Constructive model predictive control for constrained nonlinear systems

This paper develops a new model predictive control (MPC) design for stabilization of continuous‐time nonlinear systems subject to state and input constraints. The key idea is to construct an analytic form of the controller with some undetermined parameters and to calculate the parameters by minimizing online a performance index. By using the method of control Lyapunov functions (CLFs), we construct an appropriate variation on Sontag's formula, with one degree of freedom reflecting ‘decay rate’ of CLFs. Moreover, the constructed univariate control law is used to characterize the terminal region that guarantees the feasibility of the optimal control problem. Provided that the initial feasibility of the optimization problem is satisfied, the stability of the control scheme can be guaranteed. An example is given to illustrate the application of the constructive MPC design. Copyright © 2008 John Wiley & Sons, Ltd.     

Distributed model predictive control for continuous‐time nonlinear systems based on suboptimal ADMM

This paper presents a distributed model predictive control (DMPC) scheme for continuous‐time nonlinear systems based on the alternating direction method of multipliers (ADMM). A stopping criterion in the ADMM algorithm limits the iterations and therefore the required communication effort during the DMPC solution at the expense of a suboptimal solution. Stability results are presented for the suboptimal DMPC scheme under two different ADMM convergence assumptions. In particular, it is shown that the required iterations in each ADMM step are bounded, which is also confirmed in simulation studies.     

Engine idle speed control using nonlinear multiparametric model predictive control

In this article, a real-time nonlinear model predictive idle speed controller based on multiparametric programming is designed for an SI engine. Idle speed is a crucial recurring condition in urban vehicles demanding proper control to avoid stall. As will be seen, the nonlinear model predictive control (NMPC) system designed, besides complying with the predefined constraints, demonstrates a far better performance than the prevalent industrial controllers and even conventional linear MPC controllers. More importantly, a new special structure combining offline nonlinear MPC and classical controller is employed to provide both robustness and fast response. Not only is the computational burden of the controller within that of the ordinary ECU controllers, it is also able to readily damp a disturbance of 20 N·m in less than 2.5 seconds and easily deal with parameter uncertainties. The control system also regulates engine gas pedal release, and converges to the set point with a settling time of less than 3 seconds and minimum fluctuations.     

Delay‐dependent robust passive control for a class of nonlinear systems with time‐varying delays

In this paper, the problem of robust passive control for a class of nonlinear systems with time‐varying delays is considered. The uncertainties investigated in this paper are norm bounded and time varying, and they enter all system matrices. Based on the Lyapunov–Krasovskii functionals approach, a new robust passive control criterion is proposed in terms of linear matrix inequalities, which is dependent on the size of time delay. We also design a state feedback controller that guarantees a robust asymptotically stable and strictly passive closed‐loop system for all admissible uncertainties. Finally, two numerical examples are given to illustrate the effectiveness of the developed techniques. Copyright © 2007 John Wiley & Sons, Ltd.     

Stochastic model predictive control for tracking linear systems

This note presents a stochastic formulation of the model predictive control for tracking (MPCT), based on the results of the work of Lorenzen et al. The proposed controller ensures constraints satisfaction in probability, and maintains the main features of the MPCT, that are feasibility for any changing setpoints and enlarged domain of attraction, even larger than the one delivered by Lorenzen et al, thanks to the use of artificial references and relaxed terminal constraints. The asymptotic stability (in probability) of the minimal robust positively invariant set centered on the desired setpoint is guaranteed. Simulations on a DC-DC converter show the benefits and the properties of the proposal.     

A robust control system scheme based on model predictive controller (MPC) for continuous‐time systems

In this paper, an LMI framework based on model predictive strategy is addressed to design a robust dynamical control law in a typical control system. In the proposed method, instead of traditional static controller, a dynamic control law is used. With a suitable matrix transformation, the controller parameters selection are translated into an optimization problem with some LMI constraints. The plant input and output constraints are also handled with another LMIs. The controller is represented in state space form, and its parameters are computed in real‐time operation. For achieving this goal, by solving an optimization problem, a dynamic controller is designed, which meets the required plant performances. These results are used in 2 numerical examples to demonstrate the effectiveness of the proposed approach.     

Distributed model predictive control for energy management in a network of microgrids using the dual decomposition method

This paper deals with the application of model predictive control (MPC) to optimize power flows in a network of interconnected microgrids (MGs). More specifically, a distributed MPC (DMPC) approach is used to compute for each MG how much active power should be exchanged with other MGs and with the outer power grid. Due to the presence of coupled variables, the DMPC approach must be used in a suitable way to guarantee the feasibility of the consensus procedure among the MGs. For this purpose, we adopt a tailored dual decomposition method that allows us to reach a feasible solution while guaranteeing the privacy of single MGs (ie, without having to share private information like the amount of generated energy or locally consumed energy). Simulation results demonstrate the features of the proposed cooperative control strategy and the obtained benefits with respect to other classical centralized control methods.     

A robust and accurate disturbance damping control design for nonlinear dynamical systems

The principle result of this paper is the following disturbance rejection control scheme for a class of nonlinear dynamical systems. By using the internal model principle, the problem of disturbance damping control is converted into a nonlinear quadratic regulator (NQR) problem for an undisturbed augmented system. Then, an iterative technique is designed to solve this NQR problem effectively. The proposed iterative method is also extended through the use of a nonlinear model predictive control in an offline framework. In this case and in the presence of unknown disturbances, the Lyapunov stability of the closed‐loop system is guaranteed. Numerical simulations and comparative results verify the effectiveness of the proposed approach.     

A direct search approach to optimization for nonlinear model predictive control

Nonlinear model predictive control (NMPC) depends on performing a constrained nonlinear optimization, based on predictions of future system behavior, during a sampling interval to determine the control action to be applied to the system during the next time step. The difficulty in designing an optimization procedure to solve a constrained NMPC problem is due to the finite time horizon to which the predictive model is evaluated, the state and control actuator constraints, and sampling interval length. The resulting objective function, which is to be optimized is typically not differentiable. Although there are many commercial, shareware, and open‐source optimization packages available that can perform a nonlinear constrained optimization for most cases, there are NMPC implementations requiring embedded code or that must meet stringent timing requirements that preclude the use of off‐the‐shelf packages. In cases where the predictive model is known, such as aerodynamic or hydrodynamic systems, a direct‐search optimization algorithm can perform well enough in a real‐time environment. Direct search algorithms are simple to implement and can be made more efficient by applying differential geometric techniques to the search methodology. The typical smoothness of the equations of motion for vehicular systems allows the objective function's stationarities to be handled in a straight‐forward way. Copyright © 2013 John Wiley & Sons, Ltd.     

Optimal weighting design for distributed parameter systems estimation

This paper presents a method which aims at improving parameter estimation in dynamical systems. The general principle of the method is based on a modification of the least‐squares objective function by means of a weighting operator, in view to improve the conditioning of the identification problem. First we recall a previous work using variational calculus in order to obtain the weighting operators through a linear equation. Then we propose a new approach which consists of determining the weights by formulating an optimization problem including positive semidefinite constraints (linear matrix inequalities, LMI). Copyright © 2001 John Wiley & Sons, Ltd.     

PolyMPC: An efficient and extensible tool for real-time nonlinear model predictive tracking and path following for fast mechatronic systems

This paper presents PolyMPC, an open-source C++ library for pseudospectral-based real-time predictive control of nonlinear systems. It provides a necessary background on the computational aspects of the pseudospectral approximation of optimal control problems and explains how various model predictive control and parameter estimation algorithms can be implemented using the software. We discuss the key algorithmic modules and architectural features of the PolyMPC library. The workflow of a path following controller design for a highly nonlinear mechatronic system is demonstrated in a tutorial example. Another example illustrates how the core functionality might be used to approximate and solve a custom optimal control problem.     

Stable impulsive zone model predictive control for type 1 diabetic patients based on a long-term model

In this work, the problem of regulating blood glucose (glycemia) in type I diabetic patients is studied by means of an impulsive zone model predictive control (iZMPC), which bases its predictions on a novel long-term glucose-insulin model. Taking advantage of the impulsive version of the model—which features real-life properties of diabetes patients that some other popular models do not—the given control guarantees the stability under moderate-to-severe plant-model mismatch and disturbances. Long-term scenarios—including meals and physiological parameter variations—are simulated and the results are satisfactory as every hyperglycemic and hypoglycemic episodes are suitably controlled.     

A primal‐dual active‐set method for distributed model predictive control

We present a novel distributed primal‐dual active‐set method for model predictive control. The primal‐dual active‐set method is used for solving model predictive control problems for large‐scale systems with quadratic cost, linear dynamics, additive disturbance, and box constraints. The proposed algorithm is compared with dual decomposition and an alternating direction method of multipliers. Theoretical and experimental results show the effectiveness of the proposed approach for large‐scale systems with communication delays. The application to building control systems is thoroughly investigated. Copyright © 2016 John Wiley & Sons, Ltd.     

Design of robust nonfragile H∞ controller for uncertain nonlinear polynomial systems

This paper is concerned with the robust H_∞ nonfragile controller design for a particular class of nonlinear systems, namely, the perturbed polynomial systems, which are subject to unstructured bounded uncertainties in both the system model and the control law. Combining the Lyapunov stability theory, properties of linear matrix inequality, and Kronecker product properties, a sufficient condition of robust H_∞ nonfragile control design is proposed. More specifically, we propose a robust H_∞ controller of nonlinear polynomial systems with additive unstructured uncertainties and variation in the control law itself that guarantee the stability and the attenuation of external perturbations. Two examples are provided to illustrate the effectiveness of the proposed approach.     

Multiobjective predictive cruise control for connected vehicle systems on urban conditions with InPA‐SQP

The connected vehicle (CV) system is one of the most effective core technologies in intelligent transportation systems. In order to solve the optimal velocity prediction problem for a CV system on urban roads, a multiobjective predictive cruise controller (MOPCC) for vehicles in the CV system is proposed to coordinate multiple performances including safety, tracking ability, ride comfort, and fuel economy. Firstly, with the ad hoc wireless communication technology, the signal phase and timing information is obtained to calculate the feasible velocity range for improving mobility. Then, the optimal target velocity of vehicles is computed by minimizing the fuel economic polynomial models of the vehicle system. Secondly, in order to systematically cope with those multiple performances, the Utopia point method is applied to change the multiobjective optimization problem into Utopia tracking problem. Furthermore, the MOPCC problem is formulated and solved by a fast numerical algorithm, ie, integrated perturbation analysis and sequential quadratic programming. Finally, simulations are presented to demonstrate the effectiveness of the proposed method in terms of improved the multiple performances.     

Robust model predictive control for uncertain step response

The design of robust model predictive control for handling bounded uncertainties in step response of unconstrained MIMO processes is considered. The control law is obtained by minimizing an upper bound of the objective function and it consists of an optimal state feedback gain and a robust state observer. The separation principle is found to be applicable between the state feedback gain and the robust state observer. Simulation results show that the proposed algorithm can provide an improved handling of the uncertainty in step response as compared with a nominal MPC algorithm. Copyright © 2000 John Wiley & Sons, Ltd.     

Load frequency predictive control for power systems concerning wind turbine and communication delay

This article addresses a model predictive control (MPC) technique for load frequency control (LFC) system in the presence of wind power, communication delay, and denial-of-service (DoS) attack. In this article, communication delay is incorporated into a single area control error transmission for simplicity, wind power and load disturbance are regarded as Lipschitz nonlinear terms, as for the randomly occurring DoS attack, it is modeled as Bernoulli processes with known conditional probability. Thinking all these adverse factors to stability and the limitation of input constraint synthetically, the stability of LFC system can be guaranteed by delay-dependent Lyapunov function lemma and a state feedback MPC controller is designed to solve the LFC problems by minimizing the infinite-horizon objective function. Although some scholars have studied the performance degradation and instability of LFC system caused by cyber attack and/or communication delay and some very nice results have been addressed, limited works have considered the MPC approach to deal with both the problems of cyber attack and communication delay which explicitly considers the physical constraints. In addition, the delay-dependent Lyapunov function is adopted to deal with the problem of communication delay, which results in less conservatism of the presented method. Finally, the optimization problem with input constraint is solved and proven to be recursive feasibility, and the closed-loop system turns out to be stable. The reasonability and validity of the provided strategy is verified through several groups of simulation experiments. It illustrates that the proposed control method can keep the system frequency steady in the standard range in spite of various attack conditions.     

Dissipative control for singular Markovian jump systems with time delay

This paper focuses on the problem of dissipative control for continuous‐time singular time‐delayed systems with Markovian jump parameters. Different from usually mode‐dependent or mode‐independent controller design methods, a partially mode‐dependent dissipative controller is firstly proposed via using a mode‐dependent Lyapunov function. The stochastic property of the mode available to a controller operation is taken into consideration in the corresponding controller design. Moreover, the existence of the established controller is given in terms of strict linear matrix inequalities. Finally, numerical examples are used to demonstrate the effectiveness of the given theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

Economic model predictive control for time-varying system: Performance and stability results

We consider economic model predictive control (MPC) without terminal conditions for time-varying optimal control problems. Under appropriate conditions, we prove that MPC yields initial pieces of approximately infinite horizon optimal trajectories and that the optimal infinite horizon trajectory is practically asymptotically stable. The results are illustrated by numerical examples motivated by energy-efficient heating and cooling of a building.