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In this article, the prescribed‐time global stabilization problem is taken into consideration when it comes to multi‐input‐multi‐output (MIMO) systems with unknown mismatched coupling nonlinear items. It is assumed that the unknown nonlinearities satisfy the linear growth conditions. First, a class of MIMO coupling nonlinear systems with controllable canonical form are considered. Then, by wielding a time‐varying Lyapunov‐like function and properties of parametric Lyapunov equations, a high‐gain linear time‐varying state feedback control law is developed to attenuate the impact of unknown nonlinear terms. Meanwhile, all state signals and control inputs are globally bounded and the target system becomes stable within the prescribed‐time. Finally, the simulation results on an example system with 3 inputs and 11 state variables verify that the developed control mechanism accomplishes the goal of global stabilization in the pre‐defined time. [ABSTRACT FROM AUTHOR]

Summary: In this article, the problem of finite‐time attitude‐tracking control for rigid spacecraft is addressed. Uncertainties caused by external disturbances, unknown inertial matrix, actuator failures, and saturation constraints are tackled simultaneously. First, a smooth function that is more qualified to approximate the standard saturation characteristics is presented to deal with the actuator saturation constraints. Second, a fast nonsingular terminal sliding mode (FNTSM) manifold is constructed as a foundation of controllers design. By incorporating the fuzzy logic system into FNTSM technique, a less demanding solution of coping with model uncertainties is provided because the requirement of a prior knowledge of unknown inertial parameters and external disturbances in many existing achievements is removed. To reduce the number of parameters to be estimated, the norm approximation approach is exploited. Subsequently, an antichattering attitude controller is presented such that all the tracking errors converge into arbitrary small domains around the origin in finite time. The result is further extended to obtain a fault‐tolerant controller against completely failed actuators. Finally, numerical simulation is conducted to verify the effectiveness of the proposed control scheme and comparison with relevant literature demonstrates its high performance. Furthermore, an experiment for the large satellite Hubble Space Telescope is carried out to validate the practical feasibility. [ABSTRACT FROM AUTHOR]

SUMMARY A new adaptive controller is designed on the basis of dynamic scaling and filter for lower triangular systems. Compared with the available adaptive results in the literature, the proposed adaptive approach does not necessarily need to satisfy the certainty equivalence principle and allows for prescribed dynamics to be assigned to the parameter estimation error. The proposed adaptive state feedback controller that ensures all signals of closed-loop systems are globally bounded while keeping the output tracking error to the origin simultaneously. It is interesting to note that, viewed from a Lyapunov perspective, the proposed method provides a procedure to add cross terms between the parameter estimates and the system states in every design step. Finally, two comparatively simulation examples are given, highlighting the advantages of the proposed methodology. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This paper poses and solves a new problem of state feedback stabilization for a class of high-order stochastic nonlinear systems in which the power order restriction and growth condition are relaxed to a more general form. Based on the ideas of the homogeneous systems theory and the adding of a power integrator technique, a state feedback controller is constructed to ensure that the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability and that the problem of inverse optimal stabilization in probability is solved. The efficiency of the state feedback controller is demonstrated by a simulation example. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is concerned with the design of positive L1$$ {L}_1 $$ filter for positive Markovian jump systems (PMJSs) with adaptive event‐triggered mechanism and quantization. Considering the mode jump of the system, a new adaptive event‐triggered condition is established, which not only can regulate the communication threshold according to the error of dynamic systems, but also can avoid the asynchronous phenomenon between the system mode and the filter mode. In order to further reduce the burden of communication, a new positive L1$$ {L}_1 $$ filter with the quantized measure system output is developed, and the design condition which ensures the filter error system to be stochastically stable with L1$$ {L}_1 $$ performance is presented which can be solved in terms of linear programming (LP) technique. It is illustrated that there is no Zeno phenomenon. The proposed results are applied to the power allocation in a mobile telecommunication system, and it is shown that compared with the existing results, the event‐triggered filter of this paper has some advantages. [ABSTRACT FROM AUTHOR]

Summary: This paper focuses on an adaptive practical preassigned finite‐time control problem for a class of unknown pure‐feedback nonlinear systems with full state constraints. Two new concepts, called preassigned finite‐time function and practical preassigned finite‐time stability, are defined. In order to achieve the main result, the pure‐feedback system is first transformed into an affine strict‐feedback nonlinear system based on the mean value theorem. Then, an adaptive preassigned finite‐time controller is obtained based on a modified barrier Lyapunov function and backstepping technique. Finally, simulation examples are exhibited to demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]