Positive real control of two-dimensional systems: Roesser models and linear repetitive processes

This paper considers the problem of positive real control for two-dimensional (2-D) discrete systems described by the Roesser model and also discrete linear repetitive processes, which are another distinct sub-class of 2-D linear systems of both systems theoretic and applications interest. The purpose of this paper is to design a dynamic output feedback controller such that the resulting closed-loop system is asymptotically stable and the closed-loop system transfer function from the disturbance to the controlled output is extended strictly positive real. We first establish a version of positive realness for 2-D discrete systems described by the Roesser state space model, then a sufficient condition for the existence of the desired output feedback controllers is obtained in terms of four LMIs. When these LMIs are feasible, an explicit parameterization of the desired output feedback controllers is given. We then apply a similar approach to discrete linear repetitive processes represented in their equivalent 1-D state-space form. Finally, we provide numerical examples to demonstrate the applicability of the approach.     

Robust incoherent control of qubit systems via switching and optimisation

A robust incoherent quantum control scheme via projective measurements plus unitary transformations is proposed for driving a qubit system from an unknown initial mixed state to an arbitrary target pure state. This scheme consists of two main steps: projective measurement on the initial mixed state and optimal control between two pure states. The first step projects the initial state into an eigenstate of the qubit system by projective measurement and guarantees that the proposed scheme is robust to different initial mixed states. The second step finds a set of suitable optimal controls to drive the qubit system from the conditional eigenstate to the target pure state. The connection between the two steps is accomplished by a switching strategy. To accomplish the second step, two approaches are presented in detail. These approaches are time-optimal transition with unbounded control and bang-bang control with minimal switches. The minimal time and minimal number of switches in these approaches can be calculated by simple analytical expressions. The proposed approaches provide two relatively straightforward optimal design methods.     

Robust stability region of fractional order PIλ controller for fractional order interval plant

In this article, by using the fractional order PI^λ controller, we propose a simple and effective method to compute the robust stability region for the fractional order linear time-invariant plant with interval type uncertainties in both fractional orders and relevant coefficients. The presented method is based on decomposing the fractional order interval plant into several vertex plants using the lower and upper bounds of the fractional orders and relevant coefficients and then constructing the characteristic quasi-polynomial of each vertex plant, in which the value set of vertex characteristic quasi-polynomial in the complex plane is a polygon. The D-decomposition method is used to characterise the stability boundaries of each vertex characteristic quasi-polynomial in the space of controller parameters, which can obtain the stability region by varying λ orders in the range (0,?2). These regions of each vertex plant are computed by using three stability boundaries: real root boundary (RRB), complex root boundary (CRB) and infinite root boundary (IRB). The method gives the explicit formulae corresponding to these boundaries in terms of fractional order PI^λ controller parameters. Thus, the robust stability region for fractional order interval plant can be obtained by intersecting stability region of each vertex plant. The robustness of stability region is tested by the value set approach and zero exclusion principle. Our presented technique does not require sweeping over the parameters and also does not need linear programming to solve a set of inequalities. It also offers several advantages over existing results obtained in this direction. The method in this article is useful for analysing and designing the fractional order PI^λ controller for the fractional order interval plant. An example is given to illustrate this method.     

An algorithm to estimate soil moisture over vegetated areas based on in situ and remote sensing information

An algorithm is proposed for estimating soil moisture over vegetated areas. The algorithm uses in situ and remote sensing information and statistical tools to estimate soil moisture at 1 km spatial resolution and at 20 cm depth over Puerto Rico. Soil moisture within the study region is characterized by spatial and temporal variability. The temporal variability for a given area exhibits long- and short-term variations that can be expressed by two empirical models. The average monthly soil moisture exhibits the long-term variability and is modelled by an artificial neural network (ANN), whereas the short-term variability is determined by hourly variation and is represented by a nonlinear stochastic transfer function model. Monthly vegetation index, land surface temperature, accumulated rainfall and soil texture are the major drivers of the ANN to estimate the monthly soil moisture. Radar, satellite and in situ observations are the major sources of information of the soil moisture empirical models. A self-organized ANN was also used to identify spatial variability to be able to determine a similar transfer function that best resembles the properties of a particular grid point and estimate the hourly soil moisture across the island. Validation techniques reveal an average absolute error of 3.34% of volumetric water content and this result shows that the proposed algorithm is a potential tool for estimating soil moisture over vegetated areas.     

Stabilization of remote control systems with unknown time varying delays by LMI techniques

In this paper, the stabilization of one class of remote control systems with unknown time varying delays is analysed and discussed using LMI techniques. A discrete time state space model under a static control law for remote control systems is first introduced based on some assumptions on the uncertain term. The time delay is unknown, time varying, and can be decomposed into two parts: one fixed part which is unknown and is an integer multiple of the sampling time; the other part which is randomly varying but bounded by one sampling time. Static controller designs based on delay dependent stability conditions are presented. This system is then extended to a more general case when the randomly varying part of the time delay is not limited to one sampling time. The derivative of the time delay is not limited to be bounded. Hence, the contributions are as follow: (i) for a given controller, we can use these stability criteria to test stability of the resulted system; (ii) we can design a remote controller to stabilize an unstable system. Finally, simulation examples are presented to show the effectiveness of the proposed method and to demonstrate remote stabilization of open loop unstable systems.     

Global practical tracking of a class of nonlinear systems using linear sampled-data control

This paper considers the problem of global practical tracking via sampled-data control for a class of uncertain nonlinear systems. Under a lower triangular linear growth condition, a sampled-data state feedback controller is first constructed such that the states are globally bounded and the error between the system output and the reference signal will be rendered smaller than a given tolerance. When only the output of the system is measurable, a sampled-data output feedback controller, whose observer and control law are both linear, is constructed to solve the global practical tracking problem.     

Finite-time stability analysis of impulsive discrete-time switched systems with nonlinear perturbation

The problem of finite-time stability for a class of discrete-time switched systems in the presence of both non-Lipschitz perturbation and impulse effects is studied in this paper. Based on the average dwell-time approach, a criterion is proposed which ensures that the system’s state trajectory remains in a bounded region of the state space over a pre-specified finite-time interval if we impose a bound on the initial condition. It is shown that the finite-time stability degree could be greater than one, which is quite different from the existing results for asymptotic stability. Moreover, the total activation time of the Schur stable subsystems does not need to be greater than that of the unstable subsystems. A numerical example is presented to illustrate the effectiveness of the proposed design method.     

Non-minimal state-space model-based continuous-time model predictive control with constraints

This article proposes a model predictive control scheme based on a non-minimal state-space (NMSS) structure. Such a combination yields a continuous-time state-space model predictive control system that permits hard constraints to be imposed on both plant input and output variables, whilst using NMSS output-feedback without the need for an observer. A comparison between the NMSS and observer-based approaches using Monte Carlo uncertainty analysis shows that the former design is considerably less sensitive to plant-model mismatch than the latter. Through simulation studies, the article also investigates the role of the implementation filter in noise attenuation, disturbance rejection and robustness of the closed-loop predictive control system. The results show that the filter poles become a subset of the closed-loop poles and this provides a straightforward method of tuning the closed-loop performance to achieve a reasonable balance between speed of response, disturbance rejection, measurement noise attenuation and robustness.     

Constrained intermittent model predictive control

The generalised hold formulation of intermittent control is re-examined and shown to have some useful theoretical and practical properties. It is shown that this provides a foundation for constrained model predictive control in an intermittent context. The method is illustrated using an example and verified with experimental results.