Discrete-time Linear Plant Research Articles

Explicit model predictive control for PDEs: The case of a heat equation

Explicit model predictive control design is carefully developed for discrete-time linear plants on Hilbert spaces, and we highlight the role of the so-called Slater condition in the reliable explicit solution of the MPC optimization. We then proceed to present an explicit MPC algorithm that accounts for the stabilization and input constraints satisfaction. We do structure preserving temporal discretization of the infinite-dimensional parabolic PDE system by application of the Cayley transformation. The salient feature of explicit MPC design is the realization of the region-free approach in explicit MPC design with identification of active constraint sets to realize optimal stabilization and constraints satisfaction. Finally, the resulting design is illustrated by the application to the PDE model given by an unstable heat equation with boundary actuation and Neumann boundary conditions. The example demonstrates simultaneous stabilization and input constraints satisfaction on the one hand, and on the ability to deal with a relatively high plant dimension and a long optimization horizon on the other hand.

Feedback Stabilization Robust Against Communication Constraints for Disturbed Linear Plants via Sparse Packetized Predictive Control

This paper investigates closed-loop stability of linear discrete-time plants subject to bounded disturbances when controlled according to packetized predictive control (PPC) policies. In the considered feedback loop, the controller is connected to the actuator via a digital communication channel imposing bounded dropouts. Two PPC strategies are taken into account. In both cases, the control packets are generated by solving sparsity-promoting optimization problems. One is based upon an l2-constrained £° optimization problem. Such problem is relaxed by an l1- l2 optimization problem in the other sparse PPC setting. We show that the l2-constrained £° sparse PPC and unconstrained l1- l2 sparse PPC render system states bounded if the design parameters satisfy certain conditions. The bounds we derive on states are increasing with respect to the disturbance magnitude. We illustrate the results via simulation.

Secure Networked Control Systems

Cyber-vulnerabilities are being exploited in a growing number of control systems. As many of these systems form the backbone of critical infrastructure and are becoming more automated and interconnected, it is of the utmost importance to develop methods that allow system designers and operators to do risk analysis and develop mitigation strategies. Over the last decade, great advances have been made in the control systems community to better understand cyber-threats and their potential impact. This article provides an overview of recent literature on secure networked control systems. Motivated by recent cyberattacks on the power grid, connected road vehicles, and process industries, a system model is introduced that covers many of the existing research studies on control system vulnerabilities. An attack space is introduced that illustrates how adversarial resources are allocated in some common attacks. The main part of the article describes three types of attacks: false data injection, replay, and denial-of-service attacks. Representative models and mathematical formulations of these attacks are given along with some proposed mitigation strategies. The focus is on linear discrete-time plant models, but various extensions are presented in the final section, which also mentions some interesting research problems for future work.

Fixed-Dynamics Antiwindup Design: Application to Pitch-Limited Position Control of Multirotor Unmanned Aerial Vehicles

In this brief, we present and validate an antiwindup (AW) control design suitable to deal with saturated discrete-time linear plants. Following the modern approach to AW design, the proposed synthesis procedure is based on the compensator paradigm in which the AW controller acts on top of a baseline one, tuned to achieve desirable performance in the unsaturated regime. After extending existing ideas for continuous-time plants to their discrete-time counterparts, the design of the AW compensator is carried out with a focus on computational efficiency and optimized performance in practical operating scenarios. The proposed approach allows one to design fixed-dynamics AW compensators for possibly open-loop unstable plants using generalized sector conditions. Then, the synthesis procedure is applied to tune a fixed-dynamics compensator having the structure of a static compensator cascaded with a unit delay to avoid algebraic loops. Finally, the benefits of such AW augmentation are assessed experimentally to counteract windup effects arising in the position control of multirotor unmanned aerial vehicles (UAVs) when pitch limitations are imposed.

On stochastic and deterministic event-based state estimation

This paper investigates the problem of remote event-based state estimation for a linear discrete-time plant. Both stochastic and deterministic event-based transmission policies are considered for the systems implemented with smart sensors, where local Kalman filters are embedded. Based on the concept of generalized closed skew normal distributions, the exact probability density functions of the remote event-based state estimation processes are provided. With the properties of smart sensors, the explicit form of the remote event-based state estimators can be derived, without involving numerical integration. In addition, in the case of scalar plants, the estimation and transmission performances under different kinds of event-based scheduling policies are compared theoretically. An important inequality on a truncated covariance of some particular multivariate Gaussian distribution is proved, which builds a bridge between performances of the two event-based policies. Based on this inequality, it is proved that for any considered stochastic event-based transmission policy, there always exists a deterministic counterpart that leads to better estimation performance using the same communication and computational resources. Numerical simulations are provided to illustrate the theoretical results.

Mean Square Stability of Model Based Networked Control Systems with Multiplicative Noise

This paper presents a necessary and sufficient condition of mean square stability of a model based networked control systems (MB-NCS) with multiplicative noise, where a linear discrete time plant is controlled by using a model state feedback. The lifting approach is employed, and the original time varying system is recast as an equivalent time invariant system whose mean square stability is investigated. The necessary and sufficient condition derived here is given as a set of a linear matrix inequality and linear equations, which enjoys an advantage on numerical computation.

Discrete-time hands-off control by sparse optimization

Maximum hands-off control is a control mechanism that maximizes the length of the time duration on which the control is exactly zero. Such a control is important for energy-aware control applications, since it can stop actuators for a long duration and hence the control system needs much less fuel or electric power. In this article, we formulate the maximum hands-off control for linear discrete-time plants by sparse optimization based on the l 1 norm. For this optimization problem, we derive an efficient algorithm based on the alternating direction method of multipliers (ADMM). We also give a model predictive control formulation, which leads to a robust control system based on a state feedback mechanism. Simulation results are included to illustrate the effectiveness of the proposed control method.

Quantized Control Under Round-Robin Communication Protocol

This paper analyzes the exponential stability of a discrete-time linear plant in feedback control over a communication network with $N$ sensor nodes, dynamic quantization, large communication delays, variable sampling intervals, and round-robin scheduling. The closed-loop system is modeled as a switched system with multiple-ordered time-varying delays and bounded disturbances. We propose a time-triggered zooming algorithm implemented at the sensors that preserves exponential stability of the closed-loop system. A direct Lyapunov approach is presented for initialization of the zoom variable. The proposed framework can be applied to the plants with polytopic type uncertainties. The effectiveness of the method is illustrated on cart-pendulum and quadruple-tank processes.

Separated Design of Encoder and Controller for Networked Linear Quadratic Optimal Control

For a networked control system, we consider the problem of encoder and controller design. We study a discrete-time linear plant with a finite horizon performance cost, comprising a quadratic function of the states and controls, and an additive communication cost. We study separation in design of the encoder and controller, along with related closed-loop properties such as the dual effect and certainty equivalence. The encoder outputs are quantized samples, but our results also apply to two other formats for encoder outputs: real-valued samples at event-triggered times, and real-valued samples over additive noise channels. If the controller and encoder are dynamic, then we show that the performance cost is minimized by a separated design: the controls are updated at each time instant as per a certainty equivalence law, and the encoder is chosen to minimize an aggregate quadratic distortion of the estimation error. This separation is shown to hold even though a dual effect is present in the closed-loop syst...

Generalized H ∞-optimal filtering for discrete-time plants over finite and infinite time horizons

We consider linear discrete-time plants subjected to exogenous disturbances and initial perturbations induced by the unknown initial conditions. A performance index for the accuracy of filtering is introduced which accounts for the effects of exogenous and initial perturbations on the filtering error over finite and infinite time horizons. Linear generalized H?-optimal discrete-time filters in the form of observer are designed, which minimize the criterion adopted. Design is performed by using the minimax approach and the apparatus of linear matrix inequalities.

Sliding-mode control of discrete-time linear plants with input saturation: application to a twin-rotor system

This paper investigates the stabilisation problem for discrete-time linear controllable systems subject to actuator saturation. In the case of completely known plants, a control design technique based on a time-varying sliding surface is proposed ensuring stabilisation under the assumption of availability of all state measurements. Further, in the presence of matched disturbances with a known constant bound, a discrete-time sliding-mode controller is proposed ensuring plant practical stabilisation, and a conservative estimate of the attraction domain is given. Theoretical results have been validated by experimental data using a twin-rotor system.

Robust control of multi-input periodic discrete-time systems with saturating actuators

This paper proposes the use of a time-varying sliding surface for robust transient shaping of periodic linear discrete-time plants subject to saturating actuators, in the presence of bounded matched uncertainties. A constructive procedure is presented, and ultimate boundedness of state trajectories is proved.

Practical stabilisation and transient shaping of discrete-time plants with saturating actuators and matched disturbances

This study proposes the use of a time-varying sliding surface for robust transient shaping of linear discrete-time multi-input plants subject to saturating actuators, in the presence of bounded matched uncertainties. A constructive procedure is presented, ultimate boundedness of state trajectories is proved and a result about the choice of tuning parameters for robust transient shaping is given. Simulation results show remarkable improvements in dynamic performances with respect to existing literature.

Sliding mode control of periodic discrete-time linear systems with saturating actuators and input disturbances

AbstractThis paper proposes the use of a time-varying sliding surface for robust transient shaping of periodic linear discrete-time plants subject to saturating actuators, in the presence of bounded matched uncertainties. A constructive procedure is presented, ultimate boundedness of state trajectories is proved and a result about the choice of tuning parameters for robust transient shaping is given.

Data-Driven Tracking Control Insensitive to Noise

AbstractThis paper presents a data-driven algorithm for tracking control of a linear discrete-time plant. No traditional mathematical model of the plant such as transfer function or state equation is employed. Instead, the plant dynamics is represented by an array whose elements are plant input-output data. Sensitivity of the array to input and output noise is introduced. Then, it is shown that, for an arbitrary reference signal, the tracking control input which minimizes the sensitivity can readily be computed by solving a linear matrix inequality which is composed of the array.

A Developed Modified OSAP Controller with Repetitive Control Action for UPS

Abstract In this work, a developed modified one sampling ahead preview (OSAP) controller with repetitive control action for single – phase voltage source PWM inverters used in (UPS) systems is proposed. The proposed technique minimizes largely the plant modeling errors resulted from simplification made to obtain a linear discrete time plant model. In addition, due to the repetitive control action, this digital control scheme can minimize the steady-state error and periodic distortions caused by nonlinear cyclic loads. Hence, the Total Harmonic Distortion (THD) will be reduced. This technique utilizes a switching frequency greater than the sampling frequency, yielding additional minimization in the plant modeling errors. As the sampling frequency is less than the switching frequency, it is possible to implement this controller on a low speed microcontroller. Plant model and theoretical analysis of the control scheme are discussed. Simulation results are presented to verify the performance of the proposed approach under different load conditions.

Minimax forecasting model in the control system with identifier

For the class of bounded perturbations with an a priori defined boundary, the problem of forecasting the output of a linear discrete-time plant was considered. The "dead zone" algorithm was used for real-time adjustment of the model. The extreme minimax nature of the forecast in the averaged performance index was established.

Degenerate Problems of Designing the Control System of a Linear Discrete Plant

Consideration was given to the class of degenerate problems of designing controller for a multidimensional discrete-time linear plant under stationary perturbations. An algorithm to design an iteratively structured controller providing the desired control performance in the steady-state conditions was proposed.

Constrained stabilization problems for discrete‐time linear plants

AbstractIn this paper we study discrete‐time linear systems with full or partial constraints on both input and state. It is shown that the solvability conditions of stabilization problems are closely related to important concepts, such as the right‐invertibility of the constraints, the location of constraint invariant zeros and the order of constraint infinite zeros. The main results show that for right‐invertible constraints the order of constrained infinite zeros cannot be greater than one in order to achieve global or semi‐global stabilization. This is in contrast to the continuous‐time case. Controllers for both state feedback and measurement feedback are constructed in detail. Issues regarding non‐right invertible constraints are discussed as well. Copyright © 2004 John Wiley & Sons, Ltd.

An algebraic approach to iterative learning control

In this paper discrete-time iterative learning control (ILC) systems are analysed from an algebraic point of view. The algebraic analysis shows that a linear-time invariant single-input–single-output model can always represented equivalently as a static multivariable plant due to the finiteness of the time-axis. Furthermore, in this framework the ILC synthesis problem becomes a tracking problem of a multi-channel step-function. The internal model principle states that for asymptotic tracking (i.e. convergent learning) it is required that an ILC algorithm has to contain an integrator along the iteration axis, but at the same time the resulting closed-loop system should be stable. The question of stability can then be answered by analysing the closed-loop poles along the iteration axis using standard results from multivariable polynomial systems theory. This convergence theory suggests that time-varying ILC control laws should be typically used instead of time-invariant control laws in order to guarantee good transient tracking behaviour. Based on this suggestion a new adaptive ILC algorithm is derived, which results in monotonic convergence for an arbitrary linear discrete-time plant. This adaptive algorithm also has important implications in terms of future research work—as a concrete example it demonstrates that ILC algorithms containing adaptive and time-varying components can result in enhanced convergence properties when compared to fixed parameter ILC algorithms. Hence it can be expected that further research on adaptive learning mechanisms will provide a new useful source of high-performance ILC algorithms.