Prediction-Based Control of Linear Systems by Compensating Input-Dependent Input Delay of Integral-Type

International audienceThis study addresses the problem of delay compensation via a predictor-based output feedback for a class of linear systems subject to input delay which itself depends on the input. The equation defining the delay is implicit and involves past values of the input through an integral relation, the kernel of which is a polynomial function of the input. This modeling represents systems where transport phenomena take place at the inlet of a system involving a nonlinearity, which frequently occurs in the processing industry. The conditions of asymptotic stabilization require the magnitude of the feedback gain to comply with the initial conditions. Arguments for the proof of this novel result include general Halanay inequalities for delay differential equations and take advantage of recent advances in backstepping techniques for uncertain or varying delay systems

Output Feedback control of time delay systems with adaptation of delay estimate

Abstract: This paper extends recent results for the literature which employ a backstepping transformation under the form of an infinite dimensional system to address robust control of time delay systems. The contribution treats the case of output feedback through a state observer, while allowing online adaptation of the delay system. A theoretical result is proven and an example illustrates the approach. 1

Invoking Halanay inequality to conclude on closed-loop stability of a process with input-varying delay

International audienceAt the light of a simple tutorial example, this paper discusses the merits of a recently introduced technique to control a class of systems with a delay depending on the past values of the control variables. The convergence proof of the proposed control strategy is obtained by a boundedness analysis of a class of delay differential equation, inspired by the Halanay inequality. The relations of the proposed technique with previous works from the literature on predictor-based controllers are discussed. The treated example is representative of a wide class of systems often observed in process control and distributed parameter systems

Boundary control of partial differential equations using frequency domain optimization techniques

International audienceWe present a frequency domain based H ∞-control strategy to solve boundary control problems for systems governed by parabolic or hyperbolic partial differential equation, where controllers are constrained to be physically implementable and of simple structure suited for practical applications. The efficiency of our technique is demonstrated by controlling a reaction-diffusion equation with input delay, and a wave equation with boundary anti-damping