Myung Hwan Tak

Local stability analysis of continuous-time Takagi-Sugeno fuzzy systems: A fuzzy Lyapunov function approach

This paper proposes a strategy to estimate invariant subsets of the domain of attraction (DA) for asymptotically stable zero equilibrium points of continuous-time Takagi-Sugeno (T-S) fuzzy systems. Specifically, by using Lyapunovs stability theory and the linear matrix inequality (LMI) technique, sufficient conditions for proving the local stability are provided in terms of single-parameter minimization problems subject to LMI constraints or eigenvalue problems, which are solvable via convex optimizations. The fuzzy Lyapunov functions (FLFs), expressed by the so-called multi-dimensional fuzzy summations, are employed to characterize invariant subsets of the DA as sublevel sets of the FLFs. To compute a larger inner estimate of the DA, an iterative LMI algorithm is also developed. Finally, illustrative examples show the efficacy of the approach.

Periodically Time-Varying

This technical note focuses on the development of a general periodically time-varying memory filter (PTVMF) to improve the robust H∞ filtering performance for discrete-time linear time-invariant (LTI) systems with polytopic parameter uncertainties. A sufficient condition to design the H∞-PTVMF is given in terms of convex optimizations expressed as linear matrix inequalities (LMIs). Finally, examples demonstrate its potential less conservatism.

{\cal H}_{\infty}

This paper addresses the problem of static output feedback (SOF) stabilization for discrete-time LTI systems. We approach this problem using the recently developed periodically time-varying memory state-feedback controller (PTVMSFC) design scheme. A bilinear matrix inequality (BMI) condition which uses a pre-designed PTVMSFC is developed to design the periodically time-varying memory SOF controller (PTVMSOFC). The BMI condition can be solved by using BMI solvers. Alternatively, we can apply two-steps and iterative linear matrix inequality algorithms that alternate between the PTVMSFC and PTVMSOFC designs. Finally, an example is given to illustrate the proposed methods.

Memory Filter Design for Discrete-Time LTI Systems With Polytopic Uncertainty

In this paper, we propose the localization algorithm for the cooperative behavior of the swarm robots based on WSN (Wireless Sensor Network). The proposed method is as follows: First, we measure positions of the L-bot (Leader robot) and F-bots (Follower robots) by using the APIT (Approximate Point In Triangle) and the RSSI (Received Signal Strength Indication). Second, we measure relative positions of the F-bots against the pre-measured position of the L-bot by using trilateration. Then, to revise a position error caused by noise of the wireless signal, we use the particle filter. Finally, we show the effectiveness and feasibility of the proposed method though some simulations.

Periodically time-varying memory static output feedback control design for discrete-time LTI systems

In this paper, we propose the novel behavior control algorithm by using the efficient searching method based on the characteristic of the swarm robots in unknown space. The proposed method consists of identifying the position and moving state of a robot by the dynamic modelling of a wheel drive vehicle, and planing behavior control rules of the swarm robots based on the sensor range zone. The cooperative search for unknown space is carried out by the proposed behavior control. Finally, some experiments show the effectiveness and the feasibility of the proposed method.

Localization for Cooperative Behavior of Swarm Robots Based on Wireless Sensor Network

This paper proposes the implementation of robust fuzzy controller for designing intelligent wind farm and mitiagating the fluctuation of wind power generator. The existing researches are limited to individual wind turbine with variable speed so that it is necessary to study the multi-agent wind turbine power system. The scopes of these studies include from the arrangements of each power turbine to the control algorithms for the wind farm. For solving these problems, we introduce the composition of intelligent wind farm and use the T-S (Takagi-Sugeno) fuzzy model which is suitable for designing fuzzy controller. The control object in wind farm enables the minimizing the fluctuation of wind power generator. Simulation results for wind fram which is modelled as mathematically are demonstrated to visualize the feasibility of the proposed method.

Behavior Control Algorithm for Space Search Based on Swarm Robots

In this paper, the problem of robust discretisation of linear time-invariant (LTI) systems with polytopic uncertainties is introduced. More specifically, the main objective is to provide a systematic way to find an approximate discrete-time (DT) model of a continuous-time (CT) plant with uncertainties in polytopic domain. The system matrices of polytopic DT model to be found are expressed as parameter-dependent matrices which are homogeneous polynomials of arbitrary degree with respect to the uncertain variables in the simplex, and is obtained in such a way that the norm between the system matrices and the truncated power series of the exact DT model is minimised while preserving the polytopic structure of the original CT plant. The solution procedures proposed are presented in terms of single-parameter minimisation problems subject to linear matrix inequality (LMI) constraints which are numerically tractable via LMI solvers. Finally, examples are given to show the validity and effectiveness of the proposed techniques.

Robust Fuzzy Controller for Mitigating the Fluctuation of Wind Power Generator in Wind Farm

This paper addresses local H∞ controller design problems for continuous-time Takagi-Sugeno (T-S) systems with magnitude- and energy-bounded disturbances. The design procedure is formulated as optimizations subject to linear matrix inequalities (LMIs) which can be solved by means of convex optimization techniques. The designed controllers not only guarantee the H∞ performance but also ensure the state not to escape an invariant set that is included by the region where the T-S fuzzy model is defined. Finally, examples are given to illustrate the proposed method.

An asymptotically exact LMI solution to the robust discretisation of LTI systems with polytopic uncertainties and its application to sampled-data control

In swarm robot systems, it is very important to maintain the network connectivity for cooperative behavior between robots. This paper deals with the behavior control algorithm of the swarm robots for maintaining network connectivity. To do this, we divide swarm robot by search-robot, base-robot, and relay-robot. Using these robots, we propose behavior control algorithm for maintaining network connectivity. The behavior control algorithm for maintaining network connectivity are proposed the local path planning using the virtual force and the global path planning using the Delaunay triangulation, respectively. Finally, we show the effectiveness and applicability of the proposed method through some simulations.

Local H ∞ control and invariant set analysis for continuous-time T-S fuzzy systems with magnitude- and energy-bounded disturbances

This paper addresses the problem of stabilizing discrete-time LTI systems with polytopic uncertainties via a static output feedback controller. We approach this problem using the recently developed periodically time-varying memory state-feedback controller design scheme, and a sufficient linear matrix inequality condition for the static output control design is proposed. Finally, numerical examples are given to demonstrate the usefulness of the proposed method.