Feedback tuning of bifurcations

The present paper studies a feedback regulation problem that arises in at least two different biological applications. The feedback regulation problem under consideration may be interpreted as an adaptive control problem for tuning bifurcation parameters, and it has not been studied in the control literature. The goal of the paper is to formulate this problem and to present some preliminary results.     

Fundamental properties of reset control systems

Reset controllers are linear controllers that reset some of their states to zero when their input is zero. We are interested in their feedback connection with linear plants, and in this paper we establish fundamental closed-loop properties including stability and asymptotic tracking. This paper considers more general reset structures than previously considered, allowing for higher-order controllers and partial-state resetting. It gives a testable necessary and sufficient condition for quadratic stability and links it to both uniform bounded-input bounded-state stability and steady-state performance. Unlike previous related research, which includes the study of impulsive differential equations, our stability results require no assumptions on the evolution of reset times.     

A global output-feedback controller for stabilization and tracking of underactuated ODIN: A spherical underwater vehicle

This paper presents a method to design an output-feedback controller that simultaneously solves global asymptotic stabilization and tracking of an underactuated omni-directional intelligent navigator—a spherical underwater vehicle moving in a horizontal plane (i.e. at a constant depth). The vehicle does not have a sway actuator and has only position and orientation measurements available. The control development is based on Lyapunov's direct method, backstepping technique and use of interconnected structure of the vehicle dynamics. Numerical simulations demonstrate the results.     

A direct numerical simulation of transition phenomena in a mixed convection channel flow

This study intends to provide an increased understanding of the laminar-turbulent transition phenomena for the buoyancy-assisted heated vertical channel flow during the early transient stage. The spectral method with weak formulation is applied in the direct numerical simulation. Initial disturbances consist of the finite-amplitude two-dimensional TS wave and a pair of three-dimensional oblique waves for the K-type disturbances. The results from the harmonic energy competitions of different wave modes show that for the buoyancy-assisted heated flow, the (k_x=1, k_z=1) or (1,1) and (1,0) modes would gain energy immediately and start to rise at almost the same rate. This phenomenon is different from that of the buoyancy-opposed flow, where the (1,1) mode decays slowly in the beginning until other modes gain enough energy and then it begins to grow quickly and overtakes the (1,0) mode after a short time period. These different transition patterns match with the experimental results that the flow transition is supercritical and subcritical for the buoyancy-assisted and -opposed flows, respectively. Buoyancy-assisted heated flow transition follows the general trend of an isothermal flow in the beginning, but the thermal-buoyant force is crucial in accelerating the instability and also causing notable differences during the subsequent transition process. All of the results for the vortex structures development, kinetic energy budget of the disturbances, flow visualization by tagged fluid particles, and the local temperature fluctuations are consistent in pointing to a clear pattern for the buoyancy-assisted heated flow transition.     

Frequency domain identification of Wiener models

This paper proposes a frequency domain algorithm for Wiener model identifications based on exploring the fundamental frequency and harmonics generated by the unknown nonlinearity. The convergence of the algorithm is established in the presence of white noise. No a priori knowledge of the structure of the nonlinearity is required and the linear part can be nonparametric.     

On a three-dimensional axisymmetric boundary-value problem of nonlinear elastic deformation: Asymptotic solution and exponentially small error

In this paper, we study a three-dimensional axisymmetric boundary-value problem of a slender cylinder composed of a nonlinearly elastic material subjected to an axial force. Starting from the field equations, after a transformation and proper scalings, we identify a small variable and two small parameters, which characterize the present problem. Then, by an approach involving compound series-asymptotic expansions, a nonlinear ODE is derived, which governs the axial strain (the first-term in the series expansion). By imposing the zero radial displacement conditions at two ends, we manage to get the analytical solution of the axial strain, from which all other physical quantities can be deduced and thus the three-dimensional displacement field can be determined. Graphical results are presented, which show that there are two boundary layers near the two ends while the middle part is in a state of almost uniform extension. The asymptotic structure of the analytical solution is derived, which offers clear explanations to the structure of the deformed configuration and shows that the thickness of both boundary layers is of the order of the radius. We also point out the relevance of the present results to the St. Venant’s problem. In particular, we obtain the explicit uniformly-valid exponentially small error term, when the obtained deformed configuration is compared to the configuration of a uniform extension.     

建筑工程投标报价优选模型

通过建立区间二次规划数学模型、灰色模型、多目标规划等模型，建立材料价格和用量的选择模型，提供投标单位一种便捷的调整工程造价和控制造价的手段。     

Nonlinear model predictive control with polytopic invariant sets

Ellipsoidal invariant sets have been widely used as target sets in model predictive control (MPC). These sets can be computed by constructing appropriate linear difference inclusions together with additional constraints to ensure that the ellipsoid lies within a given inclusion polytope. The choice of inclusion polytope has a significant effect on the size of the target ellipsoid, but the optimal inclusion polytope cannot in general be computed systematically. This paper shows that use of polytopic invariant sets overcomes this difficulty, allowing larger stabilizable sets without loss of performance. In the interests of online efficiency, consideration is focused on interpolation-based MPC.     

On regional nonlinear H-filtering

The structure of the nonlinear H^∞-filter in the neighborhood of the estimated trajectory is investigated and a bound on the size of the neighborhood that allows this structure is determined, both for finite and infinite horizons. Riccati inequalities that depend on the estimated trajectory are derived for finding the filter gain matrix and an algorithm for calculating the bound on the size of the above neighborhood is presented. Explicit formulas are obtained in the infinite horizon case for the minimum achievable disturbance attenuation level, the size of the neighborhood, and the corresponding filter gain.