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This paper presents for the first time a fault detection and identification technique for bimodal piecewise affine (PWA) systems. A Luenberger-based observer structure is applied to the state estimation problem of the PWA system. The unknown value of the fault parameter is estimated by an observer equation obtained from a Lyapunov function. The design procedure is formulated as a set of linear matrix...
This paper defines a new class of hybrid systems called piecewise polynomial (PWP) systems in strict form and develops a backstepping controller synthesis methodology for these systems. The main contribution of the paper is to formulate controller design for a large class of PWP systems as a convex feasibility problem. The controller synthesis problem for PWP systems in strict feedback form is divided...
In this paper, fault-tolerant, state feedback controllers are synthesized for piecewise-affine (PWA) systems while minimizing an upper bound of a quadratic cost function. The controllers are designed to deal with partial loss of control authority in the closed loop PWA system. The proposed controller design technique stabilizes and satisfies performance bounds for both the nominal and faulty systems...
This paper addresses backstepping controller synthesis for piecewise affine (PWA) systems. The main contribution of the paper is to formulate controller design for a large class of PWA systems as a convex problem. Integrator backstepping is proposed as the principal design step in constructing Lyapunov functions for PWA systems in strict feedback form. The controller synthesis problem is divided into...
The main contribution of this paper is the development of a two step integrated and systematic approach for modeling and control of large angle maneuvers of a rigid body through convex optimization. In the first step, the attitude dynamics of the rigid body are represented by modified Rodriguez parameters (MRP). In the second step, a Lyapunov- based controller synthesis is performed based on the Sum...
This work presents new analysis and state feedback synthesis methods for piecewise-affine (PWA) systems with additive noise. The analysis problem can be cast as an optimization program subject to linear matrix inequalities (LMIs) and can be solved very efficiently using currently available software packages. The synthesis problem can also be cast as am optimization program subject to a set of linear...
This paper develops a piecewise-affine (PWA) controller for a nonlinear three degree of freedom (DDF) helicopter model. To design this controller a local linear controller is designed for a PWA approximation of the model in the region where the desired closed-loop equilibrium point lies. An optimization problem subject to bilinear matrix inequalities (BMIs) is then solved to find a PWA semi-global...
The path following problem for a simplified model of an unhabited aerial vehicle (UAV) in longitudinal motion is investigated using a piecewise-affine (PWA) control law and a Lyapunov based controller design technique. The search for the parameters corresponding to the controller and to a piecewise quadratic Lyapunov function is formulated as an optimization problem subject to linear and bilinear...
This paper shows that Lyapunov-based state feedback controller synthesis for piecewise-affine systems can be cast as an optimization problem subject to a set of LMIs analytically parameterized by a vector. Furthermore, it is shown that continuity of the control inputs at the switchings can be guaranteed by adding equality constraints to the problem without affecting its parameterization structure...
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