Ton J. J. van den Boom

Properties of MPC for Max-Plus-Linear Systems

Model predictive control (MPC) is a very popular controller design method in the process industry. One of the main advantages of MPC is that it can handle constraints on the inputs and outputs. Usually MPC uses linear discrete-time models. Recently, we have extended this framework to max-plus-linear discrete event systems. In this paper, we further explore this topic. More specifically, we focus on implementation and timing aspects, closed-loop behavior and tuning rules for model predictive control of max-plus-linear (MPL) systems.

Brief Optimizing the end-point state-weighting matrix in model-based predictive control

In this paper a linear model-based predictive control (MPC) algorithm is presented, for which nominal closed-loop stability is guaranteed. The input is obtained by minimizing a quadratic performance index over a finite horizon plus an end-point state (EPS) penalty, subject to input, state and output constraints. Under certain conditions, the weighting matrix in the EPS penalty enables one to specify an invariant ellipsoid in which the input, state and output constraints are satisfied. In existing MPC algorithms this weighting matrix is calculated off-line. The main contribution of this paper is to incorporate the calculation of the EPS-weighting matrix into the on-line optimization problem of the controller. The main advantage of this approach is that a natural and automatic trade-off between feasibility and optimality is obtained. This is demonstrated in a simulation example.

A survey on optimal trajectory planning for train operations

Because of the rising energy prices and environmental concerns, the calculation of energy-optimal reference trajectories for trains is significant for energy saving. On the other hand, with the development automatic train operation (ATO), the optimal trajectory planning is significant to the performance of train operation. In this paper, we present an integrated survey of this field. First, a nonlinear continuous-time train model and a continuous-space model of train operations are described, after which the optimal trajectory planning problem is formulated based on these two models. The various approaches in the literature to calculate the reference trajectory are reviewed and categorized into two groups: analytical solutions and numerical optimization. Finally, a short discussion of some open topics in the field of optimal trajectory planning for train operations are given.

Predictive control based on neural network models with I/O feedback linearization

This paper presents an approach for the constrained non-linear predictive control problem based on the input-output feedback linearization (IOFL) of a general non-linear system modelled by a discrete-time affine neural network model. Using the resulting linear system in the formulation of the original non-linear predictive control problem enables to restate the optimization problem as the minimization of a quadratic function, which solution can be found using reliable and fast quadratic programming (QP) routines. However, the presence of a non-linear feedback linearizing controller maps the original linear input constraints onto non-linear and state dependent constraints on the controller output, which invalidates a direct application of QP routines. In order to cope with this problem and still be able to use QP routines, an approximate method is proposed which simultaneously guarantees a feasible solution without constraints violation over the complete prediction horizon within a finite number of steps, ...

Brief paper: Input signal design for identification of max-plus-linear systems

The present contribution addresses the problem of designing an adequate persistent excitation for state space identification of max-plus-linear systems. The persistent excitation is designed using the same techniques that have recently been developed for model predictive control for max-plus-linear systems. The application of this method for input signal design allows to incorporate additional objectives which are desirable for the input signals and the resulting process behaviour such that an optimal persistent excitation is obtained.

Efficient Bilevel Approach for Urban Rail Transit Operation With Stop-Skipping

The train scheduling problem for urban rail transit systems is considered with the aim of minimizing the total travel time of passengers and the energy consumption of the trains. We adopt a model-based approach, where the model includes the operation of trains at the terminus and at the stations. In order to adapt the train schedule to the origin-destination-dependent passenger demand in the urban rail transit system, a stop-skipping strategy is adopted to reduce the passenger travel time and the energy consumption. An efficient bilevel optimization approach is proposed to solve this train scheduling problem, which actually is a mixed-integer nonlinear programming problem. The performance of the new efficient bilevel approach is compared with the existing bilevel approach. In addition, we also compare the stop-skipping strategy with the all-stop strategy. The comparison is performed through a case study inspired by real data from the Beijing Yizhuang line. The simulation results show that the efficient bilevel approach and the existing bilevel approach have a similar performance but the computation time of the efficient bilevel approach is around one magnitude smaller than that of the bilevel approach.

Model Predictive Control for Max-Min-Plus Systems

Model predictive control (MPC) is a widely used control design method in the process industry. Its main advantage is that it allows the inclusion of constraints on the inputs and outputs. Usually MPC uses linear discrete-time models. We extend MPC to max-min-plus discrete event systems. In general the resulting optimization problems are nonlinear and nonconvex. However, if the state equations are decoupled and if the control objective and the constraints depend monotonically on the states and outputs of system, the max-min-plus-algebraic MPC problem can be recast as problem with a convex feasible set. If in addition the objective function is convex, this leads to a convex optimization problem, which can be solved very efficiently.

Optimal trajectory planning for trains using mixed integer linear programming

The optimal trajectory planning for trains under constraints and fixed maximal arrival time is considered. The variable line resistance (including variable grade profile, tunnels, and curves) and arbitrary speed restrictions are included in this approach. The objective function is a trade-off between the energy consumption and the riding comfort. First, the nonlinear train model is approximated by a piece-wise affine model. Next, the optimal control problem is formulated as a mixed integer linear programming (MILP) problem, which can be solved efficiently by existing solvers. The good performance of this approach is demonstrated via a case study.

Robust stability of feedback linearised systems modelled with neural networks: dealing with uncertainty

Abstract This paper presents a systematic procedure to analyse the stability robustness to modelling errors when a neural network model is integrated in an approximate feedback linearisation control scheme. The propagation through the control loop of the structured uncertainty from the neural network model parameters enables the construction of a polytopic uncertainty description for the overall linear closed-loop system. By using computationally efficient algorithms the solution of a set of linear matrix inequalities provides a Lyapunov function for the uncertain system, therefore proving robust stability of the overall control system. A nonlinear multivariable water vessel system is chosen as the case study for the application of this control strategy.

Constrained Nonlinear Predictive Control Based on Input-Output Linearization Using a Neural Network

Abstract Affine neural network models can be used as good aproximators of the dynamics of a nonlinear process, and are easily included in a input-output feedback linearization (IOFL) scheme. This paper proposes a new solution for solving a constrained optimization problem using IOFL imbedded in a predictive control scheme. The linearization of the nonlinear feedback law over the entire prediction horizon, enables an optimal solution to be found by solving a general quadratic programming problem. The procedure here presented also guarantees convergenceto a feasible solution without constraint violation.