) dynamics. By graph theory and matrix theory, we establish sufficient and necessary conditions for consensus of the first-order HMAS with two proposed protocols. The second-order HMAS is composed of agents whose states are determined by the Nash equilibrium of a multiplayer game and agents whose states are governed by second-order C-T dynamics. Similarly, sufficient and necessary conditions are given for consensus of the second-order HMAS with two proposed protocols. Several numerical simulations are provided to verify the effectiveness of our theoretical results.

A 77.3-dB SNDR 62.5-kHz Bandwidth Continuous-Time Noise-Shaping SAR ADC With Duty-Cycled Gm-C Integrator

This article presents a first-order continuous-time (CT) noise-shaping successive-approximation-register (NS-SAR) analog-to-digital converter (ADC). Different from other NS-SAR ADCs in literature, which are discrete-time (DT), this ADC utilizes a CT Gm-C integrator to realize an inherent anti-aliasing function. To cope with the timing conflict between the DT SAR ADC and the CT integrator, the sampling switch of the SAR ADC is removed, and the integrator is duty cycled to leave 5% of the sampling clock period for the SAR conversion. Redundancy is added to track the varying ADC input due to the absence of the sampling switch. A theoretical analysis shows that the 5% duty-cycling has negligible effects on the signal transfer function (STF) and the noise transfer function. The output swing and linearity requirements for the integrator are also relaxed thanks to the inherent feedforward path in the NS-SAR ADC architecture. Fabricated in 65-nm CMOS, the prototype achieves 77.3-dB peak signal-to-noise and distortion ratio (SNDR) in a 62.5-kHz bandwidth while consuming <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$13.5~\mu \text{W}$ </tex-math></inline-formula> , leading to a Schreier figure of merit (FoM) of 174.0 dB. Moreover, it provides 15-dB attenuation in the alias band.

Accelerated First-Order Continuous-Time Algorithm for Solving Convex-Concave Bilinear Saddle Point Problem

First-order methods have simple structures and are of great importance to big data problems because first-order methods are easy to implement in a distributed or parallel way. However, in the worst cases, first-order methods often converge at a rate O(1/t), which is slow. This paper considers a class of convex-concave bilinear saddle point problems and proposes an accelerated first-order continuous-time algorithm. We design the accelerated algorithm by using both increasing and decreasing damping coefficients in the saddle point dynamics. If parameters of the proposed algorithm are proper, the algorithm owns O(1/t2) convergence without any strict or strong convexity requirement. Finally, we apply the algorithm to numerical examples to show the superior performance of the proposed algorithm over existing ones.

Identification of Multiple First-Order Continuous-Time Dynamic Models From Special Segments in Historical Data

Continuous-time dynamic models are often required for controller design, process monitoring, and operation optimization. This paper proposes an approach to estimate unknown parameters of multiple first-order continuous-time dynamic models from special segments in historical data. The approach is composed by two main steps. First, special segments are defined as the ones with two ends in steady states and the middle part having significant amplitude variations in transient states; the special segments are found automatically by exploiting a piece-wise linear representation technique from a large amount of historical data samples. Second, static gains are estimated by solving a set of linear equations based on steady-state values of inputs and outputs; sums of time constants and delays are obtained by solving another set of linear equations based on integrals of model output errors from data samples in transient states; the sums are used as an optimization constraint for maximizing the fitness value between measured and simulated outputs, from which separated estimates of time constants and delays are yielded. Numerical examples are provided to illustrate the proposed approach and compare with existing ones.

Consensus of hybrid multi-agent systems with heterogeneous dynamics

ABSTRACT This paper addresses the consensus problems for two kinds of hybrid multi-agent systems. The first kind of hybrid multi-agent system is composed of first-order discrete-time and second-order continuous-time dynamical agents. Based on different interactive modes, two effective protocols are presented for the hybrid multi-agent system, respectively. By using graph theory and system transformation method, some criteria are obtained for solving the consensus problem. The second one consists of first-order continuous-time and second-order discrete-time dynamical agents. The effective protocols are also proposed to guarantee the consensus. Meanwhile, the necessary and sufficient conditions are established for solving the consensus problem. Simulation examples are provided to demonstrate the effectiveness of theoretical results.

A Study of the First-Order Continuous-Time Bilinear Processes Driven by Fractional Brownian Motion

The continuous-time bilinear (COBL) process has been used to model non linear and/or non Gaussian datasets. In this paper, the first-order continuous-time bilinear COBL (1,1) model driven by a fractional Brownian motion (fBm for short) process is presented. The use of fBm processes with certain Hurst parameter permits to obtain a much richer class of possibly long-range dependent property which are frequently observed in financial econometrics, and thus can be used as a power tool for modelling irregularly series having memory. So, the existence of Itô’s solutions and there chaotic spectral representations for time-varying COBL (1, 1) processes driven by fBm are studied. The second-order properties of such solutions are analyzed and the long-range dependency property are studied.

Moment method estimation of first-order continuous-time bilinear processes

ABSTRACTIn the present paper, we propose an estimation method of the first order continuous-time bilinear (COBL) process based on Euler-Maruyama discretization of the Itô solution asociated with the stochastic differerential equation (SDE) defining the process, and we suggest a standard moment method (MM) estimates of the unknown parameters involving in COBL process. So, some relationships linking the parameters and the theoretical moments of the process and its quadratic version are given. These relationships we allow to construct two algorithms to estimate the parameters based on MM. Using the fact that the incremented processes are strongly mixing with exponential rate whenever certain conditions are fulfilled, we show that the resulting estimators are strongly consistent and asymptotically normal. The theory can be applied to the COGARCH(1, 1), Gaussian Ornstein-Uhlenbeck (OU) models and among other specifications. Finite sample properties are also considered throught Monte-Carlo experimencts. In end, this algorithm is then used to model the exchanges rate of the Algerian Dinar against the US-dollar and against the single European currency.

A Study of the First-Order Continuous-Time Bilinear Processes Driven by Fractional Brownian Motion

A Study of the First-Order Continuous-Time Bilinear Processes Driven by Fractional Brownian Motion

Adaptive Stabilization of Nonnecessarily Inversely Stable First-Order Continuous-Time Systems under Saturated Input

This paper presents an indirect adaptive stabilization scheme forfirst-order continuous-time systems under saturated input which isdescribed by a sigmoidal function. The singularities are avoided througha modification scheme for the estimated plant parameter vector so thatits associated Sylvester matrix is guaranteed to be nonsingular andthen the estimated plant model is controllable. The modificationmechanism involves the use of a hysteresis switching function. Analternative hybrid scheme, whose estimated parameters are updated atsampling instants is also given to solve a similar adaptivestabilization problem. Such a scheme also uses hysteresis switching formodification of the parameter estimates so as to ensure thecontrollability of the estimated plant model.

An Exact Discrete Analog to a Closed Linear First-Order Continuous-Time System with Mixed Sample

This article deals with the derivation of the exact discrete model that corresponds to a closed linear first-order continuous-time system with mixed stock and flow data. This exact discrete model is (under appropriate additional conditions) a stationary autoregressive moving average time series model and may allow one to obtain asymptotically efficient estimators of the parameters describing the continuous-time system.