Search

This paper deals with the finite-time stabilization problem for a class of uncertain disturbed systems using linear robust control. The proposed algorithm is designed to provide the robustness of a linear feedback control scheme such that system trajectories arrive at a small-size attractive set around an unstable equilibrium in a finite time. To this end, an optimization problem with a linear matrix inequality constraint is presented. This means that the effects of external disturbances, as well as matched and mismatched uncertain dynamics, can be significantly reduced. Finally, the performance of the suggested closed-loop control strategies is shown by the trajectory tracking of an unmanned aerial vehicle flight.

A new passivity-based voltage tracker for islanded Direct Current (DC) microgrids is presented in this paper. The proposed design develops a new sufficient condition for passivity-based state feedback with proportional and integral control using the attracting ellipsoid method. In this paper, we consider the time behavior of the extended vector, which completely describes the principle properties of the closed-loop system such as the boundedness of the trajectories within some ellipsoid and the dependence of its "size" on the feedback gains. The next step, which we are realizing in this paper, is the minimization of the attractive ellipsoid by selecting the "best" admissible feedback parameters. Here, it is important to note that the applied feedback is of PD-type (proportional differential) on the system state and I-type (integral) on the output. This is a new construction of the suggested feedback which gives several advantages for a designer. The suggested control is decentralized and uses only the local states; it is cost-effective and avoids the time delays in the communication networks which are needed if centralized control is used. The suggested control is carried out in the bilinear matrix inequality (BMI) framework. Extensive simulation is performed on a test system composed of renewable energy sources, under plug and play (PnP) operations, and uncertainties in distribution lines and loads. The performance of the proposed decentralized voltage controller is compared with that of a voltage tracker present in the literature. The comparison shows the improvements introduced by the proposed control ensure the stability of the dc bus voltage and a quick response under different scenarios of operating conditions. [ABSTRACT FROM AUTHOR]

This paper presents a study of a robust control strategy based on the Attractive Ellipsoid Method (AEM) to achieve trajectory tracking for a Permanent Magnet Synchronous Generator (PMSG). For the PMSG system, trajectory tracking control is necessary such that the maximum power point tracking can be carried out, which depends on controlling time-varying references (the generator angular speed), mainly when the generator motion is originated from a variable and intermittent energy source such as the wind. The proposed controller is based on the selection of the best gain matrix by numerically employing the AEM with the bilinear matrix inequality technique application. The controller guarantees that the trajectory tracking error reaches an ellipsoid of small enough size, which is determined in an optimized way, such that the practical stability for the tracking error is ensured. The effectiveness of the proposed controller is verified via simulations for a PMSG coupled with a three-phase rectifier, where the variables to be controlled reach the desired time-varying references, additionally a comparison is made against a classical Proportional Integral (PI) control scheme and a state feedback LQR controller. [ABSTRACT FROM AUTHOR]

This paper presents the design of a new control scheme for a group of omnidirectional robots in a multi-robot system operating in an environment with obstacles. The control scheme uses a decision agent based on discrete-time Markov chains and takes into account the state of the system, obstacle positions, and geometries to manipulate targets, providing robustness against measurement uncertainties. The decision process is dynamic, with state information updating at each time step and tasks being executed based on the hierarchy determined by quadratic hierarchical programming. The system's stability in the mean-square sense is analyzed through the study of a closed-loop stochastic system, and the effectiveness of the proposed control scheme is demonstrated through numerical simulations, including a comparative analysis with a finite-state machine decision agent. [ABSTRACT FROM AUTHOR]

Power system stability is greatly affected by two types of stochastic or random disturbances: (1) topological and (2) parametric. The topological stochastic disturbances due to line faults caused by a series of lightning strikes (associated with circuit breaker, C.B., opening, and auto-reclosing) are modeled in this paper as continuous-time Markov jumps. Additionally, the stochastic parameter changes e.g., the line reactance, are influenced by the phase separation, which in turn depends on the stochastic wind speed. This is modeled as a stochastic disturbance. In this manuscript, the impact of the above stochastic disturbance on power system small-disturbance stability is studied based on stochastic differential equations (SDEs). The mean-square stabilization of such a system is conducted through a novel excitation control. The invariant ellipsoid and linear matrix inequality (LMI) optimization are used to construct the control system. The numerical simulations are presented on a multi-machine test system. [ABSTRACT FROM AUTHOR]

This paper focuses on the embedded super twisting control for the orientation dynamics of a quadrotor. The Newton-Euler approach is applied to obtain the dynamic model of the quadrotor and a functional description of the experimental platform is described. In order to implement the control algorithm and perform real-time flights, a commercial flight computer is used. Experimental results are obtained in real-time during the autonomous flight. [ABSTRACT FROM PUBLISHER]

This work concerns the robust stabilization of a class of "Quasi- Lipschitz" nonlinear uncertain systems governed by stochastic Differential Equa- tions (SDE) subject to both multiplicative and additive stochastic noises mod- eled by a vector Brownian motion. The state-vector is admitted to be non- completely available, and be estimated by a Luenberger-type filter. The stabi- lization around the origin is realized by a linear feedback proportional to the current state-estimates. First, the class of feedback matrices and filter matrix- gains, providing the boundedness of the stochastic trajectories with probability one in a vicinity of the origin, is specified. Then a corresponding ellipsoid, con- taining these trajectories, is found. Its"size" (the trace of the ellipsoid matrix) is derived as a function of the applied gain matrices. To make this ellipsoid"as small as possible" the corresponding constrained optimization problem is suggested to be solved. These constraints are given by a system of Matrix In- equalities (MI's) which under a specific change of variables may be converted into a conventional system of Bilinear Matrix Inequalities (BMI's). The last may be resolved by the standard MATLAB toolboxes such as "penbmiTL, Tomlab toolbox". Finally, a numerical example, containing the arctangent- type nonlinearities, is presented to illustrate the effectiveness of the suggested methodology [ABSTRACT FROM AUTHOR]

This paper concerns the robust ‘practical’ stabilization for a class of linear controlled stochastic differential equations subject to both multiplicative and additive stochastic noises. Sufficient conditions of the stabilization are provided in two senses. In the first sense, it is proven that almost all trajectories of the stochastic model converge in a ‘mean-square sense’ to a bounded zone located in an ellipsoidal set, while the second one ensures the convergence to a zero zone in probability one. The considered control law is a linear state feedback. The stabilization problem is converted into the corresponding attractive averaged ellipsoid ‘minimization’ under some constraints of bilinear matrix inequalities (BMIs) type. Some variables permit to represent the BMIs problem in terms of linear matrix inequalities (LMIs) problem, which are resolved in a straight manner, using the conventional LMI-MATLAB toolbox. Finally, the numerical solutions of a benchmark example and a practical example are presented to show the efficiency of the proposed methodology. [ABSTRACT FROM AUTHOR]

In this paper, we consider the inventory robust constraint control problem with an uncertain demand. The considered system deals with a non-linear discrete-time stochastic model of a special structure. The robust control designing, consisting in the inventory product level minimization by the corresponding adjustment of the production rate, is shown to be converted into certain attractive ellipsoid ‘minimization’ problem under some specific constraints of bilinear matrix inequalities (BMI's) type. The application of an adequate coordinate changing transforms these BMI's into a set of linear matrix inequalities that permits to use directly the standard MATLAB-toolbox. The matrix generalization of the strong law of large numbers provides an instrument for the stochastic analyses of the considered process. [ABSTRACT FROM PUBLISHER]