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Consideration is given to the problem inverse to the problem of designing the optimal (in the sense of minimization of a quadratic functional) controller for a linear periodic system. Problem statement: given matrices describing the dynamics of the system and a control matrix, determine the weighting matrices of the quadratic functional. To solve this problem, an algorithm based on linear matrix inequalities is proposed

A nonholonomic model of a wheeled robot with two steerable wheels is considered. The model accounts for dynamic effects. The motion-planning problem for this model is solved by reducing it to a linear two-point boundary-value problem Introduction. The maneuvering capabilities of mobile robots can be improved by increasing the number of controlled wheels [10]. However, this would noticeably complicate the description of such nonholonomic systems and the solution of the corresponding motion-planning problem, which is still of interest [2][3][4]11]. Apart from mobile robots, such systems include hopping machines [11] (motion-planning problems for hoppers were discussed in, e.g., [7][8][9]).The path-planning problem for a mobile robot with two steerable wheels was solved in [4] (dynamic effects disregarded [2]). We will use the approach from [5, 6] to solve the motion-planning problem for a mobile robot with two steerable wheels (dynamic effects taken into account). Equations of Motion.Consider a mobile robot with two steerable wheels. It moves in the plane XOY. Its motion is plane-parallel and its position is described by the interval ab (Fig. 1). Let | | | | ao bo L = = , ψ 1 and ψ 2 be the angles of rotation of the front and back steerable wheels, respectively, and θ be the angle between the robot's body and the OX -axis.Denoting the projections of the velocities of the point o onto the OX-and OY-axes by V xo and V yo , we can write the relations