Krylov projection framework for Fourier model reduction

This paper analyzes the Fourier model reduction (FMR) method from a rational Krylov projection framework and shows how the FMR reduced model, which has guaranteed stability and a global error bound, can be computed in a numerically efficient and robust manner. By monitoring the rank of the Krylov subspace that underlies the FMR model, the projection framework also provides an improved criterion for determining the number of Fourier coefficients that are needed, and hence the size of the resulting reduced-order model. The advantages of applying FMR in the rational Krylov projection framework are demonstrated on a simple example.     

Multisensor switching control strategy with fault tolerance guarantees

In this paper we propose a novel fault tolerant multisensor switching strategy for feedback control. Each sensor of the proposed multisensor scheme has an associated state estimator which, together with a state feedback gain, is able to individually stabilise the closed-loop system. At each instant of time, the switching strategy selects the sensor-estimator pair that provides the best closed-loop performance, as measured by a control-performance criterion. We establish closed-loop stability of the resulting switching scheme under normal (fault-free) operating conditions. More importantly, we show that closed-loop stability is preserved in the presence of faulty sensors if a set of conditions on the system parameters (such as bounds on the sensor noises, maximum and minimum values of the reference signal, etc.) is satisfied. This result enhances and broadens the applicability of the proposed multisensor scheme since it provides guaranteed properties such as fault tolerance and robust closed-loop stability under sensor fault. The results are applied to the problem of automotive longitudinal control.     

Trading a mean-reverting asset: Buy low and sell high

This paper is concerned with an optimal trading (buy and sell) rule. The underlying asset price is governed by a mean-reverting model. The objective is to buy and sell the asset so as to maximize the overall return. Slippage cost is imposed on each transaction. The associated HJB equations (quasi-variational inequalities) are used to characterize the value functions. It is shown that the solution to the original optimal stopping problem can be obtained by solving two quasi-algebraic equations. Sufficient conditions are given in the form of a verification theorem. A numerical example is reported to demonstrate the results.     

Solving the Beck and Wieland model with optimal experimentation in DualPC

Currently, there is a renewed interest in the use of optimal experimentation (adaptive control) in economics. Example are found in [Amman and Kendrick, 1999], [Amman and Kendrick, 2003], [Cosimano, in?press], [Cosimano and Gapen, 2005b], [Cosimano and Gapen, 2005a], [Cosimano and Gapen, 2006], [Tesfaselassie et?al., 2007], [Tucci, 1997], [Wieland, 2000a] and [Wieland, 2000b]. In this paper we present the Beck & Wieland model [Beck, G., & Wieland, V. (2002). Learning and control in a changing economic environment. Journal of Economic Dynamics and Control, 26, 1359-1378] and the methodology to solve this model with time-varying parameters using the various control methods described in [Kendrick, 1981] and [Kendrick, 2002]. Furthermore, we also provide numerical results using the DualPC software [Amman, H. M., & Kendrick, D. A. (1999). The DualI/DualPC software for optimal control models: User’s guide. Working paper, Austin, TX 78712, USA: Center for Applied Research in Economics, University of Texas] and show first evidence that optimal experimentation or Dual Control may produce better results than Expected Optimal Feedback.     

Pinning adaptive synchronization of a general complex dynamical network

There are two challenging fundamental questions in pinning control of complex networks: (i) How many nodes should a network with fixed network structure and coupling strength be pinned to reach network synchronization? (ii) How much coupling strength should a network with fixed network structure and pinning nodes be applied to realize network synchronization? To fix these two questions, we propose a general complex dynamical network model and then further investigate its pinning adaptive synchronization. Based on this model, we attain several novel adaptive synchronization criteria which indeed give the positive answers to these two questions. That is, we provide a simply approximate formula for estimating the detailed number of pinning nodes and the magnitude of the coupling strength for a given general complex dynamical network. Here, the coupling-configuration matrix and the inner-coupling matrix are not necessarily symmetric. Moreover, our pinning adaptive controllers are rather simple compared with some traditional controllers. A Barabási-Albert network example is finally given to show the effectiveness of the proposed synchronization criteria.     

On hybrid control of a class of stochastic non-linear Markovian switching systems

In this paper, we address the problem of hybrid control for a class of stochastic non-linear Markovian switching systems. First, a hybrid controller is introduced for the systems. Then under some appropriate assumptions, the stabilization condition for the systems under pure impulsive control is given. Further under impulsive control, the output feedback stabilization problem of the systems is discussed and linear output feedback controllers are designed. Finally a numerical example is provided to illustrate the effectiveness of the proposed methods.     

Supervisory control of modular systems with global specification languages

The paper presents sufficient conditions for modular (supervisory) control synthesis to equal global control synthesis. In modular control synthesis a supervisory control is synthesized for each module separately and the supervisory control consists of the parallel composition of the modular supervisory controls. The general case of the specification that is indecomposable and not necessarily contained in the plant language, which is often the case in practice, is considered. The usual assumption that all shared events are controllable is relaxed by introducing two new structural conditions relying on the global mutual controllability condition. The novel concept used as a sufficient structural condition is strong global mutual controllability. The main result uses a weaker condition called global mutual controllability together with local consistency of the specification. An example illustrates the approach.     

Consensus protocols for discrete-time multi-agent systems with time-varying delays

This paper addresses consensus problems for discrete-time multi-agent systems with time-varying delays and switching interaction topologies and provides a class of effective consensus protocols that are built on repeatedly using the same state information at two time-steps. We show that those protocols can solve consensus problems under milder conditions than the popular consensus algorithm proposed by Jadbabaie et al., specifically, the presented protocols allow for the case that agents can only use delayed information of themselves, whereas the popular one is invalid. It is proved that if the union of the interaction topologies across the time interval with some given length always has a spanning tree, then in the presence of bounded time-varying delays, those protocols solve consensus problems.     

Control of frictional dynamics of a one-dimensional particle array

Control of frictional forces is required in many applications of tribology. While the problem is approached by chemical means traditionally, a recent approach was proposed to control the system mechanically to tune frictional responses. We design feedback control laws for a one-dimensional particle array sliding on a surface subject to friction. The Frenkel-Kontorova model describing the dynamics is a nonlinear interconnected system and the accessible control elements are average quantities only. We prove local stability of equilibrium points of the un-controlled system in the presence of linear and nonlinear particle interactions, respectively. We then formulate a tracking control problem, whose control objective is for the average system to reach a designated targeted velocity using accessible elements. Sufficient stabilization conditions are explicitly derived for the closed-loop error systems using the Lyapunov theory based methods. Simulation results show satisfactory performances. The results can be applied to other physical systems whose dynamics is described by the Frenkel-Kontorova model.