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A model predictive control (MPC) is proposed for the piecewise affine (PWA) systems with constrained input and time delay. The corresponding operating region of the considered systems in state space is described as ellipsoid which can be characterized by a set of vector inequalities. And the constrained control input of the considered systems is solved in terms of linear matrix inequalities (LMIs). An MPC controller is designed that will move the PWA system with time delay from the current operating point to the desired one. Multiple objective functions are used to relax the monotonically decreasing condition of the Lyapunov function when the control algorithm switches from a quasi-infinite horizon to an infinite horizon strategy. The simulation results verify the effectiveness of the proposed method. It is shown that, based on LMI constraints, it is easy to get the MPC for the PWA systems with time delay. Moreover, it is suitable for practical application.

In engineering practice, there are many hybrid systems described by piecewise affine systems (PWA) which are composed of linear subsystems and convex polytopic regions. Hybrid systems are composed of discrete event dynamic systems and continuous time dynamic systems or discrete time dynamic systems, which interact with each other [

Model predictive control (MPC), also known as receding horizon control, is a popular technique for the control of dynamical systems, such as those encountered in chemical process control in the petrochemical, pulp and paper industries, and in industrial hot strip mill [

Closed-loop stability in multiple model/control approaches has also been studied [

Time delay systems are very common in industry. However, few works on control algorithms development for time delay PWA system have been reported [

Consider a discrete time-delay PWA systems with input constraints:

Find a piecewise affine state feedback controller that exponentially stabilizes the PWA system when

It is the same as Problem

The state region

In application of this formulation to multiple regions, we assume that we know the order of regions that the states will go through starting from the current region of the system to the terminal region.

We also assume that we know the number of moves that the system has to take to go from one region to another adjacent operating region.

Model predictive control, also known as moving horizon control or receding horizon control, has become very successful in process industries, especially in the control of processes that are constrained, multivariable and uncertain. In general, MPC solves online an open-loop optimal control problem subject to system dynamics and constraints at each time instant and implements only the first element of the control profile. At each sampling time

In this section, the problem formulation for MPC using piecewise linear models of the form (

Consider a time-delay PWA system (

The modified MPC law is given by

Substituting (

Using the previous techniques, the problem of minimizing an upper bound on the worst-case objective function, subject to input and terminal operating ellipsoid constraints, is reduced to a convex optimization of

Although derived for a time-delay PWA system with ellipsoidal partitions, the optimization problem LMI (

If the ellipsoidal region

We use the ALV (autonomous land vehicle) model formulated by [^{2} is the moment of inertia of the cart with respect to the center of mass,

Underactuated surface vessel.

The constant

Figures

States trajectories.

Control action.

This example considers a circuit with a nonlinear resistor taken from [

A circuit with a nonlinear resistor.

Following [

Characteristic of the nonlinear resistor.

By using Lemma

Using forward differential

Figures

Trajectory of the current.

Trajectory of the voltage.

Control input.

This work presented a stabilizing multimodel predictive control algorithm which has a contractive constraint to guarantee closed-loop stability. Moreover, the stability of the closed-loop is analyzed by employing the Lyapunov functions approach. Depending on the system state (in the terminal region or outside) the corresponding Lyapunov functions are assigned. The use of multiple objective functions has enabled us to relax the monotonically decreasing condition of the Lyapunov function when the control algorithm switches from a quasi-infinite horizon to an infinite horizon strategy. We have developed a new controller design technique for MPC of piecewise affine systems with time-delay and input constraints. The two simulation examples proposed in Section

The authors are grateful to the reviewers for their valuable comments. This work is partially supported by National Natural Science Foundation of China (51379044, 61304060, 61201410, and 61104037), Fundamental Research Funds for the Central Universities (HEUCF130804), and Heilongjiang Province Natural Science Foundation Projects (F200916).

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