A state-defect constraint pairing graph coarsening method is described for improving computational efficiency during the numerical factorization of large sparse Karush–Kuhn–Tucker matrices that arise from the discretization of optimal control problems via an Legendre–Gauss–Radau orthogonal collocation method. The method takes advantage of the particular sparse structure of the Karush–Kuhn–Tucke...

It is known that the optimal control may introduce significant economical benefits into production processes, thus being an important and challenging research area with practical relevance. The modeling and optimization of biotechnological processes has been object of research and their related results have generated improvements in operating conditions and strategies, however, the inherent fea...

A novel approach to solving the optimal nonlin-ear control problem is presented. Instead of seeking a global approximation to the Hamilton-Jacobi-Bellman equation, a local approximation is obtained by successively solving the Generalized Hamilton-Jacobi-Bellman (GHJB) equation on a local region of the state space. The optimal control is generated by solving the GHJB equation algebraically at se...

The paper proposed to use recurrent Fuzzy-Neural Multi-Model (FNMM) identifier for decentralized identification of a distributed parameter anaerobic wastewater treatment digestion bioprocess, carried out in a fixed bed and a recirculation tank. The distributed parameter analytical model of the digestion bioprocess is used as a plant data generator. It is reduced to a lumped system using the ort...

Two methods are presented for approximating the costate of optimal control problems in integral form using orthogonal collocation at Legendre–Gauss (LG) and Legendre–Gauss–Radau (LGR) points. It is shown that the derivative of the costate of the continuous-time optimal control problem is equal to the negative of the costate of the integral form of the continuous-time optimal control problem. Us...

In this paper, a simple transformation of coordinates is proposed that facilitates the efficient simulation of the non-isothermal lithium-ion pseudo 2-D battery model. The transformed model is then conveniently discretized using orthogonal collocation with the collocation points in the spatial direction. The resulting system of differential algebraic equations (DAEs) is solved using efficient a...

In this Paper, we have proposed a new weighted residual method known as orthogonal collocation-based on mixed interpolation (OCMI). Mixed interpolation uses the classical polynomial approximation with two correction terms given in the form of sine and cosine function. By these correction terms, we can control the error in the solution. We have applied this approach to a non-linear boundary valu...

The discovery of the catalytic synthesis of ammonia must rank as one of the important discoveries by mankind. In addition to providing the fertilizer needed to feed an expanding population, Fritz Haber’s recognition of recycle processing combined with the developing German technology to handle high pressures of hydrogen, led a major revolution in the chemical industry. In rapid succession, the ...

Fischer−Tropsch synthesis (FTS, CO + H 2 → long-chain hydrocarbons) for its great significance in the industry has attracted huge attention since discovery. For Fe-based catalysts, after decades of...