Abstract
The study focuses on a certain kind of discrete-continuous systems (DCS): the linear hybrid DCS with state-dependent coefficients. The authors proposed a problem similar to the analytical design of optimal controllers (ADOC). For this study, we generalized the Krotov sufficient optimality conditions. The paper includes several examples.
Highlights
This study focuses on a certain kind of discrete-continuous systems (DCS) linearly dependent on the state and control variables
This paper presents a model of a linear discrete-continuous system with state-dependent coefficients and defines a problem similar to the well-known analytical design of optimal controllers (ADOC)
By generalizing the Krotov sufficient optimality conditions, we proposed a solution algorithm that finds the first- and second-order Krotov function derivatives at both upper and lower levels
Summary
In some of the widely used control processes [1–7], the definitions of controlled differential or discrete systems change over time. The coefficient matrix elements of this DCS depend on the upper and lower level state variables. Such systems are the closest to the so-called weakly nonlinear systems [15–17]. We describe a model of a linear discrete-continuous system with state-dependent coefficients and formulate a problem similar to the well-known analytical design of optimal controllers (ADOC) [14]. We should find the vector-matrix system solution for both first- and second-order Krotov function derivatives at both levels with similar reasoning. In such systems, the coefficient matrices for the above-specified derivatives (just like in the original problem) depend on the state variables at the same levels.
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