Energy management in buildings is addressed in this paper. The energetic impact of buildings in the current energetic context is first depicted. Then the studied optimization problem is defined as the optimal manageme...
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Energy management in buildings is addressed in this paper. The energetic impact of buildings in the current energetic context is first depicted. Then the studied optimization problem is defined as the optimal management of production and consumption activities in houses. A scheduling problem is identified to adjust the energy consumption to both the energy cost and the inhabitant's comfort. The available flexibilities of the services provided by domestic appliances are used to compute optimal energy plans. These flexibilities are associated to time windows or heating storage abilities. A constraints formulation of the energy allocation problem is given. A derived mixed linear program is used to solve this problem. The energy consumption in houses is very dependent to uncertain data such as weather forecasts and inhabitants' activities. Parametric uncertainties are introduced in the home energy management problem in order to provide robust energy allocation. robust linear programming is implemented. Event related uncertainties are also addressed through stochastic programming in order to take into account the inhabitant's activities. A scenario based approach is implemented to face this robust optimization problem.
We investigate here the class-denoted R-LP-RHSU-of two-stage robust linear programming problems with right-hand-side uncertainty. Such problems arise in many applications e.g: robust PERT scheduling (with uncertain ta...
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We investigate here the class-denoted R-LP-RHSU-of two-stage robust linear programming problems with right-hand-side uncertainty. Such problems arise in many applications e.g: robust PERT scheduling (with uncertain task durations);robust maximum flow (with uncertain arc capacities);robust network capacity expansion problems;robust inventory management;some robust production planning problems in the context of power production/distribution systems. It is shown that such problems can be formulated as large scale linear programs with associated nonconvex separation subproblem. A formal proof of strong NP-hardness for the general case is then provided, and polynomially solvable subclasses are exhibited. Differences with other previously described robust LP problems (featuring row-wise uncertainty instead of column wise uncertainty) are highlighted.
作者：
Briat, CorentinKTH
ACCESS Linnaeus Ctr Div Optimizat & Syst Theory SE-10044 Stockholm Sweden
Copositive Lyapunov functions are used along with dissipativity theory for stability analysis of uncertain linear positive systems. At the difference of standard results, linear supply-rates are employed for robustnes...
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ISBN:
(纸本)9781612848013
Copositive Lyapunov functions are used along with dissipativity theory for stability analysis of uncertain linear positive systems. At the difference of standard results, linear supply-rates are employed for robustness and performance analysis and lead to L-1- and L-infinity-gain characterizations. This naturally guides to the definition of Integral linear Constraints (ILCs) for the characterization of input-output nonnegative uncertainties. It turns out that these integral linear constraints can be linked to the Laplace domain, in order to be tuned adequately, by exploiting the L-1-norm and input/output signals properties. This dual viewpoint allows to prove that the static-gain of the uncertainties, only, is critical for stability. This fact provides a new explanation for the surprising stability properties of linear positive time-delay systems. The obtained stability and performance analysis conditions are expressed in terms of (robust) linearprogramming problems that are transformed into finite dimensional ones using the Handelman's Theorem. Several examples are provided for illustration.
Copositive Lyapunov functions are used along with dissipativity theory for stability analysis of uncertain linear positive systems. At the difference of standard results, linear supply-rates are employed for robustnes...
详细信息
ISBN:
(纸本)9781612848006
Copositive Lyapunov functions are used along with dissipativity theory for stability analysis of uncertain linear positive systems. At the difference of standard results, linear supply-rates are employed for robustness and performance analysis and lead to L_(1)- and L_(infinity)-gain characterizations. This naturally guides to the definition of Integral linear Constraints (ILCs) for the characterization of input-output nonnegative uncertainties. It turns out that these integral linear constraints can be linked to the Laplace domain, in order to be tuned adequately, by exploiting the L_(1)-norm and input/output signals properties. This dual viewpoint allows to prove that the static-gain of the uncertainties, only, is critical for stability. This fact provides a new explanation for the surprising stability properties of linear positive time-delay systems. The obtained stability and performance analysis conditions are expressed in terms of (robust) linearprogramming problems that are transformed into finite dimensional ones using the Handelman's Theorem. Several examples are provided for illustration.
We show that the celebrated Farkas lemma for linear inequality systems continues to hold for separable sublinear inequality systems. As a consequence, we establish a qualification-free characterization of optimality f...
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We show that the celebrated Farkas lemma for linear inequality systems continues to hold for separable sublinear inequality systems. As a consequence, we establish a qualification-free characterization of optimality for separable sublinearprogramming problems which include classes of robust linear programming problems. We also deduce that the Lagrangian duality always holds for these programming problems without qualifications.
The optimal solution of a geometric program (GP) can be sensitive to variations in the problem data. robust geometric programming can systematically alleviate the sensitivity problem by explicitly incorporating a mode...
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The optimal solution of a geometric program (GP) can be sensitive to variations in the problem data. robust geometric programming can systematically alleviate the sensitivity problem by explicitly incorporating a model of data uncertainty in a GP and optimizing for the worst-case scenario under this model. However, it is not known whether a general robust GP can be reformulated as a tractable optimization problem that interior-point or other algorithms can efficiently solve. In this paper we propose an approximation method that seeks a compromise between solution accuracy and computational efficiency. The method is based on approximating the robust GP as a robustlinear program (LP), by replacing each nonlinear constraint function with a piecewise-linear (PWL) convex approximation. With a polyhedral or ellipsoidal description of the uncertain data, the resulting robust LP can be formulated as a standard convex optimization problem that interior-point methods can solve. The drawback of this basic method is that the number of terms in the PWL approximations required to obtain an acceptable approximation error can be very large. To overcome the "curse of dimensionality" that arises in directly approximating the nonlinear constraint functions in the original robust GP, we form a conservative approximation of the original robust GP, which contains only bivariate constraint functions. We show how to find globally optimal PWL approximations of these bivariate constraint functions.
Motivated by a robust positive real synthesis problem, we consider robust linear programming problems with the main goal of verifying whether the computed solution of a particular LMI relaxation is exact. It it shown ...
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Motivated by a robust positive real synthesis problem, we consider robust linear programming problems with the main goal of verifying whether the computed solution of a particular LMI relaxation is exact. It it shown that this requires to solve a polynomial system of equations. The main contribution of this paper is an algorithm to solve polynomial systems. Contrary to existing approaches, we suggest a technique which does not require the computation of a Gröbner basis of the ideal generated by the polynomials that define the equations.
An optimum downlink power control that maximizes the user-capacity of a Direct Sequence-Code Division Multiple Access (DS-CDMA) cellular system is proposed based on a convex programming method. First, the downlink bea...
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An optimum downlink power control that maximizes the user-capacity of a Direct Sequence-Code Division Multiple Access (DS-CDMA) cellular system is proposed based on a convex programming method. First, the downlink beamforming weights for the base-station antenna-array are designed based on the maximum Signal-Interference-Ratio (SIR) criterion. Then by optimizing the downlink power subject to a fixed total transmit power constraint, we further increase the Signal-Interference-Noise-Ratio (SINR) at the mobile terminal, thus increasing the capacity of the system. With the same methodology, we can also minimize the required transmit power while satisfying the SINR threshold constraints. Additionally, a robust downlink power control approach for mitigating the performance degradation due to channel estimates error is also proposed. Computer simulations are given to demonstrate the improvement of downlink capacity, received SINR, robustness, and the minimization of the required transmit power for a DS-CDMA system with antenna-array at the base-station.
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