Synthesis method of nonlinear quasi-optimal control laws for multidimensional systems based on the maximum condition of the generalized power function and the analysis of a beam of quadratic forms
Abstract:
The synthesis of the control law structure for multidimensional dynamic system according to a quadratic criterion based on the reduction of the Lagrange problem to an isoperimetric problem was carried out taking into account the analysis of a quadratic forms bundle, which ensures the fulfillment of transversality conditions. This makes it possible to take into account the dynamic properties of the controlled system when constructing quasi-optimal control. Indeterminate coupling multipliers of the second kind can be established as a result of using the principle of releasability, taking into account the property of Poisson brackets based on numerical modeling. The analysis of the modeling results of the control process of a dual pendulum shows that the developed quasi-optimal control law of a nonlinear dynamic system with several degrees of freedom results in a gain in terms of speed when improving the value of the quadratic criterion in comparison with the known control based on the principle of decomposition and the game approach.
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