Uncertainties exist at all levels of the industrial design and manufacturing. Hitherto, all the studies that handle multi-parametric programming (mp-LP, mp-QP, mp-NLP, mp-MILP, and mp-MINLP) treat uncertainties to be ...
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ISBN:
(纸本)9783319083773;9783319083766
Uncertainties exist at all levels of the industrial design and manufacturing. Hitherto, all the studies that handle multi-parametric programming (mp-LP, mp-QP, mp-NLP, mp-MILP, and mp-MINLP) treat uncertainties to be independent of each other;while under some circumstances, there might exist some kinds of quantitative relationship among them. There is still a lack of research studies on the relationship between these uncertainties, which can help simply the complexity of multi-parametric optimization problems in terms of reducing the dimension of uncertainty space or the region of uncertainty space. This paper presents multiple types of relationships among uncertainty parameters, which can be generalized into two categories: strong relationship and weak relationship. The strong relationship can be used to reduce the dimension of uncertainty space while the weak relationship can be used to reduce the region of uncertainty space. With the combination of the above relationships, different kinds of multi-parametric programming problems can be solved more efficiently and effectively toward global optimality.
In this paper, we outline the foundations of a general global optimisation strategy for the solution of multilevel hierarchical and general decentralised multilevel problems, based on our recent developments on multi-...
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In this paper, we outline the foundations of a general global optimisation strategy for the solution of multilevel hierarchical and general decentralised multilevel problems, based on our recent developments on multi-parametric programming and control theory. The core idea is to recast each optimisation subproblem, present in the hierarchy, as a multi-parametric programming problem, with parameters being the optimisation variables belonging to the remaining subproblems. This then transforms the multilevel problem into single-level linear/convex optimisation problems. For decentralised systems, where more than one optimisation problem is present at each level of the hierarchy, Nash equilibrium is considered. A three person dynamic optimisation problem is presented to illustrate the mathematical developments.
With the rapid growth of distributed energy resource integration, the power system is facing increased challenge of operation security. Demand response, as an underutilized resource, has shown great potential to suppo...
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ISBN:
(纸本)9781728131030
With the rapid growth of distributed energy resource integration, the power system is facing increased challenge of operation security. Demand response, as an underutilized resource, has shown great potential to support system security. This paper proposes a novel scheme to integrate heterogeneous demand side resources in the N-1 security assessment, which contains two steps: demand feature compression and joint scheduling with demand response. The general control model is formulated by multi-parametric programming to analyze various demand response resources and eliminate the privacy concerns. Cases studies validate the efficiency of proposed method, showing the underlying benefit of demand side participation.
The energy storage unit (ESU) is helpful for shaving the peak and filling the valley demands, as well as compensating the volatility of renewable generation. The performance mainly depends on the maximum charging/disc...
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ISBN:
(纸本)9789881563903
The energy storage unit (ESU) is helpful for shaving the peak and filling the valley demands, as well as compensating the volatility of renewable generation. The performance mainly depends on the maximum charging/discharging power (in MW) and energy capacity (in MWh). This paper proposes a multi-parametric linear programming model to investigate and describe the impact of MW/MWh parameters of the energy storage unit on the economic operation of bulk power systems in a geometric manner. By employing duality theory, the optimal value function of the economic dispatch problem is approximated via piecewise linear functions which are convenient for visualization. The optimal value function delivers useful information on energy storage sizing subject to a given budget, which is elaborated as an application of the proposed method. The effectiveness of the model and method is validated via a modified IEEE 39-bus system.
In this work, we demonstrate how constrained Moving Horizon Estimation (MHE) and Model Predictive Control (MPC) can be simultaneously addressed via multi-parametric programming. First, we present a method for obtainin...
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ISBN:
(纸本)9781424477463
In this work, we demonstrate how constrained Moving Horizon Estimation (MHE) and Model Predictive Control (MPC) can be simultaneously addressed via multi-parametric programming. First, we present a method for obtaining the error dynamics of constrained MHE for linear, time-invariant systems by solving the constrained optimization problem of the MHE by multi-parametric programming methods. Set-theoretical methods are then used to derive bounds on the estimation error - it is shown that the estimation error is bounded in an invariant set for the error dynamics described by a set of linear inequalities. The error dynamics and the error bounds can then be used for the design of a robust output feedback explicit/multi-parametric MPC yielding a simultaneous estimation and control design which is illustrated with an example of robust tube-based MPC.
An off-line controller design method of a tension and looper system is derived based on hybrid systems approach. By employing a multiparametricprogramming method, a nonlinear feedback control law, which is equivalent...
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An off-line controller design method of a tension and looper system is derived based on hybrid systems approach. By employing a multiparametricprogramming method, a nonlinear feedback control law, which is equivalent to the model predictive control, is constructively given. The feature of resulting control system is illustrated with numerical example.
Motivated by explicit model predictive control, we address infeasibility in multi-parametric quadratic programming according to the exact penalty function approach, where some user-chosen parameter dependent constrain...
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Motivated by explicit model predictive control, we address infeasibility in multi-parametric quadratic programming according to the exact penalty function approach, where some user-chosen parameter dependent constraints are relaxed and the 1-norm of their violation is penalized in the cost function. We characterize the relation between the resulting multi-parametric quadratic program and the original one and show that, as the penalty coefficient grows to infinity, the solution to the former provides a piecewise affine continuous function, which is an optimal solution for the latter over the feasibility region, while it minimizes the 1-norm of the relaxed constraints violation over the infeasibility region.& COPY;2023 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).
In this paper we address the slotting problem for metal interconnections in integrated circuit automation design for high current conducting metal layers. We show how to design a slotting approach by means of multi-pa...
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In this paper we address the slotting problem for metal interconnections in integrated circuit automation design for high current conducting metal layers. We show how to design a slotting approach by means of multi-parametric programming. We present a definition of optimization problem for convex shapes of metal layers. Constraints of the problem will reflect restrictions of the production technology and a solution will avoid usage of a commercial optimization solver on a user's side. We will present the approach on an application for generating a power transistor. The approach is applied for specific very-large-scale integration (VLSI) production technology. The solution exhibits simple implementation and gives results in an acceptable response time.
multi-parametric programming has proven to be an invaluable tool for optimisation under uncertainty. Despite the theoretical developments in this area, the ability to handle uncertain parameters on the left-hand side ...
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multi-parametric programming has proven to be an invaluable tool for optimisation under uncertainty. Despite the theoretical developments in this area, the ability to handle uncertain parameters on the left-hand side remains limited and as a result, hybrid, or approximate solution strategies have been proposed in the literature. In this work, a new algorithm is introduced for the exact solution of multi-parametric linear programming problems with simultaneous variations in the objective function's coefficients, the right-hand side and the left-hand side of the constraints. The proposed methodology is based on the analytical solution of the system of equations derived from the first order Karush-Kuhn-Tucker conditions for general linear programming problems using symbolic manipulation. Emphasis is given on the ability of the proposed methodology to handle efficiently the LHS uncertainty by computing exactly the corresponding nonconvex critical regions while numerical studies underline further the advantages of the proposed methodology, when compared to existing algorithms. (C) 2017 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers.
The energy storage unit（ESU） is helpful for shaving the peak and filling the valley demands, as well as compensating the volatility of renewable generation. The performance mainly depends on the maximum charging/dis...
详细信息
The energy storage unit（ESU） is helpful for shaving the peak and filling the valley demands, as well as compensating the volatility of renewable generation. The performance mainly depends on the maximum charging/discharging power（in MW）and energy capacity（in MWh）. This paper proposes a multi-parametric linear programming model to investigate and describe the impact of MW/MWh parameters of the energy storage unit on the economic operation of bulk power systems in a geometric manner. By employing duality theory, the optimal value function of the economic dispatch problem is approximated via piecewise linear functions which are convenient for visualization. The optimal value function delivers useful information on energy storage sizing subject to a given budget, which is elaborated as an application of the proposed method. The effectiveness of the model and method is validated via a modified IEEE 39-bus system.
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