Model predictive control synthesis algorithm based on polytopic terminal region for Hammerstein-Wiener nonlinear systems

An improved model predictive control algorithm is proposed for Hammerstein-Wiener nonlinear systems.The proposed synthesis algorithm contains two parts:offline design the polytopic invariant sets,and online solve the min-max optimization problem.The polytopic invariant set is adopted to replace the traditional ellipsoid invariant set.And the parameter-correlation nonlinear control law is designed to replace the traditional linear control law.Consequently,the terminal region is enlarged and the control effect is improved.Simulation and experiment are used to verify the validity of the wind tunnel flow field control algorithm.

State and Mode Feedback Control for Discrete-time Markovian Jump Linear Systems With Controllable MTPM

In this note, the state and mode feedback control problems for a class of discrete-time Markovian jump linear systems(MJLSs) with controllable mode transition probability matrix(MTPM) are investigated. In most achievements, controller design of MJLSs pays more attention to state/output feedback control for stability, while the system cost in practice is out of consideration. In this paper, we propose a control mechanism consisting of two parts: finite-path-dependent state feedback controller design with which uniform stability of MJLSs can be ensured, and mode feedback control which aims to decrease system cost. Differing from the traditional state/output feedback controller design, the main novelty is that the proposed control mechanism not only guarantees system stability, but also decreases system cost effectively by adjusting the occurrence probability of system modes. The effectiveness of the proposed mechanism is illustrated via numerical examples.

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.

Static Output Feedback H_∞ Controllers Design for Descriptor Linear Systems Based on LMI

This paper considers the design problem of static output feedback H ∞ controllers for descriptor linear systems with linear matrix inequality (LMI) approach. Necessary and sufficient conditions for the existence of a static output feedback H ∞ controller are given in terms of LMIs. Furthermore, the design method of H ∞ controllers is provided using the solutions to the LMIs.

Time domain analysis for discrete difference equation on discrete linear system controllable problem's research

We usually describle a comparatively more complex control system,especially a multi-inputs and multi-outputs system by time domation analytical procedure.While the system's controllability means whether the system is controllable according to certain requirements.It involves not only the system's outputs' controllability but also the controllability of the system's partial or total conditions.The movement is described by difference equation in the linear discrete-time system.Therefore,the problem of controllability of the linear discrete-time system has been converted into a problem of the controllability of discrete-time difference equation.The thesis makes out the determination method of the discrete-time system's controllability and puts forward the sufficient and necessary conditions to determine it's controllability by making a study on the controllability of the linear discrete-time equation.

BLOCK DIAGONAL FORM AND BLOCK DIAGONAL CONTROLLER OF NONLINEAR SYSTEMS

A block diagonal form about a nonlinear system is defined. Based on the de finition, a design method ca1led block diagonal controller (BDC) is proPOsed bo feedbacklinearization. Thus, a linearization design of a class of nonlinear system can be simply re-alized. The result of design has been proved by mathematical simulation of a certain anti-ship missile.

Global robust optimal sliding mode control for uncertain affine nonlinear systems

The problem of robustifying linear quadratic regulators （LQRs） for a class of uncertain affine nonlinear systems is considered. First, the exact linearization technique is used to transform an uncertain nonlinear system into a linear one and an optimal LQR is designed for the corresponding nominal system. Then, based on the integral sliding mode, a design approach to robustifying the optimal regulator is studied. As a result, the system exhibits global robustness to uncertainties and the ideal sliding mode dynamics is the same as that of the optimal LQR for the nominal system. A global robust optimal sliding mode control （GROSMC） is realized. Finally, a numerical simulation is demonstrated to show the effectiveness and superiority of the proposed algorithm compared with the conventional optimal LQR.

Parallel Control for Continuous-Time Linear Systems:A Case Study

In this paper,a new parallel controller is developed for continuous-time linear systems.The main contribution of the method is to establish a new parallel control law,where both state and control are considered as the input.The structure of the parallel control is provided,and the relationship between the parallel control and traditional feedback controls is presented.Considering the situations that the systems are controllable and incompletely controllable,the properties of the parallel control law are analyzed.The parallel controller design algorithms are given under the conditions that the systems are controllable and incompletely controllable.Finally,numerical simulations are carried out to demonstrate the effectiveness and applicability of the present method.Index Terms-Continuous-time linear systems,digital twin,parallel controller,parallel intelligence,parallel systems.

Eigenstructure Assignment in a Class of Second-order Descriptor Linear Systems: A Complete Parametric Approach

In this paper eigenstructure assignment via proportional-plus-derivative feedback is investigated for a class of second-order descriptor linear systems. Under certain conditions, simple, general and complete parametric solutions of both finite closed-loop eigenvector matrices and feedback gain matrices are derived. The parametric approach utilizes directly original system data, involves manipulations only on n-dimensional matrices, and reveals all the design degrees of freedom which can be further utilized to achieve certain additional system specifications. A numerical example shows the effect of the proposed approach.

Static output feedback control for discrete-time fuzzy bilinear system

The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system （DFBS） is presented. Based on parallel distribution compensation method, some sufficient conditions are derived to guarantee the stability of the overall fuzzy system. The stabilization conditions are further formulated into linear matrix inequality （LMI） so that the desired controller can be easily obtained by using the Matlab LMI toolbox. In comparison with the existing results, the drawbacks, such as coordinate transformation, same output matrices, have been elim- inated. Finally, a simulation example shows that the approach is effective.

Distributed Model Predictive Control with Actuator Saturation for Markovian Jump Linear System

This paper is concerned with the distributed model predictive control (MPC) problem for a class of discrete-time Markovian jump linear systems (MJLSs) subject to actuator saturation and polytopic uncertainty in system matrices. The global system is decomposed into several subsystems which coordinate with each other. A set of distributed controllers is designed by solving a min-max optimization problem in terms of the solutions of linear matrix inequalities (LMIs). An iterative algorithm is developed to achieve the online computation. Finally, a simulation example is employed to show the effectiveness of the proposed algorithm. © 2014 Chinese Association of Automation.

Adaptive fault-tolerant control of linear systems with actuator saturation and L_2-disturbances

This paper studies the problem of designing adaptive fault-tolerant H-infinity controllers for linear timeinvariant systems with actuator saturation. The disturbance tolerance ability of the closed-loop system is measured by an optimal index. The notion of an adaptive H-infinity performance index is proposed to describe the disturbance attenuation performances of closed-loop systems. New methods for designing indirect adaptive fault-tolerant controllers via state feedback are presented for actuator fault compensations. Based on the on-line estimation of eventual faults, the adaptive fault-tolerant controller parameters are updated automatically to compensate for the fault effects on systems. The designs are developed in the framework of the linear matrix inequality （LMI） approach, which can guarantee the disturbance tolerance ability and adaptive H-infinity performances of closed-loop systems in the cases of actuator saturation and actuator failures. An example is given to illustrate the efficiency of the design method.

Robust model-reference control for descriptor linear systems subject to parameter uncertainties

Robust model-reference control for descriptor linear systems with structural parameter uncertainties is investigated. A sufficient condition for existing a model-reference zero-error asymptotic tracking controller is given. It is shown that the robust model reference control problem can be decomposed into two subproblems： a robust state feedback stabilization problem for descriptor systems subject to parameter uncertainties and a robust compensation problem. The latter aims to find three coefficient matrices which satisfy four matrix equations and simultaneously minimize the effect of the uncertainties to the tracking error. Based on a complete parametric solution to a class of generalized Sylvester matrix equations, the robust compensation problem is converted into a minimization problem with quadratic cost and linear constraints. A numerical example shows the effect of the proposed approach.

Novel Adaptive Learning Control of Linear Systems with Completely Unknown Time Delays

A novel output-feedback adaptive learning control approach is developed for a class of linear time-delay systems. Three kinds of uncertainties： time delays, number of time delays, and system parameters are all assumed to be completely unknown, which is dfferent from the previous work. The design procedure includes two steps. First, according to the given periodic desired reference output and the allowed bound of tracking error, a suitable finite Fourier series expansion （FSE） is chosen as a practical reference output to be tracked. Second, by expressing the delayed practical reference output as a known time-varying vector multiplied by an unknown constant vector, we combine three kinds of uncertainties into an unknown constant vector and then estimate the vector by designing an adaptive law. By constructing a Lyapunov-Krasovskii functional, it is proved that the system output can asymptotically track the practical reference signal. An example is provided to illustrate the effectiveness of the control scheme developed in this paper.

H_∞ controller synthesis of piecewise discrete time linear systems

This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ performance and the controller can be obtained by solving a set of bilinear matrix inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global quadratic Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.

State Feedback Control for a Class of Fractional Order Nonlinear Systems

Using the Lyapunov function method, this paper investigates the design of state feedback stabilization controllers for fractional order nonlinear systems in triangular form, and presents a number of new results. First, some new properties of Caputo fractional derivative are presented, and a sufficient condition of asymptotical stability for fractional order nonlinear systems is obtained based on the new properties. Then, by introducing appropriate transformations of coordinates, the problem of controller design is converted into the problem of finding some parameters, which can be certainly obtained by solving the Lyapunov equation and relevant matrix inequalities. Finally, based on the Lyapunov function method, state feedback stabilization controllers making the closed-loop system asymptotically stable are explicitly constructed. A simulation example is given to demonstrate the effectiveness of the proposed design procedure. © 2014 Chinese Association of Automation.

Exact uncertainty compensation of linear systems by continuous fixed-time output-feedback controller

This paper studies the fixed-time output-feedback control for a class of linear systems subject to matched uncertainties.To estimate the uncertainties and system states,we design a composite observer which consists of a high-order sliding mode observer and a Luenberger observer.Then,a robust output-feedback controller with fixed-time convergence guarantee is constructed.Rigorous theoretical proof shows that with the proposed controller,the system states can converge to zero in fixed-time free of the initial conditions.Finally,simulation comparison with existing algorithms is given.Simulation results verify the effectiveness of the proposed controller in terms of its fixed-time convergence and perfect disturbance rejection.

An improved constrained model predictive control approach for Hammerstein-Wiener nonlinear systems

Many industry processes can be described as Hammerstein-Wiener nonlinear systems. In this work, an improved constrained model predictive control algorithm is presented for Hammerstein-Wiener systems. In the new approach, the maximum and minimum of partial derivative for input and output nonlinearities are solved in the neighbourhood of the equilibrium. And several parameter-dependent Lyapunov functions, each one corresponding to a different vertex of polytopic descriptions models, are introduced to analyze the stability of Hammerstein-Wiener systems, but only one Lyapunov function is utilized to analyze system stability like the traditional method. Consequently, the conservation of the traditional quadratic stability is removed, and the terminal regions are enlarged. Simulation and field trial results show that the proposed algorithm is valid. It has higher control precision and shorter blowing time than the traditional approach.

Decoupled nonsingular terminal sliding mode control for affine nonlinear systems

A decoupled nonsingular terminal sliding mode control（DNTSMC） approach is proposed to address the tracking control problem of affine nonlinear systems.A nonsingular terminal sliding mode control（NTSMC） method is presented,in which the nonsingular terminal sliding surface is defined as a special nonsingular terminal function and the convergence time of the system states can be specified.The affine nonlinear system is firstly decoupled into linear subsystems via feedback linearization.Then,a nonsingular terminal sliding surface is defined and the NTSMC method is applied to each subsystem separately to ensure the finite time convergence of the closed-loop system.The verification example is given to demonstrate the effectiveness and robustness of the proposed approach.The proposed approach exhibits a considerable advantage in terms of faster tracking error convergence and less chattering compared with the conventional sliding mode control（CSMC）.

Linear systems toolkit in Matlab :structural decompositions and their applications

This paper presents a brief description of the software toolbox, linear systems toolkit, developed in Matlab environment. The toolkit contains 66 m-functious, including structural decompositions of linear autonomous systems, unforced/uuseused systems, proper systems, and singular systems, along with their applications to system factorizations, sensor/actuator selection, H-two and H-infinity control, and disturbance decoupling problems.