Decentralised reliable guaranteed cost control of uncertain systems: an LMI design

Abstract

The problem of designing a decentralised control scheme for a class of linear large scale interconnected systems with norm-bounded time-varying parameter uncertainties under a class of control failures is addressed. These failures are described by a model that considers possible outages or partial failures in every single actuator of each decentralised controller. The control design is performed through two steps. First, a decentralised reliable guaranteed cost control set is derived and, second, a feasible linear matrix inequalities procedure is presented for the effective construction of the control set. A numerical example illustrates the efficiency of the proposed control scheme.

A new LMI-based robust finite-time sliding mode control strategy for a class of uncertain nonlinear systems

“…Consider the uncertain nonlinear system described by (2) with [5]: Figure 1 shows the system states controlled using the control signal (20). It is shown from this figure that the states reach zero rapidly and the offered control structure is able to overcome the parameter uncertainties and system nonlinearities.…”

“…LMI has appeared as an influential computational tool in solving of the control problems due to its computational flexibility and efficiency and to treat with a large category of design problems. It helps to solve some minimization convex problems, for instance, H ∞ control [3], H 2 control [34] and guaranteed cost control [20]. An LMI procedure is a semi-definite inequality which is a linear relation in unknown variables.…”

LMI approach to reliable guaranteed cost control with multiple criteria constraints: The actuator faults case

“…Proof By Schur complement [6], inequalities (9) and (10) are equivalent to the following inequalities:…”

“…Consider system (1) and cost function (6). For the given control constraint (7), if there exist matrices Q > 0, G and scalars > 0, > 0, such that the following matrix inequalities (21)- (23) hold, then for all possible faults L(k), the faulty closed-loop system (5) is quadratic stable with the control input satisfying constraint (7), and the closed-loop cost function J < , where N, U, R 1 and R 2 are known constant matrices:…”

Adaptive Fault-Tolerant H∞ Power and Rate Control for Wireless Networks with Receiver Failures

“…The existing fault-tolerant controllers can be divided into two design approaches, i.e., passive approach and active approach. Robust control is useful method in passive approach, in which linear matrix inequality (LMI) methods can be used to describe the performances of fixed gain closed-loop systems [12][13][14][15][16][17]. While adaptive control is very important technique in active approach, in which the parameters can be adjusted online to ensure reliability of closed-loop systems in the presence of a wide range of unknown faults [18][19][20][21][22][23].…”