The object of the study is a class of switched nonlinear systems with uncontrollable and unobservable linearized models, such as those arising in aerospace, power electronic, and robotics applications, where only output information is available for feedback. The problem to be solved is the global finite-time control for a class of high-order switched nonlinear time-delay systems via output feedback under arbitrary switching, where the powers and nonlinearities depend on the switching signal. First, using the adding-a-power-integrator technique, a homogeneous output-feedback controller is developed for the nominal part of the switched nonlinear system. Then, the constructed observer and controller are rescaled via the homogeneous domination approach and a common coordinate transformation is introduced to eliminate the dependence of the transformed dynamics on the switching signal. Together with an appropriately constructed Lyapunov-Krasovskii functional, this approach guarantees that the closed-loop switched high-order nonlinear system with time-varying delay is globally finite-time stable. The proposed framework simultaneously addresses switching-dependent nonlinearities, time-varying delays and output-feedback-based finite-time stabilization within a unified design, unlike existing results that handle these difficulties only separately. A numerical example demonstrates the effectiveness of the proposed controller and observer: the system states converge to zero in finite time, the control input remains bounded and the observer accurately reconstructs the unmeasured state despite the time-varying delays, confirming the practical applicability of the method to switched systems with output-only sensing and communication delays
K. Alimhan, Zhansaya Yergazy, A. Zhambulatova· Eastern-European Journal of...· 0 citations
A new method is presented for synthesising a control algorithm for second-order nonlinear dynamic systems based on the concept of fixed-time stabilisation with output feedback. The study focuses on a broad class of planar nonlinear systems for which full access to state variables is not possible. The proposed methodology is based on a combination of the theory of bi-limit homogeneity and the principles of classical Lyapunov stability analysis. This approach has enabled the development of a continuous observer with a fixed convergence time, which reliably estimates the unmeasurable state of the system regardless of initial conditions and initial estimation errors. Based on this estimation, a continuous controller is constructed that ensures system stabilisation within a predetermined time.
The method has a number of advantages: stability and convergence do not depend on the magnitude and sign of the initial conditions; control remains continuous, which eliminates oscillation of the actuators; high robustness to limited external disturbances and measurement noise is achieved. The algorithm can be implemented on microcontrollers without the need for high-frequency sampling, making it attractive for practical use. As an example, the dynamics of a microelectromechanical system (MEMS) mirror are considered, which is a striking example of a highly non-linear electromechanical object. Numerical simulations were carried out, the results of which confirm the effectiveness of the proposed control scheme. Compared to existing finite-time controllers, the transient response time is reduced by more than a factor of four, whilst the system error and energy consumption are reduced by almost half. The results obtained confirm the applicability of the developed method to high-precision control of micro- and macro-mechanical actuators, as well as in intelligent robotic and vibro-optical systems.
Zhansaya Yergazy, K. Alimhan, N. Mukatayev· Bulletin of Shakarim Univers...· 0 citations
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