Fault-tolerant control for a class of n-order systems based on fast terminal sliding mode and extended state observer

This paper focuses on fast terminal sliding mode fault-tolerant control for a class of n-order nonlinear systems. Firstly, when the actuator fault occurs, the extended state observer (ESO) is used to estimate the lumped uncertainty and its derivative of the system, so that the fault boundary is not needed to know. The convergence of ESO is proved theoretically. Secondly, a new type of fast terminal sliding surface is designed to achieve global fast convergence, non-singular control law and chattering reduction, and the Lyapunov stability criterion is used to prove that the system states converge to the origin of the sliding mode surface in finite time, which ensures the stability of the closed-loop system. Finally, the effectiveness and superiority of the proposed algorithm are verified by two simulation experiments of different order systems.

Singular Control of the Drift of a Brownian System

We consider a standard Brownian motion whose drift can be increased or decreased in a possibly singular manner. The objective is to minimize an expected functional involving the time-integral of a running cost and the proportional costs of adjusting the drift. The resulting two-dimensional degenerate singular stochastic control problem has interconnected dynamics and it is solved by combining techniques of viscosity theory and free boundary problems. We provide a detailed description of the problem’s value function and of the geometry of the state space, which is split into three regions by two monotone curves. Our main result shows that those curves are continuously differentiable with locally Lipschitz derivative and solve a system of nonlinear ordinary differential equations.

Quasi-singular control in Goursat-Darboux stochastic systems

В одной стохастической задаче управления, описываемой нелинейным гиперболическим уравнением с краевым условием типа Гурса-Дарбу, получено необходимое условие оптимальности первого порядка в форме линеаризованного принципа максимума Понтрягина. Рассмотрен случай вырождения линеаризованного принципа максимума. Установлены различные необходимые условия оптимальности для квазиособых управлений. Квазиособыми называются управления, для которых линеаризованное условие максимума вырождается.

Ergodic control of diffusions with random intervention times

We study an ergodic singular control problem with constraint of a regular one-dimensional linear diffusion. The constraint allows the agent to control the diffusion only at the jump times of an independent Poisson process. Under relatively weak assumptions, we characterize the optimal solution as an impulse-type control policy, where it is optimal to exert the exact amount of control needed to push the process to a unique threshold. Moreover, we discuss the connection of the present problem to ergodic singular control problems, and illustrate the results with different well-known cost and diffusion structures.

VIBRATION PROTECTION SYSTEMS OF VEHICLES: ACTIVE CONTROL AND OPTIMIZATION

The article presents the results of studies of the dynamic properties of a vibration-protective system with active control, which is directly identified with the compensatory effect and is charac-terized as direct control, as well as a vibration-protective system with indirect control, which forms a compensatory effect mediated through the implementation of an intermittent process of changes in the parameters of the inertial link. To find the optimal positional control function of direct (ac-tive) control, as well as indirect (singular) control of the inertial link, information technologies for solving boundary value problems were used in relation to the canonical Hamilton equations for the vibration protection systems under study. The parameters are established at which vibration protection systems of this type eliminate resonance phenomena and provide comparable indicators of vibration safety for protected objects under kinematic disturbance.