Kenta Hoshino

Global Asymptotic Stabilization of Nonlinear Deterministic Systems Using Wiener Processes

The objective of this study is to present a noise-assisted stabilization method and a constructive method for designing a stabilizing controller. We investigate the stabilization of a deterministic nonlinear affine system by using a controller with a Wiener process. Our approach focuses on the global asymptotic stabilization of nonholonomic systems. The proposed method for designing a stabilizing controller is based on the notion of a stochastic control Lyapunov function. We show that if there exists a stochastic control Lyapunov function with small control property, the designed controller globally asymptotically stabilizes a given system with probability one.

Static output feedback control design for Takagi-Sugeno descriptor fuzzy systems

The paper is concerned with control design via static output feedback controller for a fuzzy descriptor system. A fuzzy descriptor system describes a natural representation for physical systems, which are usually modeled as a nonlinear system. In the actual situation, the state of the system is rarely measured and the output feedback control design is desired. In this paper, static output feedback control for fuzzy descriptor systems is considered and a control design of admissible controllers is proposed. The stability analysis of the closed-loop system and controller design are given in terms of Linear Matrix Inequality(LMI) conditions.

Non-fragile static output feedback control design with guaranteed cost of uncertain Takagi-Sugeno fuzzy systems

The paper is concerned with non-fragile control design via output feedback controller for uncertain fuzzy systems. In control design for physical systems, there are chances that malfunction in actuator happens and an exact value of the control input may not be applied. Hence controller gain variations should be considered in the control design. Additionally, many results on the state feedback control design have been given in the literature. However, in the actual situation, the state of the system is rarely measured and the output feedback control design is desired. In this paper, non-fragile guaranteed cost control via output feedback control for uncertain fuzzy systems is considered and a control design of stabilizing controllers with guaranteed cost and robustness against uncertainties of system parameters and control gains is proposed. The robust stability analysis of the closed-loop system and controller design are given in terms of LMI conditions, which are less conservative than the existing results.

Static output feedback control design with guaranteed cost of Takagi-Sugeno fuzzy systems

The paper is concerned with control design via static output feedback controller for fuzzy systems. Many results on the state feedback control design have been given in the literature. In the actual situation, however, the state of the system is rarely measured and the output feedback control design is desired. In this paper, guaranteed cost control via output feedback control for fuzzy systems is considered and a control design of stabilizing controllers with guaranteed cost is proposed. The stability analysis of the closed-loop system and controller design are given in terms of LMI conditions, which are less conservative than the existing results.

Homogeneous stabilization of driftless input-affine systems using Wiener processes

This paper presents a method for the homogeneous stabilization of homogeneous driftless input-affine systems using feedback controllers with Wiener processes. Although previous studies have shown methods for the stabilization of nonholonomic systems by using Wiener processes, the closed-loop systems sometimes show slow convergence. To improve the convergence rate, we show a method that gives a homogeneous controller by redesigning the controllers designed by the previous methods. By the virtue of the homogeneity, the closed-loop systems exhibit almost sure exponential stability with respect to homogeneous norms. A numerical example shows the effectiveness of the proposed method.

A new approach to non-fragile output feedback controller design for uncertain Takagi-Sugeno fuzzy systems

The paper discusses non-fragile output feedback control design Takagi-Sugeno fuzzy systems with uncertain parameters. In control design for physical systems, there are chances that malfunction in actuator and round-off error of the control gain calculation may occur. Hence, controller gain variations as well as uncertainty in the system parameters should be considered in the control design. For an uncertain fuzzy system, a design method of a non-fragile output feedback controller is proposed by introducing a new type of controllers where the integrals of the membership functions are involved. A non-parallel distributed compensator(Non-PDC) is a generalization of a parallel distributed compensator(PDC), which is a traditional controller for fuzzy systems, and is used for the control design. A non-fragile non-PDC output feedback controller for uncertain fuzzy systems is obtained from new fuzzy multiple Lyapunov functions and its control design conditions are given in terms of a set of linear matrix inequalities(LMIs), which are easily numerically solvable. The descriptor system formulation, which leads to relaxation in controller design conditions, is also employed. These approaches reduce the conservatism of the control design conditions. Finally, numerical examples are given to illustrate our nonlinear control design and to show the effectiveness over other existing results.

Output feedback stabilization of discrete-time fuzzy systems

This paper is concerned with output feedback control design for a discrete-time Takagi-Sugeno fuzzy system where the premise variable is not necessarily measurable. The Takagi-Sugeno fuzzy system generally describes nonlinear systems by employing local linear system representations, and a fuzzy system to be considered in this paper describes even a wider class of nonlinear systems. For a fuzzy system, a design method of a stabilizing output feedback controller is proposed by employing a fuzzy multiple Lyapnunov functional and descriptor system approach. These techniques reduce the conservatism in stabilizing controller design conditions. Such conditions are given in terms of a set of linear matrix inequalities(LMIs), which are easily numerically solvable. In addition, a relaxation method is used to further reduce the conservatism in design conditions. A proposed controller can be of reduced-order, which is practically useful for large-scale systems. Finally, numerical examples are given to illustrate our nonlinear control design and to show the effectiveness over other existing results.

A novel non-fragile output feedback controller design for uncertain Takagi-Sugeno fuzzy systems

The paper is concerned with non-fragile control design via output feedback controller for uncertain fuzzy systems. In control design for physical systems, there are chances that malfunction in actuator happens and an exact value of the control input may not be applied. Hence, controller gain variations as well as uncertainty in the system parameters should be considered in the control design. For an uncertain fuzzy system, a design method of a non-fragile output feedback controller is proposed by introducing a new class of non-parallel distributed compensators(non-PDCs) where the integrals of the membership functions are involved. Non-PDC is a generalized controller of PDC, which is a traditional controller for fuzzy systems. A non-PDC non-fragile output feedback controller for uncertain fuzzy systems is obtained from new fuzzy multiple Lyapunov functions and its control design conditions are given in terms of a set of linear matrix inequalities(LMIs), which are easily numerically solvable. The descriptor system approach, which leads to relaxation in controller design conditions, is also employed. Finally, a numerical example is given to illustrate our nonlinear control design and to show the effectiveness over other existing results.

Design of Dynamic Output Feedback Laws Based on Sums of Squares of Polynomials

We consider the stabilization of nonlinear polynomial systems and the design of dynamic output feedback laws based on the sums of squares (SOSs) decompositions. To design the dynamic output feedback laws, we show the design conditions in terms of the state-dependent linear matrix inequalities (SDLMIs). Because the feasible solutions of the SDLMIs are found by the SOS decomposition, we can obtain the dynamic output feedback laws by using numerical solvers. We show numerical examples of the design of dynamic output feedback laws.

Stabilization of Artstein's circle by continuous stochastic feedback

This paper presents the asymptotic stabilization of the Artsteins circle using stochastic processes in a control law. To construct a C2 control Lyapunov function (CLF) for a stabilization method using stochastic processes, we synthesize a nonsmooth CLF for a nonsmooth stabilization method and a smooth function. By synthesizing these functions, we obtain a C2 CLF. By this C2 CLF, we can obtain a continuous stabilizing feedback using stochastic processes for the Artsteins circle.