Slow State Variables Feedback Stabilization for Semi-Markov Jump Systems With Singular Perturbations

2020

Summary In this paper, globally asymptotical stabilization problem for a class of planar switched nonlinear systems with an output constraint via smooth output feedback is investigated. To prevent output constraint violation, a common tangent‐type barrier Lyapunov function (tan‐BLF) is developed. Adding a power integrator approach (APIA) is revamped to systematically design state‐feedback stabilizing control laws incorporating the common tan‐BLF. Then, based on the designed state‐feedback controllers and a constructed common nonlinear observer, smooth output‐feedback controllers, which can make the system output meet the predefined constraint during operation, are proposed to deal with the globally asymptotical stabilization problem of planar switched nonlinear systems under arbitrary switchings. A numerical example is employed to verify the proposed method.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Output‐feedback stabilization for planar output‐constrained switched nonlinear systems

Lin

2020

“…Although many mathematical or engineering tools can be used for modeling, some discrepancies will always exist between the mathematical model used for describing the dynamic behaviors of a practical system and its actual plant. This is because these discrepancies are usually derived from some unknown external disturbances, parameter perturbations, or system uncertainties, which will heavily affect the performance of the considered system . To this end, designing a controller to provide the desired performance for the considered system is a very essential and challenging task.…”

Section: Introductionmentioning

confidence: 99%

A novel adaptive nonsingular terminal sliding mode controller design and its application to active front steering system

Ding

Liu

2019

Summary Note that the amplitude of chattering existing in the sliding mode control method is proportional to the magnitude of the control gain. Therefore, the key issue to diminish the chattering is to decrease the value of sliding mode controller's gain to an acceptable minimal level defined by the so‐called reaching condition for the sliding mode's existence. For this reason, the nonsingular terminal sliding mode (NTSM) control method and the adaptive technique have been considered in this paper to develop a novel adaptive NTSM control method, which can be used to search the minimal value of the control gain automatically in the presence of the external disturbances. Meanwhile, the average value of a high‐frequency switching signal in the adaptive law can be provided by Arie Levant's differentiator rather than a low‐pass filter. The rigorous mathematical proof verifies that the system states can converge to the origin within a finite time under the proposed adaptive NTSM controller. Both the academic example and the practical application to an active front steering system are illustrated to show that the presented adaptive NTSM controller has better control performance than the conventional sliding mode controller.

“…In addition, practical systems often experience abrupt variations, resulting from stochastic component failures, changes between subsystems, unexpected environment disturbances, and so on. The Markov jump was applied to model these complicated phenomena . Furthermore, in the process of implementation, information latching phenomenon occurs constantly in neural networks, which means that the network states have finite modes switching .…”

Section: Introductionmentioning

confidence: 99%

Event‐triggered dissipative synchronization for Markovian jump neural networks with general transition probabilities

Liu

Guo

et al. 2018

Summary In this paper, dissipative synchronization problem for the Markovian jump neural networks with time‐varying delay and general transition probabilities is investigated. An event‐triggered communication scheme is introduced to trigger the transmission only when the variation of the sampled vector exceeds a prescribed threshold condition. The transition probabilities of the Markovian jump delayed neural networks are allowed to be known, or uncertain, or unknown. By employing delay system approach, a new model of synchronization error system is proposed. Applying the Lyapunov‐Krasovskii functional and integral inequality combining with reciprocal convex technique, a delay‐dependent criterion is developed to guarantee the stochastic stability of the errors system and achieve strict (Q,S,R)−α dissipativity. The event‐triggered parameters can be derived by solving a set of linear matrix inequalities. A numerical example is presented to illustrate the effectiveness of the proposed design method.