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.     

MPC for tracking piecewise constant references for constrained linear systems

In this paper, a novel model predictive control (MPC) for constrained (non-square) linear systems to track piecewise constant references is presented. This controller ensures constraint satisfaction and asymptotic evolution of the system to any target which is an admissible steady-state. Therefore, any sequence of piecewise admissible setpoints can be tracked without error. If the target steady state is not admissible, the controller steers the system to the closest admissible steady state.These objectives are achieved by: (i) adding an artificial steady state and input as decision variables, (ii) using a modified cost function to penalize the distance from the artificial to the target steady state (iii) considering an extended terminal constraint based on the notion of invariant set for tracking. The control law is derived from the solution of a single quadratic programming problem which is feasible for any target. Furthermore, the proposed controller provides a larger domain of attraction (for a given control horizon) than the standard MPC and can be explicitly computed by means of multiparametric programming tools. On the other hand, the extra degrees of freedom added to the MPC may cause a loss of optimality that can be arbitrarily reduced by an appropriate weighting of the offset cost term.     

Adaptive IIR/FIR fusion filter and its application to the INS/GPS integrated system

Motivated by the complementary features of the IIR-type filter and the FIR-type filter, this paper proposes a robust IIR/FIR fusion filter and an INS/GPS integrated system designed with the fusion filter. In the fusion filter, an IIR-type filter (SPKF) and a FIR-type filter (MRHKF filter) are processed independently, and then the two filters are merged using the mixing probability calculated using the residuals and residual covariance information of the two filters. The merits of the SPKF and the MRHKF filter are integrated and the demerits of the filters are diminished through the filter fusion. Consequently, the proposed fusion filter shows robustness against model uncertainty, temporary disturbing noise, large initial estimation error, etc. The stability of the fusion filter is verified by showing the closeness of two filters in the mixing/redistribution process and the upper bound of the error covariance matrices. This fusion filter is applied to an INS/GPS integrated system. The performance of the INS/GPS integrated system designed using the fusion filter is verified through a simulation under various error environments and is experimentally confirmed.     

Stabilization of a 3D axially symmetric pendulum

Stabilizing controllers are developed for a 3D pendulum assuming that the pendulum has a single axis of symmetry and that the center of mass lies on the axis of symmetry. This assumption allows development of a reduced model that forms the basis for controller design and global closed-loop analysis; this reduced model is parameterized by the constant angular velocity component of the 3D pendulum about its axis of symmetry. Several different controllers are proposed. Controllers based on angular velocity feedback only, asymptotically stabilize the hanging equilibrium. Then controllers are introduced, based on angular velocity and reduced attitude feedback, that asymptotically stabilize either the hanging equilibrium or the inverted equilibrium. These problems can be viewed as stabilization of a Lagrange top. Finally, if the angular velocity about the axis of symmetry is assumed to be zero, controllers are introduced, based on angular velocity and reduced attitude feedback, that asymptotically stabilize either the hanging equilibrium or the inverted equilibrium. This problem can be viewed as stabilization of a spherical pendulum.