Linear quadratic networked control of uncertain polytopic systems

Abstract

SUMMARYThis paper investigates the problem of designing robust linear quadratic regulators for uncertain polytopic continuous-time systems over networks subject to delays. The main contribution is to provide a procedure to determine a discrete-time representation of the weighting matrices associated to the quadratic criterion and an accurate discretized model, in such a way that a robust state feedback gain computed in the discretetime domain assures a guaranteed quadratic cost to the closed-loop continuous-time system. The obtained discretized model has matrices with polynomial dependence on the uncertain parameters and an additive norm-bounded term representing the approximation residual error. A strategy based on linear matrix inequality relaxations is proposed to synthesize, in the discrete-time domain, a digital robust state feedback control law that stabilizes the original continuous-time system assuring an upper bound to the quadratic cost of the closed-loop system. The applicability of the proposed design method is illustrated through a numerical experiment.

On robust state derivative feedback control for uncertain polytopic systems with uncertain sampling period and network‐induced delay

“…In the past decades, several studies have been conducted on the use of linear matrix inequalities (LMI) and state feedback techniques for controller design, as it can be viewed in earlier studies [11][12][13] among others. State feedback control laws are appropriate for controlling systems in which the measured signals correspond directly to the system states.…”

“…However, in both works, the uncertain system matrices were not addressed. In other works [21,22] and [11], a discretization procedure makes use of a truncated Taylor series associated with a bound to the approximation error. Moreover, in NCS context, Braga et al [11,21] handle polytopic systems subject to an uncertain sampling period and network-induced delay.…”

“…In other works [21,22] and [11], a discretization procedure makes use of a truncated Taylor series associated with a bound to the approximation error. Moreover, in NCS context, Braga et al [11,21] handle polytopic systems subject to an uncertain sampling period and network-induced delay. However, in previous works [21,22] and Braga et al [11], the state derivative feedback was not considered.…”

New robust LMI synthesis conditions for mixed gain‐scheduled reduced‐order DOF control of discrete‐time LPV systems

“…This paper deals with discrete‐time linear systems where the state‐space matrices have entries that depend polynomially on time‐varying parameters (that can be used for gain‐scheduled) and are affected by norm‐bounded time‐varying uncertainties. The motivation to consider such models arises from the discretization of polytopic continuous‐time linear parameter‐varying (LPV) systems (or uncertain time‐invariant systems), which comes out with several practical applications, for example, in the context of networked control systems . Using a Taylor series expansion of arbitrary fixed degree, as proposed by Braga et al, the resulting discretized system can be represented with this particular structure.…”

Parameter‐dependent preview control with robust tracking performance

“…In studying stability analysis and control synthesis of uncertain systems, several approaches have been proposed, see, for instance, robust pole placement [1, 2], linear matrix inequalities (LMI) approach for H 2 / H ∞ control [3, 4], Lyapunov‐based method [5, 6], robust filtering and estimation [7] and so on. Most of robust control studies are given in terms of state feedback which follow the assumption that the system states are available.…”