Synthesis of the Control System for a Second Order Non-Linear Object with an Incomplete Description

Synthesis of a robust stochastic regulator for the model of electrohydraulic brake system

“…Let us formulate the following requirements [4]- [7] to the initial description and the necessary a priori information for applying the procedure of synthesizing an ADAR-control: а) initial mathematical description of the control object is given by a system of ordinary differential equations or a system of difference equations for continuous and discrete control problems, respectively; b) availability of a globally stable target system for initial model, which satisfies the target analytically set invariant = 0 , → ∞ , where ∈ , is the continuously differentiated function, ∈ , ≥ ; c) boundedness of all solutions of the initial system; d) stabilizability of all object's trajectories in the neighborhood of = 0; e) implementation of the control system synthesis in the state space in the absence of any restrictions on the controls linearly included into the right-hand parts of the object's descriptions.…”

“…The article presents two algorithms for designing control in the state space of the unstable object with a different physical nature of disturbances. Let us name them conditionally NAD (Nonlinear ADaptation algorithm for a nonrandom object [7]- [9]) and NAS (Nonlinear Adaptation algorithm for a Stochastic object [10]). Note that both algorithms are correct extensions of the classic ADAR-algorithm [7], [10] (see Appendix A1).…”

“…Let us name them conditionally NAD (Nonlinear ADaptation algorithm for a nonrandom object [7]- [9]) and NAS (Nonlinear Adaptation algorithm for a Stochastic object [10]). Note that both algorithms are correct extensions of the classic ADAR-algorithm [7], [10] (see Appendix A1).…”

“…It is well known that the use of the ADAR-synthesis guarantees robust properties to the designed regulator, ensuring a suppression of the external and parametric disturbances. Given this, the disturbances can be modeled as piecewise-constant functions in the differential equations of the object, which include controls, and the system of equation is supplemented with the integrator equations [7], [9].…”

“…Proof of Statement 1 is constructive and immediate from the NAD-algorithm of control system synthesis for Eq. (1) (see, e.g., [7]).…”