On the interplay between model uncertainty and data disturbances

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Finite-horizon min-max control of max-plus-linear systems

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The interaction between scheduling and control of semi-cyclic hybrid systems

\u3cp\u3eIn this paper a new iterative approach is proposed for the design of a combined real-time scheduling and control algorithm that can be applied to industrial systems that are described by a hybrid model with a (semi-)cyclic behavior. Traditionally scheduling and control problems are considered in a sequential way. First the scheduling problem is solved and subsequently the control problem. This may result in inconsistent solutions such that the system may not operate adequately and does not reach the desired operational targets. In our approach scheduling is done with model predictive control using a switching max-plus linear model of the discrete event part of the system. The interface with a reference generator determines whether the computed reference signal will lead to a feasible response. Furthermore, it estimates the duration of the operations in the system based on the actual state, and communicates that with the scheduler. In an iterative procedure the optimal and feasible schedule can be computed. In a case study the railway traffic on a single track is considered, showing that updating the schedule results in feasible local speed profiles for the trains and less delay in the overall system in case of a delay.\u3c/p\u3

Modeling and control of switching max-plus-linear systems with random and deterministic switching

Switching max-plus-linear (SMPL) systems are discrete-event systems that can switch between different modes of operation. In each mode the system is described by a max-plus-linear state equation and a max-plus-linear output equation, with different system matrices for each mode. The switching may depend on the inputs and the states, or it may be a stochastic process. In this paper two equivalent descriptions for switching max-plus-linear systems will be discussed. We will also show that a switching max-plus-linear system can be written as a piecewise affine system or as a constrained max-min-plus-scaling system. The last translation can be established under (rather mild) additional assumptions on the boundedness of the states and the inputs. We also develop a stabilizing model predictive controller for SMPL systems with deterministic and/or stochastic switching. In general, the optimization in the model predictive control approach then boils down to a nonlinear nonconvex optimization problem, where the cost criterion is piecewise polynomial on polyhedral sets and the inequality constraints are linear. However, in the case of stochastic switching that depends on the previous mode only, the resulting optimization problem can be solved using linear programming algorithms.Delft Center for Systems and ControlMechanical, Maritime and Materials Engineerin