Estimate of Periodic Suboptimal Controls

We consider the infinite-time optimal control problem of minimizing an average functional for nonlinear control systems. For controllable systems, we give an explicit estimate for the required period T of -suboptimal T-periodic orbits. Moreover, we show that controllable systems are characterized by the existence of periodic suboptimal trajectories for any average functional.     

基于无线网络的塔吊群防碰撞系统的研究

根据无线网络的特点与塔吊群协同作业的安全要求,研究了工业环境下无线网络的实时性和可靠性,成功研制了塔吊群防碰撞系统,预防塔吊间的碰撞问题.     

Computational water purification controls using second‐order adjoint equations with stability confirmation

This paper presents a computational method for water purification using second‐order adjoint equations. In Japan, the waters of polluted rivers are purified by conveying the waters from other rivers into the main rivers or by using outflows from sewage plants. The shallow water flow equation based on the water velocity and elevation and the advection diffusion equation of COD concentration are governing equations. The control problem involves finding a flow velocity into the main river that can reduce the COD concentration as close to the target value as possible. In other words, the problem is to find a water velocity to minimize the performance function, which is the square sum of the discrepancy between the computed and the observed COD concentrations. The present research was motivated by the need to apply water purification controls to practical projects. We have found that the controls occasionally tend to be unstable, and the stability of control must be ensured. By expanding the extended performance function into the Taylor series, the necessary condition for the stationary state is derived. Based on this condition, the first‐and second‐order adjoint equations can be obtained. The backward solution of the adjoint equation leads to the gradient and the Hessian product; these serve as the basis of the quasi‐Newton method. From the condition that the performance function must be minimum, the stability confirmation index can be determined. Using this index, we have derived the trust region method, the computation of which confirms the stability of control. Verification was carried out using a simple channel model. By varying the peak value of the inflow velocity, the outlet velocity has been determined such that the water elevation at the target point is zero. Depending on the peak value of the inflow, unstable control arises; this is determined by the stability confirmation index presented in this paper. The trust region method with the stability confirmation index is shown to be adaptable to judge the stability of control. The present method was applied to the water purification of Teganuma river in Japan. The steady fundamental state was computed with the inflow, outflow, and COD concentration at the inlet being specified. The control velocity at the control point can be determined for a fixed control duration with and without the stability confirmation index. The inflow, outflow, and COD concentration are specified as functions of time. It is shown that this method is suitable for practical use because control stability can be ensured. Moreover, it is also noted that the maximum flow velocity for stable control depending on the given control duration can be obtained. Copyright © 2011 John Wiley & Sons, Ltd.     

Existence of almost periodic solution in a ratio-dependent Leslie system with feedback controls

A ratio-dependent Leslie system with feedback controls is studied. By using a comparison theorem and constructing a suitable Lyapunov function, some sufficient conditions for the existence of a unique almost periodic solution (periodic solution) and the global attractivity of the solutions are obtained. Examples show that the obtained criteria are new, general, and easily verifiable.     

Insensitizing controls for the parabolic equation with equivalued surface boundary conditions

This paper is devoted to the study of the existence of insensitizing controls for the parabolic equation with equivalued surface boundary conditions. The insensitizing problem consists in finding a control function such that some energy functional of the equation is locally insensitive to a perturbation of the initial data. As usual, this problem can be reduced to a partially null controllability problem for a cascade system of two parabolic equations with equivalued surface boundary conditions. Compared the problems with usual boundary conditions, in the present case we need to derive a new global Carleman estimate, for which, in particular one needs to construct a new weight function to match the equivalued surface boundary conditions.     

Viscosity Solutions of HJB Equations with Unbounded Data and Characteristic Points

We study a class of infinite horizon and exit-time control problems for nonlinear systems with unbounded data using the dynamic programming approach. We prove local optimality principles for viscosity super- and subsolutions of degenerate Hamilton–Jacobi equations in a very general setting. We apply these results to characterize the (possibly multiple) discontinuous solutions of Dirichlet and free boundary value problems as suitable value functions for the above-mentioned control problems.     

Optimal boundary control of hyperbolic equations with pointwise state and mixed control‐state constraints

This paper is devoted to deal with optimal control problems of semilinear hyperbolic equations with pointwise state constraints and mixed control‐state constraints. We obtain necessary optimality conditions in the form of a Pontryagin's minimum principle. Our approach is based on modern methods of variational analysis. Copyright © 2014 John Wiley & Sons, Ltd.     

Dried blood spots: Liquid chromatography–mass spectrometry analysis of Δ-tetrahydrocannabinol and its main metabolites

A sensitive and selective HPLC–MS/MS method has been developed for the first time for the analysis of Δ⁹-tetrahydrocannabinol (the most important active cannabinoid) and its hydroxylated and carboxylated metabolites in human Dried Blood Spots (DBSs). The simultaneous determination of Δ⁹-tetrahydrocannabinol and its two main metabolites allows assessing the time elapsed after the drug intake and distinguishing between acute or former consumption. This is an important information in specific contexts such as “on street” controls by police forces. DBSs have been chosen as the optimal biological matrix for this kind of testing, since they provide information on the actual state of intoxication, without storage and transportation problems usually associated with classical blood testing. The analysis is carried out on a C8 reversed phase column with a mobile phase composed of 0.1% formic acid in a water/methanol mixture and an electrospray ionisation (ESI) source, coupled to a triple quadrupole mass spectrometer. The method was validated according to international guidelines, with satisfactory results in terms of extraction yields, precision, stability and accuracy. Application to real DBS samples from Cannabis abusers gave reliable results, thus confirming the methodology suitability for roadside testing.     

Necessary optimality conditions for singular controls

A definition of singular controls with respect to components is given that includes, in particular, the conventional definition. On the basis of this definition, new necessary optimiality conditions for singular controls with respect to components are derived for the processes governed by systems of ordinary differential equations.     

Wave energy decay under fractional derivative controls

^** Present address: Division of Mathematics and Sciences, Rust College, 150 Rust Avenue, Holly Springs, MS 38635, USA In this article, we investigate the asymptotic behaviour ofsolutions of the 1D wave equation with a boundary viscoelasticdamper of the fractional derivative type. We show that the systemis well-posed in the sense of semigroup. We also prove thatthe associated semigroup is not exponentially stable, but onlystrongly asymptotically so. Finally, we establish the followingresult. Provided that the initial states of the system are chosensufficiently smooth and the relaxation function of the viscoelasticdamper is exponentially decreasing, then solutions of the systemwill decay, as time goes to infinity, as [graphic: see PDF] A > 0.