Fast Algorithm of Multivariable Generalized Predictive Control

To avoid the shortcoming of the traditional (previous) generalized predictive control (GPC) algorithms, too large amounts of computation, a fast algorithm of multivariable generalized predictive control is presented in which only the current control actions are computed exactly on line and the rest (the future control actions) are approximately done off line. The algorithm is simple and can be used in the arbitary-dimension input arbitary-dimension output (ADIADO) linear systems. Because itdose not need solving Diophantine equation and reduces the dimension of the inverse matrix, it decreases largely the computational burden. Finally, simulation results show that the presented algorithm is effective and practicable.     

Generalized Predictive Control—Part II Extensions and interpretations

The original GMV self-tuner was later extended to provide a general framework which included feedforward compensation and user-chosen polynomials with detuned model-reference, optimal Smith predictor and load-disturbance tailoring objectives. This paper adds similar refinements to the GPC algorithm which are illustrated by a set of simulations. The relationship between GPC and LQ designs is investigated to show the computational advantage of the new approach. The roles of the output and control horizons are explored for processes with nonminimum-phase, unstable and variable dead-time models. The robustness of the GPC approach to model over- and under-parameterization and to fast sampling rates is demonstrated by further simulations. An appendix derives stability results showing that certain choices of control and output horizons in GPC lead to cheap LQ, “mean-level”, state-dead-beat and pole-placement controllers.     

Synthesis of Regulators in a Control Problem with the Generalized H∞-Criterion

An issue of synthesis of linear regulators is considered, which involves a control problem with a generalized H-criterion that makes it possible to smooth out values of the maximum coefficient of attenuation of the vibrational energy. An effective theorem of existence of the desired solution is proved. An example is given.     

Generalized Predictive Control with Online Least Squares Support Vector Machines

This paper proposes a practical generalized predictive control （GPC） algorithm based on online least squares support vector machines （LS-SVM） which can deal with nonlinear systems effectively. At each sampling period the algorithm recursively modifies the model by adding a new data pair and deleting the least important one out of the consideration on realtime property. The data pair deleted is determined by the absolute value of lagrange multiplier from last sampling period. The paper gives the recursive algorithm of model parameters when adding a new data pair and deleting an existent one, respectively, and thus the inversion of a large matrix is avoided and the memory can be controlled by the algorithm entirely. The nonlinear LS-SVM model is applied in GPC algorithm at each sampling period. The experiments of generalized predictive control on pH neutralizing process show the effectiveness and practicality of the proposed algorithm.     

H∞ Robust Control Design for an Arm Manipulator

This paper deals with the application of the optimal H control design technique to derive a controller for a 3 DOF arm manipulator affected by nonmodeled dynamics, nonlinearities, actuator dynamics and sensor noise. The control objectives were to obtain a robust stable with robust performance controlled system. A family of nonparametric models for a finite number of the arm configurations was obtained. Then, a multivariable nominal model was proposed and derived together with additive nonparametric uncertainty bounds. Weighting functions were used to normalize the H norm of the uncertainty and to act on the command, sensor, and error signals. Finally, a controller was computed by solving the corresponding H optimization problem. The controller was tried on the nominal and worst case configuration models. The results showed robust stability and robust performance of the controlled system.     

H∞ Synchronization of Chaotic Systems via Delayed Feedback Control

The H∞ synchronization problem for a class of delayed chaotic systems with external disturbance is investigated. A novel delayed feedback controller is established under which the chaotic master and slave systems are synchronized with a guaranteed H∞ performance. Based on the Lyapunov stability theory, a delay-dependent condition is derived and formulated in the form of linear matrix inequality (LMI). A numerical simulation is also presented to validate the effectiveness of the developed theoretical results.     

Robust Time-varying H∞ Control for Networked Control System with Uncertainties and External Disturbance

In this paper, the robust H∞ control problem is developed for a class of linear time-varying networked control system (NCS) with uncertainties and external disturbance. In network, the network-induced delay and packet dropouts are simultaneously considered. Firstly, a discrete-time switched system model is established based on the signals transmission delay in network. Then, a time-varying H∞ controller is designed. Such the controller can vary according to delay in network. Furthermore, by constructing delay-dependent Lyapunov-Krasovskii functional, a sufficient condition is given to guarantee that the closed-loop system is stochastically stable with an H∞ disturbance attenuation level in terms of nonlinear matrix inequalities. In order to solve the controller gain, the cone complementarity linearization (CCL) algorithm is employed. Finally, a networked DC motor control system is analyzed to illustrate the effectiveness of the proposed method.     

Multi-step Predictive Control of a PDF-shaping Problem

A predictive control strategy is proposed for the shaping of the output probability density function (PDF) of linear stochastic systems. The B-spline neural network is used to set up the output PDF model and therefore converts the PDF-shaping into the control of B-spline weights vector. The Diophantine equation is then introduced to formulate the predictive PDF model, based on which a moving-horizon control algorithm is developed so as to realize the predictive PDF tracking performance.     

Robust H∞ Networked Control for Uncertain Fuzzy Systems with Time-delay

A robust H∞ networked control method for Takagi-Sugeno （T-S） fuzzy systems with uncertainty and time delay is presented. A state feedback controller is designed via the networked control system （NCS） theory. Sufficient condition for robust stability with H∞ performance is obtained. Network-induced delay in network transmission and packet dropout are analyzed. Simulation result shows the validity of this control scheme.     

H∞ State Feedback Delay-dependent Control for Discrete Systems with Multi-time-delay

In this paper, H∞ state feedback control with delay information for discrete systems with multi-time-delay is discussed. Making use of linear matrix inequality (LMI) approach, a time-delay-dependent criterion for a discrete system with multi-time-delay to satisfy H∞ performance indices is induced, and then a strategy for H1 state feedback control with delay values for plant with multi-time-delay is obtained. By solving corresponding LMI, a delay-dependent state feedback controller satisfying H∞ performance indices is designed. Finally, a simulation example demonstrates the validity of the proposed approach.     

A Nonlinear H∞ Set-point Control Method for Turbofan Engines with Disturbances

International Journal of Control, Automation and Systems - To provide desired control performance for turbofan engines subject to external disturbances, a nonlinear H∞ set-point control...     

H∞ Containment Control of Multi-agent Systems with Random Communication Time-varying Delay

International Journal of Control, Automation and Systems - This paper investigates the H∞ containment control problem of multi-agent systems with random communication time-delay. The...     

Robust H ∞ Control of Linear Uncertain Systems: Its Limiting Performance

The concept of a H norm is introduced for linear control systems with uncertain bounded parameters. A procedure for determining the lower estimate of the minimal robust H norm in the linear state feedback class is designed. An example of a system in which the estimate coincides with the minimal robust norm is given.     

Robust H∞ Control of Uncertain Stochastic Systems with Time-varying Interval Delays

International Journal of Control, Automation and Systems - A robust delay-dependent stability criterion for discrete-time uncertain stochastic systems is proposed to achieve asymptotical stability...     

Event-triggered Networked H∞ Output Tracking Control Based on Dynamic Compensation Controller

In this paper, the event-triggered H_∞ output tracking problem is investigated for networked control systems. In order to reduce the output tracking error as well as to improve network resource utilization, we propose an idea of dynamic compensation controller with the discrete-time event-triggered mechanism, that is, the integral term of tracking error and the state of the reference system are introduced to form states of the augmented system. We first examine the dynamic compensation idea by the H_∞ output tracking control problem for linear time-invariant (LTI) systems. Then, we model the closed-loop event-triggered networked control system as a time-delay augmented linear system. By constructing a Lyapunov-Krasovskii functional with the delay fractioning technique, the stability conditions with lower conservatism are derived in the form of the linear matrix inequalities (LMIs). Furthermore, a method is proposed to design the H_∞ dynamic compensation controllers and the discrete-time event-triggered mechanisms. Finally, the satellite tracking control problem is used as an example to show that the dynamical compensation idea is effective in reducing the tracking error and that the proposed method in this paper can achieve better performance than that in the existing literature.

     

Model Predictive Control of Nonlinear Systems： Stability Region and Feasible Initial Control

This paper proposes a new method for model predictive control (MPC) of nonlinear systems to calculate stability region and feasible initial control profile/sequence, which are important to the implementations of MPC. Different from many existing methods, this paper distinguishes stability region from conservative terminal region. With global linearization, linear differential inclusion (LDI) and linear matrix inequality (LMI) techniques, a nonlinear system is transformed into a convex set of linear systems, and then the vertices of the set are used off-line to design the controller, to estimate stability region, and also to determine a feasible initial control profile/sequence. The advantages of the proposed method are demonstrated by simulation study.     

Robust H∞ State-feedback Control for Nonlinear Uncertain Systems with Mixed Time-varying Delays

International Journal of Control, Automation and Systems - This paper presents a new less conservative stability and H∞ state-feedback controller design of nonlinear uncertain systems with...     

Improved Results on Robust H∞ Control of Uncertain Discrete-time Systems with Time-varying Delay

In this paper,the robust H∞ control problem for uncertain discrete-time systems with time-varying state delay is considered.Based on the Lyapunov functional method,and by resorting to the new technique for estimating the upper bound of the difference of the Lyapunov functional,a new less conservative sufficient condition for the existence of a robust H∞ controller is obtained.Moreover,the cone complementary linearisation procedure is employed to solve the nonconvex feasibility problem.Finally,several numerical examples are presented to show the effectiveness and less conservativeness of the proposed method.