Stabilizing Receding Horizon Control of Piecewise Linear Systems: an Lmi Approach
نویسنده
چکیده
Receding horizon control has recently been used for regulating discrete-time Piecewise Affine (PWA) systems. One of the obstructions for implementation consists in guaranteeing closed-loop stability a priori. This is an issue that has only been addressed marginally in the literature. In this paper we present an extension of the terminal cost method for guaranteeing stability in receding horizon control to the class of unconstrained Piecewise Linear (PWL) systems. A linear matrix inequalities set-up is developed to calculate the terminal weight matrix and the auxiliary feedback gains that ensure stability for quadratic cost based receding horizon control. It is shown that the PWL statefeedback control law employed in the stability proof globally asymptotically stabilizes the origin of the PWL system. The additional conditions needed to extend these results to constrained PWA systems are also pointed out. The implementation of the proposed method is illustrated by an example.
منابع مشابه
Control of Pwa Systems Using a Stable Receding Horizon Method
In this paper we derive stabilization conditions for the class of piecewise affine (PWA) systems using the linear matrix inequality (LMI) framework. We take into account the piecewise structure of the system and therefore the matrix inequalities that we solve are less conservative. Using the upper bound of the infinite-horizon quadratic cost as a terminal cost and constructing also a convex ter...
متن کاملReceding Horizon Neural H∞ Control for a Class of Nonlinear Unknown Systems
In this paper, we present new RHNHC (Receding Horizon Neural H∞ Control) for nonlinear unknown systems. First, we propose LMI (Linear Matrix Inequality) condition on the terminal weighting matrix for stabilizing RHNHC. Under this condition, noninceasing monotonicity of the saddle point value of the finite horizon dynamic game is shown to be guaranteed. Then, we propose RHNHC for nonlinear unkno...
متن کاملControl of PWA systems using a stable receding horizon method : Extended report ∗
In this paper we derive stabilization conditions for the class of PWA systems using the linear matrix inequality (LMI) framework. We consider the class of piecewise affine feedback controllers and the class of piecewise quadratic Lyapunov functions that guarantee stability of the closed-loop system. We take into account the piecewise structure of the system and therefore the matrix inequalities...
متن کاملProperties of a combined adaptive/second-order sliding mode control algorithm for some classes of uncertain nonlinear systems
results that include the well-known matrix equality condition [1] as a special case, still allowing arbitrary state weighting matrices. Theorem 6 and Corollary 4 are also new results that weaken the condition on the state weighting matrix. It is known that the terminal weighting matrices presented in this paper can be represented as LMI forms and computed by using existing semi-definite program...
متن کاملReceding Horizon : An easy way to improve performance in LPV systems 1 Mario
During the past few years the problem of stabilizing a Linear Parameter Varying system, while, at the same time, optimizing some measure of performance has been the object of increasing attention. In contrast to the case of linear systems where several optimal synthesis techniques (such as El,, El2 and el) are well established, the counterparts for LPV systems are just starting to emerge. Moreo...
متن کامل