A new approach to the cheap LQ regulator exploiting the geometric properties of the Hamiltonian system

The cheap LQ regulator is reinterpreted as an output nulling problem which is a basic problem of the geometric control theory. In fact, solving the LQ regulator problem is equivalent to keep the output of the related Hamiltonian system identically zero. The solution lies on a controlled invariant subspace whose dimension is characterized in terms of the minimal conditioned invariant of the original system, and the optimal feedback gain is computed as the friend matrix of the resolving subspace. This study yields a new computational framework for the cheap LQ regulator, relying only on the very basic and simple tools of the geometric approach, namely the algorithms for controlled and conditioned invariant subspaces and invariant zeros.     

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.     

Recursive identification of switched ARX systems

We consider the problem of recursively identifying the parameters of a deterministic discrete-time Switched Auto-Regressive eXogenous (SARX) model, under the assumption that the number of models, the model orders and the mode sequence are unknown. The key to our approach is to view the identification of multiple ARX models as the identification of a single, though more complex, lifted dynamical model built by applying a polynomial embedding to the input/output data. We show that the dynamics of this lifted model do not depend on the value of the discrete state or the switching mechanism, and are linear on the so-called hybrid model parameters. Therefore, one can identify the parameters of the lifted model using a standard recursive identifier applied to the embedded input/output data. The estimated hybrid model parameters are then used to build a polynomial whose derivatives at a regressor give an estimate of the parameters of the ARX model generating that regressor. The estimated ARX model parameters are shown to converge exponentially to their true values under a suitable persistence of excitation condition on a projection of the embedded input/output data. Such a condition is a natural generalization of the well known result for ARX models. Although our algorithm is designed for perfect input/output data, our experiments also evaluate its performance as a function of the level of noise for different choices of the number of models and model orders. We also present an application to temporal video segmentation.     

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.     

Adaptive robust posture control of a parallel manipulator driven by pneumatic muscles

Rather severe parametric uncertainties and uncertain nonlinearities exist in the dynamic modeling of a parallel manipulator driven by pneumatic muscles. Those uncertainties not only come from the time-varying friction forces and the static force modeling errors of pneumatic muscles but also from the inherent complex nonlinearities and unknown disturbances of the parallel manipulator. In this paper, a discontinuous projection-based adaptive robust control strategy is adopted to compensate for both the parametric uncertainties and uncertain nonlinearities of a three-pneumatic-muscles-driven parallel manipulator to achieve precise posture trajectory tracking control. The resulting controller effectively handles the effects of various parameter variations and the hard-to-model nonlinearities such as the friction forces of the pneumatic muscles. Simulation and experimental results are obtained to illustrate the effectiveness of the proposed adaptive robust controller.     

Automatic computation of the travelling wave solutions to nonlinear PDEs

Various extensions of the tanh-function method and their implementations for finding explicit travelling wave solutions to nonlinear partial differential equations (PDEs) have been reported in the literature. However, some solutions are often missed by these packages. In this paper, a new algorithm and its implementation called TWS for solving single nonlinear PDEs are presented. TWS is implemented in Maple 10. It turns out that, for PDEs whose balancing numbers are not positive integers, TWS works much better than existing packages. Furthermore, TWS obtains more solutions than existing packages for most cases.

Program summary

Program title:TWSCatalogue identifier:AEAM_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAM_v1_0.htmlProgram obtainable from:CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.:1250No. of bytes in distributed program, including test data, etc.:78 101Distribution format:tar.gzProgramming language:Maple 10Computer:A laptop with 1.6 GHz Pentium CPUOperating system:Windows XP ProfessionalRAM:760 MbytesClassification:5Nature of problem:Finding the travelling wave solutions to single nonlinear PDEs.Solution method:Based on tanh-function method.Restrictions:The current version of this package can only deal with single autonomous PDEs or ODEs, not systems of PDEs or ODEs. However, the PDEs can have any finite number of independent space variables in addition to time t.Unusual features:For PDEs whose balancing numbers are not positive integers, TWS works much better than existing packages. Furthermore, TWS obtains more solutions than existing packages for most cases.Additional comments:It is easy to use.Running time:Less than 20 seconds for most cases, between 20 to 100 seconds for some cases, over 100 seconds for few cases.References:[1] E.S. Cheb-Terrab, K. von Bulow, Comput. Phys. Comm. 90 (1995) 102.[2] S.A. Elwakil, S.K. El-Labany, M.A. Zahran, R. Sabry, Phys. Lett. A 299 (2002) 179.[3] E. Fan, Phys. Lett. 277 (2000) 212.[4] W. Malfliet, Amer. J. Phys. 60 (1992) 650.[5] W. Malfliet, W. Hereman, Phys. Scripta 54 (1996) 563.[6] E.J. Parkes, B.R. Duffy, Comput. Phys. Comm. 98 (1996) 288.     

半透明物体漫散射效果的实时绘制与材质编辑

半透明物体透明效果的真实感绘制是近年来研究的热点,提出一种针对半透明物体漫散射效果的实时真实感绘制与材质动态编辑方法--基于双向表面散射反射率函数(BSSRDF)的Dipole近似.通过主元分析将Dipole近似中的漫散射材质甬数分解为与形状相关甬数和与半透明材质相关函数的乘积形式;利用该分解表示,在预辐射传输的实时真实感绘制框架下,通过对散射传输的预计算来实现在多种光源环境下对半透明物体材质的实时编辑.此外,还提出一种对预计算辐射传输数据在空域上进行二次小波压缩的方法,利用表面点在空间分布位置的相关性,在保证绘制质量的前提下,大大压缩了数据,提升了绘制效率.实验结果表明,文中方法可以生成具有高度真实感的半透明效果并保证实时的绘制速度.