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.     

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.     

The influence of design aesthetics in usability testing: Effects on user performance and perceived usability

This article examined the effects of product aesthetics on several outcome variables in usability tests. Employing a computer simulation of a mobile phone, 60 adolescents (14-17 yrs) were asked to complete a number of typical tasks of mobile phone users. Two functionally identical mobile phones were manipulated with regard to their visual appearance (highly appealing vs not appealing) to determine the influence of appearance on perceived usability, performance measures and perceived attractiveness. The results showed that participants using the highly appealing phone rated their appliance as being more usable than participants operating the unappealing model. Furthermore, the visual appearance of the phone had a positive effect on performance, leading to reduced task completion times for the attractive model. The study discusses the implications for the use of adolescents in ergonomic research.     

Synchronization of complex dynamical networks under recoverable attacks

In this paper, the synchronization of complex dynamical networks (CDNs) under ‘successful’ but recoverable attacks is studied by utilizing the framework of switching systems. ‘Successful’ attacks refer to a class of attacks that break a network into a group of isolated clusters. Recoverable attacks refer to a class of attacks that the network can recover from after a period of time. To facilitate the investigation of the synchronization of a CDN under ‘successful’ but recoverable attacks, the attack frequency and the average recovering time are introduced. By using a piecewise Lyapunov function, the upper bounds of the attack frequency and the average recovering time are obtained to ensure that the whole network can achieve global synchronization under attacks.     

State feedback design for input-saturating quadratic systems

This paper proposes a method to design stabilizing state feedback control laws for nonlinear quadratic systems subject to input saturation. Based on a quadratic Lyapunov function, a modified sector condition and a particular representation for the quadratic terms, synthesis conditions in a “quasi”-LMI form are stated in a regional (local) context. An LMI-based optimization problem is then derived for computing the state feedback gains maximizing the estimate of the stability region of the closed-loop system.