Deriving robust counterparts of nonlinear uncertain inequalities
نویسندگان
چکیده
In this paper we provide a systematic way to construct the robust counterpart of a nonlinear uncertain inequality that is concave in the uncertain parameters. We use convex analysis (support functions, conjugate functions, Fenchel duality) and conic duality in order to convert the robust counterpart into an explicit and computationally tractable set of constraints. It turns out that to do so one has to calculate the support function of the uncertainty set and the concave conjugate of the nonlinear constraint function. Conveniently, these two computations are completely independent. This approach has several advantages. First, it provides an easy structured way to construct the robust counterpart both for linear and nonlinear inequalities. Second, it shows that for new classes of uncertainty regions and for new classes of nonlinear optimization problems tractable counterparts can be derived. We also study some cases where the inequality is nonconcave in the uncertain parameters.
منابع مشابه
A Linear Matrix Inequality (LMI) Approach to Robust Model Predictive Control (RMPC) Design in Nonlinear Uncertain Systems Subjected to Control Input Constraint
In this paper, a robust model predictive control (MPC) algorithm is addressed for nonlinear uncertain systems in presence of the control input constraint. For achieving this goal, firstly, the additive and polytopic uncertainties are formulated in the nonlinear uncertain systems. Then, the control policy can be demonstrated as a state feedback control law in order to minimize a given cost funct...
متن کاملPrimal and dual robust counterparts of uncertain linear programs: an application to portfolio selection
This paper proposes a family of robust counterpart for uncertain linear programs (LP) which is obtained for a general definition of the uncertainty region. The relationship between uncertainty sets using norm bod-ies and their corresponding robust counterparts defined by dual norms is presented. Those properties lead us to characterize primal and dual robust counterparts. The researchers show t...
متن کاملStability analysis and feedback control of T-S fuzzy hyperbolic delay model for a class of nonlinear systems with time-varying delay
In this paper, a new T-S fuzzy hyperbolic delay model for a class of nonlinear systems with time-varying delay, is presented to address the problems of stability analysis and feedback control. Fuzzy controller is designed based on the parallel distributed compensation (PDC), and with a new Lyapunov function, delay dependent asymptotic stability conditions of the closed-loop system are derived v...
متن کاملDesigning Robust Finite-Time Nonlinear Torques for a n-DOF Robot Manipulator with Uncertainties, Sector and Dead-Zone Input Nonlinearities
In this paper, a complete dynamical model is presented for an uncertain -DOF robot manipulator containing description of sector and dead-zone input nonlinearities. Next, robust finite-time tracking problem of desired trajectories is declared and formulated for the aforementioned robot manipulator. By defining innovative nonlinear sliding manifolds and developing the nonsingular terminal sliding...
متن کاملRobust H_∞ Controller design based on Generalized Dynamic Observer for Uncertain Singular system with Disturbance
This paper presents a robust ∞_H controller design, based on a generalized dynamic observer for uncertain singular systems in the presence of disturbance. The controller guarantees that the closed loop system be admissible. The main advantage of this method is that the uncertainty can be found in the system, the input and the output matrices. Also the generalized dynamic observer is used to est...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Math. Program.
دوره 149 شماره
صفحات -
تاریخ انتشار 2015