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The control-to-facet problem plays an important role in the design of feedback controllers for piecewise-affine hybrid systems on polytopes. In the literature, necessary conditions and sufficient conditions for solvability by static state feedback exist. In this paper, we extend these results to the case of continuous piecewise-affine static output feedback. For the construction of a controller, a triangulation of the output polytope is made which satisfies additional conditions to guarantee compatibility with the induced subdivision of the state polytope. In the state feedback case, the use of this special type of triangulation is not required. [ABSTRACT FROM AUTHOR]

In this technical note, we propose an approach to controller synthesis for a class of constrained nonlinear systems. It is based on the use of a hybridization, that is a hybrid abstraction of the nonlinear dynamics. This abstraction is defined on a triangulation of the state-space where on each simplex of the triangulation, the nonlinear dynamics is conservatively approximated by an affine system subject to disturbances. Except for the disturbances, this hybridization can be seen as a piecewise affine hybrid system on simplices for which appealing control synthesis techniques have been developed in the past decade. We extend these techniques to handle systems subject to disturbances by synthesizing and coordinating local robust affine controllers defined on the simplices of the triangulation. We show that the resulting hybrid controller can be used to control successfully the original constrained nonlinear system. Our approach, though conservative, can be fully automated and is computationally tractable. To show its effectiveness in practical applications, we apply our method to control a pendulum mounted on a cart. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the identification of static nonlinear components in a complex interconnected system. These nonlinear components are treated nonparametrically, in the sense that no natural parameterization is assumed to be available. A unified framework based on linear fractional transformations for exploring these identification problems is developed. Two key assumptions are made: the linear components of the interconnection are known, and the inputs to all the nonlinear components are available. Under these assumptions, a novel identification algorithm is offered. This algorithm estimates the nonlinear components by minimizing a quadratic cost function. A critical component of this cost function is the inclusion of a dispersion function that captures the requirement that the estimated nonlinearities be static. It is shown that the estimated nonlinearities converge asymptotically to their "true" values under certain identifiability and persistence of excitation conditions. Computable tests for identifiability and sufficient conditions for persistence of excitation are offered. The results in this paper strongly suggest that the most tractable identification problems for nonlinear interconnected systems are those where the inputs to all the nonlinear blocks are measured. [ABSTRACT FROM AUTHOR]

This note develops a modification of standard nonlinear least squares methods with reduced sensitivity to the quality of the initial guess. The technique is presented in the context of least squares fitting of dynamic system models, but may apply to other kinds of problems. The performance of the technique is compared to standard methods for a variety of test problems. [ABSTRACT FROM AUTHOR]