SUMMARYThis paper exposes a methodology to solve state and input constrained optimal control problems for nonlinear systems. In the presented 'interior penalty' approach, constraints are penalized in a way that guarantees the strict interiority of the approaching solutions. This property allows one to invoke simple (without constraints) stationarity conditions to characterize the unknowns. A constructive choice for the penalty functions is exhibited. The property of interiority is established, and practical guidelines for implementation are given. A numerical benchmark example is given for illustration.
Abstract-The aim of this paper is to propose a robust and accurate method for the parametric identification of the thermal behaviour of low consumption buildings. These buildings are known to have a two-time scale structure, which, if not handled properly, results in poor conditioning of the parametric identification.We compare three identification methods, one uses the data on the whole frequency domain (ARX) when the other methods use the same data but separated on local frequency domain (time scaled methods).All three methods identify a reduced second order model. Robustness is tested by corrupting the input and output before the identification, and comparing the simulation results for the various models and the original uncorrupted input. The numerical results clearly show that the time scaled methods are superior both in accuracy (noise free identification and simulation) and robustness (when identification is performed on corrupted data).
International audienceThis paper addresses the problem of solving a constrained optimal control for a general single-input single output linear time varying system by means of an unconstrained method. The exposed methodology uses a penalty function approach, commonly considered in finite dimensional optimization problem, and extended here it to the considered infinite dimensional (functional optimization) case. The main novelty is that both the bounds on the control variable and on a freely chosen output variable are considered and studied theoretically. It is shown that a relatively simple and constructive choice of penalty functions allows to completely alleviate the usual difficulties of handling such constraints in optimal control. An illustrative example is provided to show the potential of the method
International audienceThis article proposes a distributed parameters model for a pool of electric hot water tanks (EHWT). EHWT are electric appliances found in numerous homes where they produce hot water for domestic usages. Designing smart piloting for them requires a careful description of several variables of interest and their dynamics. When the number of such devices is large, these dynamics can be lumped into Fokker-Planck equations. In this case, these equations are driven by in-domain control which defines the heating policies in a stochastic manner. The main contribution of this article is the Fokker-Planck model of a pool of EHWT
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