Control to facet problems for affine systems on simplices and polytopes – With applications to control of hybrid systems
نویسنده
چکیده
In this paper, a general control-to-facet problem for affine systems on polytopes is studied: find an affine feedback law such that all trajectories of the closed-loop system leave the state polytope through an a priori specified (possibly empty) set of facets. Solutions are presented in terms of (bi)linear inequalities in the coefficients of the affine feedback. The result is applied to control synthesis for piecewiseaffine hybrid systems. Using a backward recursion algorithm, a sufficient condition for reachability of hybrid systems is obtained, and a piecewise-affine controller is computed that realizes the required reachability property.
منابع مشابه
Designing a novel structure of explicit model predictive control with application in a buck converter system
This paper proposes a novel structure of model predictive control algorithm for piecewise affine systems as a particular class of hybrid systems. Due to the time consuming and computational complexity of online optimization problem in MPC algorithm, the explicit form of MPC which is called Explicit MPC (EMPC) is applied in order to control of buck converter. Since the EMPC solves the optimizati...
متن کاملDesign of a Novel Framework to Control Nonlinear Affine Systems Based on Fast Terminal Sliding-Mode Controller
In this paper, a novel approach for finite-time stabilization of uncertain affine systems is proposed. In the proposed approach, a fast terminal sliding mode (FTSM) controller is designed, based on the input-output feedback linearization of the nonlinear system with considering its internal dynamics. One of the main advantages of the proposed approach is that only the outputs and external state...
متن کاملPassivity-Based Stability Analysis and Robust Practical Stabilization of Nonlinear Affine Systems with Non-vanishing Perturbations
This paper presents some analyses about the robust practical stability of a class of nonlinear affine systems in the presence of non-vanishing perturbations based on the passivity concept. The given analyses confirm the robust passivity property of the perturbed nonlinear systems in a certain region. Moreover, robust control laws are designed to guarantee the practical stability of the perturbe...
متن کاملAdaptive Consensus Control for a Class of Non-affine MIMO Strict-Feedback Multi-Agent Systems with Time Delay
In this paper, the design of a distributed adaptive controller for a class of unknown non-affine MIMO strict-feedback multi agent systems with time delay has been performed under a directed graph. The controller design is based on dynamic surface control method. In the design process, radial basis function neural networks (RBFNNs) were employed to approximate the unknown nonlinear functions. S...
متن کاملControl of Discrete-time Piecewise Affine Systems
In this paper we propose a new approach for the control of discrete-time piecewise affine hybrid systems on full-dimensional polytopes. The new strategy is divided into a local and a supervisory control problem. The local problem is to reach and cross one facet of a polytope ensuring that the next sample of the time-discrete trajectory is picked up in the adjacent polytope. Therefore, a local p...
متن کامل