A robust distributed model predictive control algorithm

Although distributed model predictive control (DMPC) has received significant attention in the literature, the robustness of DMPC with respect to model errors has not been explicitly addressed. In this paper, a novel online algorithm that deals explicitly with model errors for DMPC is proposed. The algorithm requires decomposing the entire system into N subsystems and solving N convex optimization problems to minimize an upper bound on a robust performance objective by using a time-varying state-feedback controller for each subsystem. Simulations examples were considered to illustrate the application of the proposed method.     

Output feedback model predictive control for LPV systems based on quasi-min–max algorithm

This paper proposes a robust output feedback model predictive control (MPC) scheme for linear parameter varying (LPV) systems based on a quasi-min–max algorithm. This approach involves an off-line design of a robust state observer for LPV systems using linear matrix inequality (LMI) and an on-line robust output feedback MPC algorithm using the estimated state. The proposed MPC method for LPV systems is applicable for a variety of systems with constraints and guarantees the robust stability of the output feedback systems. A numerical example for an LPV system subject to input constraints is given to demonstrate its effectiveness.     

An improved approach for constrained robust model predictive control

In this paper, we present a new technique to address constrained robust model predictive control. The main advantage of this new approach with respect to other well-known techniques is the reduced conservativeness. Specifically, the technique described in this paper can be applied to polytopic uncertain systems and is based on the use of several Lyapunov functions each one corresponding to a different vertex of the uncertainty's polytope.     

LMI-based model predictive control for switched nonlinear systems

This paper proposes an LMI approach to model predictive control of nonlinear systems with switching between multiple modes. In this approach, at each mode, the nonlinear system is divided to a linearized model in addition to a nonlinear term. A sum of squares (SOS) optimization problem is presented to find a quadratic bound for the nonlinear part. The stability condition of the switching system is obtained by using a discrete Lyapunov function and then the sufficient state feedback control law is achieved so that guarantees the stability of the system and also minimizes an infinite prediction horizon performance index. Moreover, two other LMI optimization problems are solved at each mode in order to find the maximum area region of convergence of the nonlinear system inscribed in the region of stability. The performance and effectiveness of the proposed MPC approach are illustrated by two case studies.     

A framework for design of scheduled output feedback model predictive control

We present a stabilizing scheduled output feedback Model Predictive Control (MPC) algorithm for constrained nonlinear systems with large operating regions. We design a set of local output feedback predictive controllers with their estimated regions of stability covering the desired operating region, and implement them as a single scheduled output feedback MPC which on-line switches between the set of local controllers and achieves nonlinear transitions with guaranteed stability. This algorithm provides a general framework for scheduled output feedback MPC design.     

Improved robust model predictive control with structured uncertainty

In this paper, a dilation of the LMI characterization is presented to address constrained robust model predictive control (MPC) for a class of uncertain linear systems with structured time-varying uncertainties. The uncertainty is described in linear fractional transformation (LFT) form. By introducing slack variables and using parameter dependent Lyapunov functions, the design conservativeness is reduced compared with other existing MPC approaches. The proposed approach is applied to an industrial CSTR benchmark system to demonstrate the merits of our proposed solution.     

Efficient robust constrained model predictive control with a time varying terminal constraint set

An efficient robust constrained model predictive control algorithm with a time varying terminal constraint set is developed for systems with model uncertainty and input constraints. The approach is novel in that it off-line constructs a continuum of terminal constraint sets and on-line achieves robust stability by using a relatively short control horizon (even N=0) with a time varying terminal constraint set. This algorithm not only dramatically reduces the on-line computation but also significantly enlarges the size of the allowable set of initial conditions. Moreover, this control scheme retains the unconstrained optimal performance in the neighborhood of the equilibrium. The controller design is illustrated through a benchmark problem.     

Realization issues,tuning, and testing of a distributed predictive control algorithm

A non-iterative, non-cooperative distributed state-feedback control algorithm based on neighbor-to-neighbor communication, named distributed predictive control (DPC), has been recently proposed in the literature for constrained linear discrete-time systems, see  [15], [14], [2], [4]. The theoretical properties of DPC, such as convergence and stability, its extensions to the output feedback and tracking problems, and applications to simulated plants have been investigated in these papers. However, for a practical use of DPC some realization issues are still open, such as the automatic selection of some tuning parameters, the initialization of the algorithm, or its response to unexpected disturbances which could lead to the lack of the recursive feasibility, a fundamental property for any model predictive control (MPC) technique.This paper presents novel solutions to all these issues, with the goal to make DPC attractive for industrial and practical applications. Three realistic simulation examples are also discussed to evaluate the proposed numerical algorithms and to compare the performances of DPC to those of a standard centralized MPC algorithm.     

An efficient model predictive controller with pole placement

For model predictive control (MPC) of constrained systems, enlarging the feasible region is usually in conflict with improving the dynamic performance. To resolve the conflict, we proposed an efficient model predictive controller with pole placement for a class of discrete-time linear systems. By specifying a group of circular regions that contain the desired closed-loop poles, appropriate terminal weighting matrices and local controllers are calculated to construct a time-varying terminal convex set, which is a significant constraint for the online optimization problem. During the online optimization, the size of the terminal convex set can adjust itself according to the actual state at each sampling time. In this way, a large initial feasible region can be achieved while maintaining the good dynamic performance. An illustrative example is used to show the effectiveness of the proposed approach.     

Stability analysis and design of fuzzy control system with bounded uncertain delays

Fuzzy control problems for systems with bounded uncertain delays were studied. Based on Lyapunov stability theory and matrix theory, a nonlinear state feedback fuzzy controller was designed by linear matrix inequalities （LMI） approach, and the global exponential stability of the closed-loop system was strictly proved. For a fuzzy control system with bounded uncertain delays, under the global exponential stability condition which is reduced to p linear matrix inequalities, the controller guarantees stability performances of state variables. Finally, the simulation shows the validity of the method in tiffs paper.     

Stability analysis and design of fuzzy control system with bounded uncertain delays

Fuzzy control problems for systems with bounded uncertain delays were studied.Based on Lyapunov stability theory and matrix theory,a nonlinear state feedback fuzzy controller was designed by linear matrix inequalities (LMI) approach,and the global exponential stability of the closed-loop system was strictly proved.For a fuzzy control system with bounded uncertain delays,under the global exponential stability condition which is reduced to p linear matrix inequalities,the controller guarantees stability performances of state variables.Finally,the simulation shows the validity of the method in this paper.     

Backstepping control integrated with Lyapunov-based model predictive control

In this study, backstepping control integrated with Lyapunov-based model predictive control (BS-MPC) is proposed for nonlinear systems in a strict-feedback form. The virtual input of the first step is designed by solving the finite-horizon optimal control problem (FHOCP), and the real input is designed by the backstepping method. BS-MPC guarantees (semiglobal) ultimate boundedness of the closed-loop system when the control is implemented in a zero-order hold manner. When the robustness of BS-MPC is analyzed for uniformly bounded disturbances, the ultimate boundedness of the solution of perturbed system is guaranteed. BS-MPC can provide a better desired value of the virtual input of the first step by solving the FHOCP, resulting in a faster stabilization of the system compared with the backstepping control. In addition, BS-MPC requires less computational load compared with MPC because the dimension of the states considered in the on-line optimization problem of BS-MPC is lower than that of MPC.     

Robust model predictive control for continuous uncertain systems with state delay

This paper is concerned with robust model predictive control for linear continuous uncertain systems with state delay and control constraints, A piecewise constant control sequence is calculated by minimizing the upper-bound of the infinite horizon quadratic cost function, At each sampling time, the sufficient conditions for the existence of the model predictive control are derived, and expressed as a set of linear matrix inequalities. The robust stability of the closed-loop svstems is guaranteed bv the proposed design method. A numerical example is given to illustrate the main results.     

Robust model predictive control for continuous uncertain systems with state delay

This paper is concerned with robust model predictive control for linear continuous uncertain systems with state delay and control constraints. A piecewise constant control sequence is calculated by minimizing the upper-bound of the infinite horizon quadratic cost function. At each sampling time, the sufficient conditions for the existence of the model predictive control are derived, and expressed as a set of linear matrix inequalities. The robust stability of the closed-loop systems is guaranteed by the proposed design method. A numerical example is given to illustrate the main results.     

Robust hybrid predictive control of nonlinear systems

In this work, we consider nonlinear systems with input constraints and uncertain variables, and develop a robust hybrid predictive control structure that provides a safety net for the implementation of any model predictive control (MPC) formulation, designed with or without taking uncertainty into account. The key idea is to use a Lyapunov-based bounded robust controller, for which an explicit characterization of the region of robust closed-loop stability can be obtained, to provide a stability region within which any available MPC formulation can be implemented. This is achieved by devising a set of switching laws that orchestrate switching between MPC and the bounded robust controller in a way that exploits the performance of MPC whenever possible, while using the bounded controller as a fall-back controller that can be switched in at any time to maintain robust closed-loop stability in the event that the predictive controller fails to yield a control move (due, e.g., to computational difficulties in the optimization or infeasibility) or leads to instability (due, e.g., to inappropriate penalties and/or horizon length in the objective function). The implementation and efficacy of the robust hybrid predictive control structure are demonstrated through simulations using a chemical process example.     

A scheduling quasi–min-max model predictive control algorithm for nonlinear systems

In this paper, a model predictive control algorithm is designed for nonlinear systems. Combination of a linear model with a linear parameter varying model approximates the nonlinear behavior. The linear model is used to express the current nonlinear dynamics, and the linear parameter varying model is used to cover the future nonlinear behavior. In the algorithm, a “quasi-worst-case” value of an infinite horizon objective function is minimized. Closed-loop stability is guaranteed when the algorithm is implemented in a receding horizon fashion by including a Lyapunov constraint in the formulation. The proposed approach is applied to control a jacketed styrene polymerization reactor.     

Stability and stabilization of nonuniform sampling systems

This paper is concerned with nonuniform sampling systems, where the sampling interval is time-varying within a certain known bound. The system is transformed into a time-varying discrete time system, where time-varying parts due to the sampling interval variation are treated as norm bounded uncertainties using robust control techniques. To reduce conservatism arising from modeling time-varying parts as a single uncertainty, the time-varying parts are modeled as N uncertainties. With larger N, a less conservative stability condition is derived at sacrifice of more computation. It is shown through a numerical example that the proposed stability condition is better than existing stability conditions.     

Max-plus-linear model-based predictive control for constrained hybrid systems：linear programming solution

In this paper, a linear programming method is proposed to solve model predictive control for a class of hybrid systems. Firstly, using the （max, ＋） algebra, a typical subclass of hybrid systems called max-plus-linear （MPL） systems is obtained. And then, model predictive control （MPC） framework is extended to MPL systems. In general, the nonlinear optimization approach or extended linear complementarity problem （ELCP） were applied to solve the MPL-MPC optimization problem. A new optimization method based on canonical forms for max-min-plus-scaling （MMPS） functions （using the operations maximization, minimization, addition and scalar multiplication） with linear constraints on the inputs is presented. The proposed approach consists in solving several linear programming problems and is more efficient than nonlinear optimization. The validity of the algorithm is illustrated by an example.     

Max-plus-linear model-based predictive control for constrained hybrid systems: linear programming solution

In this paper, a linear programming method is proposed to solve model predictive control for a class of hybrid systems. Firstly, using the (max, +) algebra, a typical subclass of hybrid systems called max-plus-linear (MPL) systems is obtained. And then, model predictive control (MPC) framework is extended to MPL systems. In general, the nonlinear optimization approach or extended linear complementarity problem (ELCP) were applied to solve the MPL-MPC optimization problem. A new optimization method based on canonical forms for max-min-plus-scaling (MMPS) functions (using the operations maximization, minimization, addition and scalar multiplication) with linear constraints on the inputs is presented. The proposed approach consists in solving several linear programming problems and is more efficient than nonlinear optimization. The validity of the algorithm is illustrated by an example.