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This paper describes structured neural models and a computationally efficient (suboptimal) nonlinear Model Predictive Control (MPC) algorithm based on such models. The structured neural model has the ability to make future predictions of the process without being used recursively. Thanks to the nature of the model, the prediction error is not propagated. This is particularly important in the case of noise and underparameterisation. Structured models have much better long-range prediction accuracy...
We study the boundary controllability of a nonlinear Korteweg–de Vries equation with the Dirichlet boundary condition on an interval with a critical length for which it has been shown by Rosier that the linearized control system around the origin is not controllable. We prove that the nonlinear term gives the local controllability around the origin.
We consider the Cauchy problem in ℝd for a class of
semilinear parabolic partial differential equations that arises in some stochastic control
problems. We assume that the coefficients are unbounded and locally Lipschitz, not
necessarily differentiable, with continuous data and local uniform ellipticity. We
construct a classical solution by approximation with linear parabolic equations. The
linear equations involved can not be solved with the traditional...
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