Receding horizon H_∞ control of time-delay systems

Abstract

This paper deals with the disturbance rejection problem for discrete-time linear systems having time-varying state delays and control constraints. The study proposes a novel receding horizon H∞ control method utilizing a linear matrix inequality based optimization algorithm which is solved in each step of run-time. The proposed controller attenuates disturbances having bounded energies on controlled output and ensures the closed-loop stability and dissipation while meeting the physical control input constraints. The originality of the work lies on the extension of the idea of the well-known H∞ receding horizon control technique developed for linear discrete-time systems to interval time-delay systems having time-varying delays. The efficiency of the proposed method is illustrated through simulation studies that are carried out on a couple of benchmark problems.

Robust Moving HorizonH∞Control of Discrete Time-Delayed Systems with Interval Time-Varying Delays

“…Next, we will extend the H ∞ controller design approach to the moving horizon scheme. Exploiting the moving horizon strategy, one could solve the optimization problem given in (37) by utilizing the actual state measurements provided at each time instant . Unfortunately, this simple implementation of the moving horizon strategy might fail to guarantee the dissipation requirement given in the statement of the problem (see [39] for details).…”

“…In this paper, we investigate the design of a stabilizing H ∞ state-feedback controller for linear state-delayed interval TDS having norm-bounded uncertainties and constrained inputs. First, based on the selection of an -functional, a stabilizing delay-dependent H ∞ controller is introduced for nominal TDS having delay in the state, similar to the previous study of authors [37]. Then, the existing result is extended to cover TDS having norm-bounded uncertainties.…”

Feedback error learning-based type-2 fuzzy neural network predictive controller for a class of nonlinear input delay systems

“…In these systems, sensors, actuators, and controllers are connected through over a network medium (Ma et al, 2018). In the modeling of systems, the delays are considered in the input of the systems and it can not only degrade the performance of the controlled systems but also may cause instability of the systems (Bhatia and Szegö, 1970; Taşçıkaraoglu et al, 2015). The Lyapunov-Krasovskii and Lyapunov-Razumikhin theorems are the main time-domain approaches for evaluating stability and designing the controller in time-delay systems (Hale and Lunel, 2013; Richard, 2003).…”

Fixed-order ℋ∞ controller design for MIMO systems via polynomial approach

“…The most common performance criteria are minimizing the H ∞ and H 2 norms of the transfer function between performance output and disturbance input and some necessary parameters, such as maximum overshoot and settling time, which are related to the dynamic response of the system. Fundamental contributions related to minimizing the H ∞ and H 2 norms have been made by Gahinet and Apkarian (1994), and there are also works for discrete-time systems based on reducing conservatism on synthesis algorithms (Chang and Yang, 2014; Chang et al, 2017; Lee et al, 2006; Taşçıkaraoğlu et al, 2015).…”