Model predictive control of directed‐graph constrained systems

The problem of feedback stabilization of linear systems with partially accessible states, constraints on the control, and parameter uncertainties is considered. An adaptive receding horizon control strategy is employed to ensure stabilization of the constrained system. The resulting model based receding horizon controller is nonlinear, so that standard convergence results in adaptive control do not appear applicable. Global stabilization is established under observability and controllability assumption on the system.

Model Predictive Control (MPC), the dominant advanced control approach in industry over the past twenty-five years, is presented comprehensively in this unique book. With a simple, unified approach, and with attention to real-time implementation, it covers predictive control theory including the stability, feasibility, and robustness of MPC controllers. The theory of explicit MPC, where the nonlinear optimal feedback controller can be calculated efficiently, is presented in the context of linear systems with linear constraints, switched linear systems, and, more generally, linear hybrid systems. Drawing upon years of practical experience and using numerous examples and illustrative applications, the authors discuss the techniques required to design predictive control laws, including algorithms for polyhedral manipulations, mathematical and multiparametric programming and how to validate the theoretical properties and to implement predictive control policies. The most important algorithms feature in an accompanying free online MATLAB toolbox, which allows easy access to sample solutions. Predictive Control for Linear and Hybrid Systems is an ideal reference for graduate, postgraduate and advanced control practitioners interested in theory and/or implementation aspects of predictive control.

Model Predictive Control (MPC), the dominant advanced control approach in industry over the past twenty-five years, is presented comprehensively in this unique book. With a simple, unified approach, and with attention to real-time implementation, it covers predictive control theory including the stability, feasibility, and robustness of MPC controllers. The theory of explicit MPC, where the nonlinear optimal feedback controller can be calculated efficiently, is presented in the context of linear systems with linear constraints, switched linear systems, and, more generally, linear hybrid systems. Drawing upon years of practical experience and using numerous examples and illustrative applications, the authors discuss the techniques required to design predictive control laws, including algorithms for polyhedral manipulations, mathematical and multiparametric programming and how to validate the theoretical properties and to implement predictive control policies. The most important algorithms feature in an accompanying free online MATLAB toolbox, which allows easy access to sample solutions. Predictive Control for Linear and Hybrid Systems is an ideal reference for graduate, postgraduate and advanced control practitioners interested in theory and/or implementation aspects of predictive control.

Dynamic optimization and its relation to classical and quantum constrained systems

This paper introduces two multilingual systems, IKUN and IKUN-C, developed for the general machine translation task in WMT24.IKUN and IKUN-C represent an open system and a constrained system, respectively, built on Llama-3-8b and Mistral-7B-v0.3.Both systems are designed to handle all 11 language directions using a single model.According to automatic evaluation metrics, IKUN-C achieved 6 first-place and 3 second-place finishes among all constrained systems, while IKUN secured 1 first-place and 2 secondplace finishes across both open and constrained systems.These encouraging results suggest that large language models (LLMs) are nearing the level of proficiency required for effective multilingual machine translation.The systems are based on a two-stage approach: first, continuous pre-training on monolingual data in 10 languages, followed by fine-tuning on high-quality parallel data for 11 language directions.The primary difference between IKUN and IKUN-C lies in their monolingual pre-training strategy.IKUN-C is pre-trained using constrained monolingual data, whereas IKUN leverages monolingual data from the OS-CAR dataset.In the second phase, both systems are fine-tuned on parallel data sourced from NTREX, Flores, and WMT16-23 for all 11 language pairs. 1

In this paper we extend the classical min–max model predictive control framework to a class of uncertain discrete event systems that can be modelled using the operations maximization, minimization, addition and scalar multiplication, and that we call max–min-plus-scaling (MMPS) systems. Provided that the stage cost is an MMPS expression and considering only linear input constraints then the open-loop min–max model predictive control problem for MMPS systems can be transformed into a sequence of linear programming problems. Hence, the min–max model predictive control problem for MMPS systems can be solved efficiently, despite the fact that the system is non-linear. A min–max feedback model predictive control approach using disturbance feedback policies is also presented, which leads to improved performance compared to the open-loop approach.

The development of robust and efficient algorithms for nonlinear optimization is an important matter; because they make possible the solution of models with increasingly sizeand complexity. In this context, the Interior Point Optimizer (IPOPT) has been proven to be a competitive algorithm, because of its ability to handle large scale problems. However, there are some specific situations in which convergence can not be guaranteed. For instancethe violation of a regularity condition given by the Linear Independence Constraint Qualification (LICQ). This property is given in terms of the consistency of local linearizationsof the set of constraints, i.e. the gradients. If the set of gradients of equality and active bound inequality are linearly independent, then the LICQ holds. It turns out that if thisproperty is not satisfied, IPOPT would attempt to regularize the system by perturbing it, with the hope to overcome regions of local inconsistency. However, if the LICQ does nothold globally or if the system has severe ill-conditioned, the regularization strategies will fail. Thus, we present the `1-exact penalty-barrier strategy to deal with this lack of regularity. This works by penalizing the infeasibility with a parameter at the objective; and then by reformulating the problem to obtain a higher dimensional problem, the LICQ property holds at all points for which the new variables are nonzero. Thus achieving higher level of robustness as opposed to the regular IPOPT. Moreover, an unified framework for nonlinear model-based state-estimation and control with parametric sensitivity is presented. Typically, control strategy of a processes is tied to the ability to accommodate online computations; in this sense nonlinear optimization strategies like Moving Horizon Estimation (MHE) and Model Predictive Control (NMPC) are overlooked. Nevertheless, it has been proposed to use the parametric nature of these optimization problems to create a scheme in which the bulk of computations is partitioned into a background phase with all the most computationally expensive steps, and an online phase, in which the sensitivity information is used to make inexpensive calculations for the state estimate or controller input. These ideas have been put together into a Python framework, that streamlines the creation of a state-estimation and control strategy with the additional benefit of having parametric sensitivity embedded into it. This framework works by using the Pyomo libraries to create optimization objects and automatically discretize the models given by the user. We demonstrate the effectiveness of the frameworkin two problems of vastly different complexity. A benchmark distillation case study and a Bubbling Fluidized Bed Reactor (BFB) for the capture of CO2. The results show thatsensitivity is effective for online implementations of the controller and it was seamlessly enabled by our framework.

This paper considers the consensus control problem of heterogeneous linear multiagent systems. A distributed proportional-integral (PI) protocol is presented to ensure consensus of heterogeneous linear multiagent systems with directed communication graphs. Sufficient conditions for the choice of control parameters are derived. For the case that the agents are subject to the external time-varying but bounded disturbances, the proposed distributed PI protocol can assure uniformly ultimate boundedness of the consensus error. The effectiveness of the results is illustrated both theoretically and numerically.

Fil: Giovanini, Leonardo Luis. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - Santa Fe. Instituto de Investigacion en Senales, Sistemas e Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de Ingenieria y Ciencias Hidricas. Instituto de Investigacion en Senales, Sistemas e Inteligencia Computacional; Argentina

Model predictive control has been recognized as one of the essential solutions to achieve considerable energy savings in buildings. However, its performance on a building zone level can be inferior to a well-tuned conventional controller, especially in situations with constant energy prices and conservative comfort constraints. Optimization problem in the background has to be chosen to guarantee recursive feasibility and considerable energy savings without compromising the users comfort at the same time. This paper gives a novel formulation of the model predictive temperature control problem in buildings and its fair comparison with conventional controllers with the same level of flexibility allowed in zone temperature control. All controllers are tested for a system with seasonal heating and cooling, which is the most common case in real applications. It is shown that the introduced formulation leads to the model predictive controller that significantly outperforms conventional controllers both in energy consumption and users comfort.

This work investigates the event‐driven model predictive control problem for perturbed nonlinear systems with input and state constraints. Firstly, a new event‐driven triggering condition, considering the gradient and accumulation of the error between the optimal and actual states at adjacent moments with a state‐dependent relative threshold is designed with a guaranteed positive inter‐event time to avoid Zeno behaviour. Secondly, an error gradient and accumulation type event‐driven model predictive control framework is designed based on the new triggering condition and the dual‐mode strategy, for effectively reducing the calculation and communication burden of the model predictive control controller while ensuring desired control performance. Furthermore, the feasibility and the input‐to‐state practical stability (ISpS) of gradient and accumulation‐type event‐driven model predictive control are rigorously guaranteed theoretically. At last, the simulation results are provided to validate the this algorithm.

In the model predictive control (MPC) framework a controller is computed using a finite horizon optimal control cost. When linear constraints are imposed on the system with a quadratic cost function, then the MPC problem can be reformulated as a constrained quadratic programming (QP) problem. In this paper active set methods are used in order to solve the QP problem associated with MPC, and it is shown that it is possible to use information from the previous sample interval in order to provide improved initial conditions for the QP problem which is applied to the subsequent sample interval. Simulations show that when real-time considerations force the used of suboptimal intermediate control values, then improved initial conditions can allow for control values which are closer to the true optimal solution than obtained when using standard initial conditions. These ideas can allow for the implementation of MPC schemes on a greater number of real industrial applications, where standard MPC control cannot be applied due to the excessive CPU time requirements

The current control problem of permanent magnet synchronous machine (PMSM) drives is a challenging problem which has to deal with quadratic and linear constraints and tight time constraint. The goal of this paper is to provide a controller synthesis method that can deal with these challenges effectively by developing an explicit predictive current control of PMSM drives. The objective is to adjust the stator voltages in order to obtain fast and monotonic transient current response while fulfilling the physical and computational constraints at all times. To this end, using a nonlinear model of the electrical subsystem of the PMSM in the rotor reference frame, an explicit one-step ahead model predictive controller (MPC) based on control Lyapunov functions is developed. A polytopic approximation of the states and control inputs is used in order to reduce the computational complexity. Then, the resulting MPC problem is reduced to a linear program. Furthermore, a piecewise affine explicit controller is obtained via multi-parametric linear programming. Comparative simulation results with the classical PI approach are reported showing significant improvement.

In this paper we propose a stochastic model predictive control (MPC) formulation based on scenario generation for linear systems affected by discrete multiplicative disturbances. By separating the problems of (1) stochastic performance, and (2) stochastic stabilization and robust constraints fulfillment of the closed-loop system, we aim at obtaining a less conservative control action with respect to classical robust MPC schemes, still enforcing convergence and feasibility properties for the controlled system. Stochastic performance is addressed for very general classes of stochastic disturbance processes, although discretized in the probability space, by adopting ideas from multi-stage stochastic optimization. Stochastic stability and recursive feasibility are enforced through linear matrix inequality (LMI) problems, which are solved off-line; stochastic performance is optimized by an on-line MPC problem which is formulated as a convex quadratically constrained quadratic program (QCQP) and solved in a receding horizon fashion. The performance achieved by the proposed approach is shown in simulation and compared to the one obtained by standard robust and deterministic MPC schemes.

The paper considers formulations of constrained model predictive control (MPC) problems for systems with dynamics defined on smooth manifolds. Generalizations of conventional nonlinear MPC stabilization techniques based on the terminal set and terminal penalty approaches are presented based on recent work by the authors. The significance of the results includes the possibility of systematically generating globally stabilizing, discontinuous, time-invariant feedback laws in situations when smooth, or even continuous, globally stabilizing, time-invariant stabilizers do not exist. To illustrate the development of nonlinear MPC on manifolds, the paper considers an example of a system with dynamics evolving on SE(3). Such systems emerge in many applications, such as quadrotor and quadcopter flight control. In the example, the paper demonstrates semi-global stabilization properties of the nonlinear MPC feedback law.