Design of ℓ1 New Suboptimal Fractional Delays Controller for Discrete Non-Minimum Phase System under Unknown-but-Bounded Disturbance

ℓ1-regularization methodologies have appeared recently in many pattern recognition and image processing tasks frequently connected to ℓ1-optimization in the control theory. We consider the problem of optimal stabilizing controller synthesis for a discrete non-minimum phase dynamic plant described by a linear difference equation with an additive unknown-but-bounded noise. Under considering the “worst” case of noise, the solving of these optimization problem has a combinatorial complexity. The choosing of an appropriate sufficiently high sampling rate allows to achieve an arbitrarily small level of suboptimality using a noncombinatorial algorithm. In this paper, we suggest to use fractional delays to achieve a small level of suboptimality without increasing the sampling rate so much. We propose an approximation of the fractional lag with a combination of rounding and a first-order fractional lag filter. The suggested approximation of the fractional delay is illustrated via a simulation example with a non-minimum phase second-order plant. The proposed methodology appears to be suitable to be used in various pattern recognition approaches.

Linear time-delay circuit and stabilizing controller

This paper is concerned with a linear time-delay circuit and its feedback control. We use electronic components such as resistors and capacitors to realize a linear time-delay system. The time-delays are generated by operational amplifiers and single-chip microcomputers. Based on the actual data measured by the oscilloscope, the parameters of the system are estimated using the least square method. Then a comparison study between the waveform image measured by the oscilloscope and the numerical simulation obtained by MATLAB verifies the effectiveness of the parameters estimations of the circuit system. Furthermore, the circuit system is unstable with a large time-delay, a feedback controller is designed to stabilize the circuit system using the optimization method in the literature. Finally, the experimental results in the linear time-delay circuit show the effectiveness of the optimization method.

Robust Controller Design for Descriptor-type Time-delay Systems

Linear time-invariant descriptor-type time-delay systems are considered. A robust stabilizing controller design approach for such systems is introduced. Uncertainties both in the time-delays and in other system parameters are considered. A frequency-dependent scalar bound on such uncertainties is first derived. Once this bound is found, the controller design is completely based on the nominal model. However, satisfying a scalar frequency-dependent condition, which uses the derived bound, guarantees robust stability. An example is also presented to illustrate the proposed approach

Adaptive Boundary Control for a Certain Class of Reaction–Advection–Diffusion System

Several phenomena in nature are subjected to the interaction of various physical parameters, which, if these latter are well known, allow us to predict the behavior of such phenomena. In most cases, these physical parameters are not exactly known, or even more these are unknown, so identification techniques could be employed in order to estimate their values. Systems for which their inputs and outputs vary both temporally and spatially are the so-called distributed parameter systems (DPSs) modeled through partial differential equations (PDEs). The way in which their parameters evolve with respect to time may not always be known and may also induce undesired behavior of the dynamics of the system. To reverse the above, the well-known adaptive boundary control technique can be used to estimate the unknown parameters assuring a stable behavior of the dynamics of the system. In this work, we focus our attention on the design of an adaptive boundary control for a parabolic type reaction–advection–diffusion PDE under the assumption of unknown parameters for both advection and reaction terms and Robin and Neumann boundary conditions. An identifier PDE system is established and parameter update laws are designed following the certainty equivalence approach with a passive identifier. The performance of the adaptive Neumann stabilizing controller is validated via numerical simulation.

Observer-Based Stabilization of Linear Discrete Time-Varying Delay Systems

This paper presents the design of an observer-based stabilizing controller for linear discrete-time systems subject to interval time-varying state-delay. In this work, the problem has been formulated in convex optimization framework by constructing a new Lyapunov-Krasovskii (LK) functional to derive a delay-dependent stabilization criteria. The summation inequality and the extended reciprocally convex inequality are exploited to obtain a less conservative delay upper bound in linear matrix inequality (LMI) framework. The derived stability conditions are delay-dependent and thus, ensure global asymptotic stability in presence of any time delay less than the obtained delay upper bound. Numerical examples are included to demonstrate the usefulness of the developed results.