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This paper deals with feedback control problem for a piecewise affine system with autonomous, state-dependent switchings, subject to unknown but bounded disturbances, with hard bounds on controls and uncertain parameters. A target control problem in finite time is considered. In order to obtain the control strategy auxiliary solvability tubes with branching structure are introduced. They can be specified by means of some value functions. The paper presents a scheme for approximating these functions and corresponding solvability tubes using the comparison principle for the first-order ODEs of the Hamilton-Jacobi-Bellman type and also a special class of piecewise quadratic approximating functions. The parameters of these functions are obtained from a set of Riccati type matrix differential equations. This enables to produce an effective computational scheme.