Time-optimal control problem for co-operative hyperbolic systems involving the Laplace operator

In this paper, the time-optimal control problem for (2 × 2)-co-operative hyperbolic system with variable coefficients and involving Laplace operator is considered. This problem is, steering the initial state ((y(0), y′(0)) so that the observation z(t) hitting a given target set in minimum time. For different cases of the observation, the time-optimal controls are characterized in terms of the adjoint, this characterization (in particular case of the space of controls) is used to derive specific properties of the optimal control (bang-bangness, uniqueness, etc.). These results are extended to the case of (n × n)-co-operative hyperbolic system.      

On Zermelo-Like Problems: Gauss–Bonnet Inequality and E. Hopf Theorem

The aim of this paper is to describe the Zermelo navigation problem on Riemannian manifolds as a time-optimal control problem and give an efficient method of evaluating its control curvature. We will show that, up to the change of the Riemannian metric on the manifold, the control curvature of the Zermelo problem has a simple to handle expression which naturally leads to a generalization of the classical Gauss–Bonnet formula in the form of an inequality. This Gauss–Bonnet inequality allows one to generalize the Zermelo problems and obtain a theorem of E. Hopf that establishes the flatness of Riemannian tori without conjugate points.      

Sub-Finsler Structures from the Time-Optimal Control Viewpoint for some Nilpotent Distributions

In this paper, we study the sub-Finsler geometry as a time-optimal control problem. In particular, we consider non-smooth and non-strictly convex sub-Finsler structures associated with the Heisenberg, Grushin, and Martinet distributions. Motivated by problems in geometric group theory, we characterize extremal curves, discuss their optimality, and calculate the metric spheres, proving their Euclidean rectifiability.     

Optimal synthesis in the Reeds and Shepp problem with a free final direction

We consider a time-optimal problem for the Reeds and Shepp model describing a moving point on a plane, with a free final direction of velocity. Using Pontryagin maximum principle, we obtain all types of extremals and, analyzing them and discarding nonoptimal ones, construct the optimal synthesis.     

Switching in Time-Optimal Problem: the 3D Case with 2D Control

We study local structure of time-optimal controls and trajectories for a 3D control-affine system with a 2D control parameter with values in the disk. In particular, we give sufficient conditions, in terms of Lie bracket relations, for optimal controls to be smooth or to have only isolated jump discontinuities.     

Stabilizing Inputs for Implicit Functional Differential Equations of the Neutral Type with Unknown Time-Varying Delays

A robust stabilization problem is investigated for a class of imperfectly known implicit systems with discrete and distributed time-varying delays. The delays are assumed to be unknown but bounded, with known bounds. The imperfections acting on the systems, which may be time-, state-, delayed state-, and/ or inputdependent, are modelled as additive nonlinear perturbations influencing a known set of implicit nonlinear functional differential equations of the neutral type. Sufficient conditions, which include delaydependent matrix inequalities and a delay-dependent stability criterion involving some bounding parameters for the uncertainty and delays in the system, are presented, and a class of robust feedback memoryless control inputs are designed to guarantee a prescribed asymptotic stability property for the class of implicit systems.      

Remarks on Fractional Discrete Cone Control Systems with <Emphasis Type="Italic">n</Emphasis>-Orders and Their Stability

In the paper, fractional discrete cone control systems with n-orders are considered. Some relations between invariance and (asymptotic) stability properties of the presented systems are discussed. Operators employed to the considered systems are Caputo-, Riemman-Louville-, and Grünwald-Letnikov type ones. Cone systems with control, which are particular invariant systems with control, together with their stability and asymptotic stability properties are examined.     

Stabilization of Linear Uncertain Delay Systems with Antisymmetric Stepwise Configurations

This paper investigates the problem of designing a linear memoryless state feedback control to stabilize a class of linear uncertain systems with state delays. Each uncertain parameter and each delay under consideration might vary with time in an arbitrarily large range. In such a situation, the locations of uncertain elements in the system matrices play an important role. Wei introduced the concept of antisymmetric stepwise configuration (ASC) and proved that it is a necessary and sufficient condition for linear uncertain systems to be quadratically stabilizable using linear state feedback control to have this configuration. However, his method is inapplicable to systems that contain delays in the state variables. On the other hand, Amemiya developed conditions for the stabilization of linear uncertain systems with state delays using linear memoryless state feedback control. This paper presents development of the conditions of this problem that have been obtained to date. Fundamentally, it is proved that having an ASC is also a sufficient condition for the stabilization of linear uncertain delay systems. For systems satisfying the stabilizability conditions, a simple control design procedure is also provided and illustrated by an example.      

A new point of view on linear controlled objects

This paper contains some refined classical results from [1]–[4] as well as some new ones on time-optimal control problems for the case of linear controlled objects. It also contains a collection of examples to illustrate the obtained results.     

THE DEPENDENCE OF THE MODULUS OF ELASTICITY ON THE REFERENCE TEMPERATURE IN GENERALIZED THERMOELASTICITY

The model of the equations of generalized thermoelasticity with two relaxation times in an isotropic elastic medium with temperature-dependent mechanical properties is established. The modulus of elasticity is taken as a linear function of reference temperature. The state-space approach developed in [Bahar and Hetnarski, J. Thermal Stresses , vol. 1, pp. 135-146, 1978] is adopted for the solution of one-dimensional problems. The technique is applied to a thermal shock problem, a problem of a layer medium, and a problem for infinite space in the presence of heat sources. Numerical results are illustrated graphically for the problems considered. A comparison was made with the results obtained in the case of temperatureindependent mechanical properties.     

Realizable growth vectors of affine control systems

In this paper, the following problem is considered: for a given nondecreasing finite sequence of positive integers, determine if there exists an affine control system whose growth vector coincides with this sequence. The answer is “yes” if and only if the Taylor series of a certain function constructed via elements of the sequence has nonnegative coefficients. It turns out that this problem is closely connected with properties of “core Lie subalgebras” of affine control systems which are responsible for a homogeneous approximation. We give a representation of core Lie subalgebras as free Lie algebras and describe sets of all possible core Lie subalgebras for systems with a fixed growth vector.     

Pd-based ternary alloys used for gas sensing applications: A review

Pd-based sensors are important gas sensing materials and possess a significant potential to improve many other engineering systems. Several Pd-based single and binary alloy systems have been reported in the past few decades. Some ternary additions of transition elements in the binary systems have been successfully added recently to further improve various aspects of sensitivity, response and mechanical stability of Pd-based sensors. Ternary alloys have shown promising mechanical stability and sensing behavior towards gas sensing behavior and are potential candidate materials for next-generation gas sensors. In addition, it is expected that a ternary alloy system possesses significant tolerance towards toxic H₂S gases, especially for the chemical and food industries applications. However, it is inherited with a problem of surface segregation which must be improved further. Various research activities are in the emerging phase and need further improvement towards ternary alloy systems. In the present work, a comprehensive review of the various Pd-based ternary system is presented in terms of sensing behavior, segregation phenomena, microstructural features, mechanical stability, and the important factors to improve the sensing performance of these alloys. Various factors that control these sensing alloys are also summarized as a future reference guide in this field.     

Constrained Optimal Control for a Class of Semilinear Infinite Dimensional Systems

The aim of this paper is to investigate a constrained optimal control problem governed by a class of semilinear infinite dimensional systems. For a state-quadratic cost functional and a closed convex set of admissible controls, the existence of an optimal control is proven, then this control is characterized for several cases of constraints. An algorithm is developed in order to compute the optimal control. The results are illustrated through simulations of a transport equation and a wave equation.     

Geometric Orbital Transfer Using Averaging Techniques

In this article, we focus on the coplanar orbital transfer of a satellite between Keplerian orbits, with low propulsion. We compute and analyze averaged systems associated with the energy minimization problem with the full control or control oriented in a single direction, tangential-normal or radial-orthoradial. This allows to understand the properties of each control direction in the optimal control problems.      

Adaptive Dynamic Surface Control of Nonlinear Switched Systems with Prescribed Performance

This paper studies the adaptive control problem for a class of switched nonlinear systems with guaranteed prescribed performance bounds under arbitrary switchings. The unknown system functions are approximated by radial basis function neural networks. We employ dynamic surface control technique to solve the explosion of the complexity problem. We control the transformed system such that it is stabilizable, by this way, the original system is stabilizable as well as the prescribed performance is guaranteed. The proposed controller and update laws guarantee the stability of the closed-loop system and the boundedness of all signals. Furthermore, the prescribed performance is ensured. Finally, a simulation example is employed to illustrate the effectiveness of the proposed method.     

一种经灰色处理的锅炉给水控制方法

汽包水位串级三冲量控制中有三个难解决的问题:虚假水位问题、信号噪声问题、控制参数失配问题。经过分析,提出微分环节存在的必要性,可以缓解虚假水位问题,但需要一定处理。提出了引入灰色预估来还原与控制模型参数匹配的信号成分,利用灰色补偿控制以及自适应方法来解决信号噪声、控制参数失配问题。最后仿真证明,经灰色处理后的具有微分作用的串级给水调节系统在多种工况下比常用的串级给水调节系统有更好的控制性能。图9参11     

Approximate Controllability for a Class of Linear Neutral Evolution Systems with Infinite Delay

This paper deals with the approximate controllability problem for a class of linear neutral evolution systems with infinite delay in Banach spaces. Since the concerned system involves additional linear terms, the fundamental solution theory is used to describe the mild solutions. Based on the spectral analysis and the adjoint system, sufficient conditions for the approximate controllability of the concerned system are established. The rank condition is also shown when the control space is finite-dimensional. A practical example is given to show the application of the obtained results.

     

Controllability of the Second-Order Nonlinear Differential Equations with Non-instantaneous Impulses

The objective of this paper is to establish the sufficient condition for the controllability of a control problem represented by second-order nonlinear differential equation with non-instantaneous impulses in a Hilbert space X. The results are obtained using the strongly continuous cosine family of linear operators and Banach fixed point method. Also, we study the controllability of the nonlocal as well as integro-differential systems. Finally, a few examples are provided to illustrate the applications of the obtained abstract results.     

新海发电有限公司200MW机组超速保护系统数字化改造

简要分析了新海发电有限公司200MW汽轮机调节系统现代化改造后数字电液控制系统与传统机械超速保护系统的不协调对机组安全、经济运行的影响,提出了对传统机械超速保护系统现代化改造的必要性,介绍了数字式电子超速保护系统的技术特点和超速保护系统现代化改造的设计思想及设计方案。改造后三年多运行表明:数字式电子超速保护系统动作正确、可靠,极大地简化了超速试验操作,缩短了超速试验时间,取得了显著的安全、经济效益。