Sergej Celikovsky | Searcharxiv

arXiv2023

Fixed-time safe tracking control of uncertain high-order nonlinear pure-feedback systems via unified transformation functions

In this paper, a fixed-time safe control problem is investigated for an uncertain high-order nonlinear pure-feedback system with state constraints. A new nonlinear transformation function is firstly proposed to handle both the constrained and unconstrained cases in a unified way. Further, a radial basis function neural network is constructed to approximate the unknown dynamics in the system and a fixed-time dynamic surface control (FDSC) technique is developed to facilitate the fixed-time control design for the uncertain high-order pure-feedback system. Combined with the proposed unified transformation function and the FDSC technique, an adaptive fixed-time control strategy is proposed to guarantee the fixed-time tracking. The proposed fixed-time control strategy can guarantee uniform control structure when addressing both constrained and unconstrained situations. Numerical examples are presented to demonstrate the proposed fixed-time tracking control strategy.

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arXiv2020

A polynomial-time scheduling approach to minimise idle energy consumption: an application to an industrial furnace

This article presents a novel scheduling approach to minimise the energy consumption of a machine during its idle periods. In the scheduling domain, it is common to model the behaviour of the machine by defining a small set of machine modes, e.g. "on", "off" and "stand-by". Then the transitions between the modes are represented by a static transition graph. In this paper, we argue that this type of model might be too restrictive for some types of machines (e.g. the furnaces). For such machines, we propose to employ the complete time-domain dynamics and integrate it into an idle energy function. This way, the scheduling algorithm can exploit the full knowledge about the machine dynamics with minimised energy consumption encapsulated in this function. In this paper, we study a scheduling problem, where the tasks characterised by release times and deadlines are scheduled in the given order such that the idle energy consumption of the machine is minimised. We show that this problem can be solved in polynomial time whenever the idle energy function is concave. To highlight the practical applicability, we analyse a heat-intensive system employing a steel-hardening furnace. We derive an energy optimal control law, and the corresponding idle energy function, for the bilinear system model approximating the dynamics of the furnace (and possibly other heat-intensive systems). Further, we prove that the idle energy function is, indeed, concave in this case. Therefore, the proposed scheduling algorithm can be used. Numerical experiments show that by using our approach, combining both the optimal control and optimal scheduling, higher energy savings can be achieved, compared to the state-of-the-art scheduling approaches.

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