In this work, control systems with higher-order state constraints and related control problems are studied. Such dynamical control systems are of a triangle-type and can often be encountered in engineering applications, in particular in Robotics, in which the control is carried out using the k-th order derivative of the position of a moving object, where k = 1, 2, .... The issue of nondegenerate optimality conditions is discussed in the k-order setting. The corresponding notions of k-order inward and outward pointing conditions are formulated. The issue of k-order regularity for such type of constrained control systems is also investigated.

This work is aimed at the study of optimal control problems with higher-order state constraints. These are due to multi-level dynamical control systems of triangle-type which are often appear in various engineering applications. One example of the k-order problem of such type is considered. The Pontryagin maximum principle is applied and the corresponding optimality conditions are analyzed. The main conclusion is that the direct landing on the boundary of the state domain is possible only when k = 1, 2. For k > 2, this is not the case in the general situation as the extremal begins to undulate before landing.

This paper concerns the quasi time-optimal motion in a simplified model of a mobile robot with constraints imposed on the state variables. As it is known, in this kind of problems involving the so-called unicycle type of dynamics, the classical assumptions of regularity with respect to the state constraints are not fulfilled. This fact greatly complicates the analysis of such control problems through the use of Pontryagin’s maximum principle. Moreover, the difficulties are also due to the presence of a singular control mode which is related to the angular velocity. The paper proposes a certain regularization approach in order to overcome the obstacles above and to develop a tool for the subsequent numerical implementation.