A strategy that calculates an explicit state feedback policy to regulate constrained uncertain discrete-time uncertain linear systems is presented. We consider uncertain processes, affected by box-bounded multiplicati...
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A strategy that calculates an explicit state feedback policy to regulate constrained uncertain discrete-time uncertain linear systems is presented. We consider uncertain processes, affected by box-bounded multiplicative uncertainty as well as bounded additive uncertainty with linear state and inputs constraints. The proposed method includes (i) the calculation of a terminal set constraint and (ii) the robust reformulation of state constraints in the prediction horizon. These features allow the derivation of the desired policy by solving a single multiparametric quadratic programming problem that guarantees feasible operation in the presence of uncertainty. Additionally, we employ variable and constraint elimination approaches to enhance the computational performance of the strategy. We demonstrate the steps and benefits of these developments with a numerical example and a chemical engineering case study.
This paper describes a set of mathematical formulations designed to include uncertainties modeled by fuzzy numbers in DC OPF studies. These approaches enhance and generalize an initial formulation and solution algorit...
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This paper describes a set of mathematical formulations designed to include uncertainties modeled by fuzzy numbers in DC OPF studies. These approaches enhance and generalize an initial formulation and solution algorithm described in several papers co-authored by the second author. The approaches described in this paper adopt multiparametric optimization techniques in order to translate to the results the uncertainties affecting loads, for one side, the generation costs, for another, and also both of them in a simultaneous way. These approaches can be very useful nowadays given the uncertainties and volatility affecting data required to run several studies. They can also be the basis for the computation of nodal short time marginal prices reflecting these uncertainties. This paper also includes results obtained from a Case Study based on the IEEE 24 bus test system.
Explicit Model Predictive Control (MPC) of highly interacting systems using multiparametric programming is challenging as the offline solution to the Optimal Control Problem (OCP) typically entails calculation of a la...
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Explicit Model Predictive Control (MPC) of highly interacting systems using multiparametric programming is challenging as the offline solution to the Optimal Control Problem (OCP) typically entails calculation of a large number of regions of the uncertainty space. This can result in the case in which the point location problem is computationally more expensive than solving the OCP online. Hence, in this paper, with an aim to reduce computational costs of explicit MPC, we reformulate the OCP and study the computational and control performance of the reformulated explicit MPC compared to the conventional explicit MPC. As a case study, we consider a highly interacting quadruple tank process. The closed-loop simulation results show that between conventional MPC and reformulated MPC, in the online case, the total computational times are comparable, whereas in the explicit MPC case, the reformulation results in significant reduction in the total computational time by 44%.
A modification of the geometric algorithm for solving multiparametric linear programs (mp-LP) is presented. The modification preserves the simplicity of the algorithm and ensures that the optimal, piecewise affine, ma...
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A modification of the geometric algorithm for solving multiparametric linear programs (mp-LP) is presented. The modification preserves the simplicity of the algorithm and ensures that the optimal, piecewise affine, mapping from parameter to solution space is continuous. When the mp-LP has non-unique solutions, the optimizer with the least Euclidian norm is selected.
Model predictive control (MPC) represents an optimal strategy where constraints on inputs, outputs and system states can be implemented as part of the control law that takes the form of a mathematical program. MPC of ...
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Model predictive control (MPC) represents an optimal strategy where constraints on inputs, outputs and system states can be implemented as part of the control law that takes the form of a mathematical program. MPC of linear systems with a quadratic objective function results in a quadratic program (QP) that needs to be solved online at each sampling instant. multiparametric programming methods that attempt an explicit solution to QPs have been successfully used in context of MPC and is termed as explicit MPC (eMPC). eMPC for linear systems results in a piecewise affine-in-state feedback control law and is determined offline. During online implementation, the control law is selected from among the different pieces based on the real-time value of the states. An ability to verify the controller output over all possible state realizations of the feasible state-space is important in any critical application including health and aerospace and is a unique feature of eMPC. Since state feedback MPC requires full state information, it is always used in conjunction with a state estimator such as a Kalman Filter. Further, fault tolerant control methodologies depend on state and parameter estimation to detect and diagnose faults followed by compensation. Conventionally, the state filtering step is performed prior to MPC and thus the interaction between the estimator and controller remains hidden and can be analyzed only via numerical simulations. In this work, we propose using multiparametric programming to find the explicit solution of the joint estimator-MPC problem. In particular, the eMPC control law now depends linearly on the joint information of states and measurements. This allows explicitly obtaining the sensitivity of the MPC control law to the measurement as well as the estimator parameters. The proposed explicit solution of the joint estimator-MPC problem is demonstrated on a SISO 2-tank system. The effect of the estimator gain on the size of the feasible region is d
Modeling uncertainties in power systems has long interested researchers. Nowadays, as in 70's, the volatility associated with generation or fuel prices, for one side, and the uncertainties related with load foreca...
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Modeling uncertainties in power systems has long interested researchers. Nowadays, as in 70's, the volatility associated with generation or fuel prices, for one side, and the uncertainties related with load forecasting and generation capacity, for another, places a new emphasis on this kind of problems. As a result of this renewed interest, in this paper we are enlarging the original Fuzzy Optimal Power Flow, FOPF, model in order to consider not only load uncertainties, but also uncertainties in generation or fuel prices, specified using trapezoidal fuzzy numbers. This new approach is based on multiparametric linear programming techniques that lead to the identification of a number of critical regions covering all the uncertainty space. This contributes to build more accurate membership functions of all variables, namely generations, branch flows and power not supplied.
The hierarchical decision making in process industries has been traditionally viewed as having a common objective, such as the overall cost, which needs to be optimized. However, a more appropriate approach is to form...
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The hierarchical decision making in process industries has been traditionally viewed as having a common objective, such as the overall cost, which needs to be optimized. However, a more appropriate approach is to formulate and solve hierarchical optimization and control problems. The solution algorithms for hierarchical optimization problems have been reported in the literature. The idea is to recast each optimization sub-problem in the hierarchy into a multiparametric programming problem, considering the variables of upper-level problems as unknown parameters. In this paper, explicit Model Predictive Control (MPC) and hierarchical optimization techniques, employing multiparametric programming, are combined for hierarchical MPC. The solution algorithm for hierarchical MPC is described in detail. Note that the solution to a hierarchical MPC problem is challenging, even for the simplest case of linear-quadratic objectives. Closed-loop simulations of a thermal mixing process, under two different hierarchical MPC formulations, are performed and the control performance is studied.
This paper describes a set of mathematical formulations designed to include uncertainties modeled by fuzzy numbers in DC OPF studies. These approaches enhance and generalize an initial formulation and solution algorit...
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ISBN:
(纸本)9781627483889
This paper describes a set of mathematical formulations designed to include uncertainties modeled by fuzzy numbers in DC OPF studies. These approaches enhance and generalize an initial formulation and solution algorithm described in several papers co-authored by the second author. The approaches described in this paper adopt multiparametric optimization techniques in order to translate to the results the uncertainties affecting loads, for one side, the generation costs, for another, and also both of them in a simultaneous way. These approaches can be very useful nowadays given the uncertainties and volatility affecting data required to run several studies. They can also be the basis for the computation of nodal short time marginal prices reflecting these uncertainties. This paper also includes results obtained from a Case Study based on the IEEE 24 bus test system.
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