where c > 0 and the supremum is taken over all admissible controls v satisfying vt 2 [ 0; 1] for all t up to = inf f t > 0 j Xt = 2 (`0; `1) g with 0 < 0 < 1 and `0 < 0 < `1 given and fixed. The following control v is proved to be optimal: ’Pull as hard as possible’ that is v t = 0 if Xt < g (St) , and ’push as hard as possible’ that is v t = 1 if Xt > g (St) , where s 7! g (s) is a switching c...

As follows from the Schwartz Impossibility Theorem, multiplication of two distributions is in general impossible. Nevertheless, often one needs to multiply a distribution by a discontinuous function, not by an arbitrary distribution. In the present paper we construct a space of distributions where the general operation of multiplication by a discontinuous function is defined, continuous, commut...

The paper extends quadratic optimal control theory to weakly regular linear systems, a rather broad class of infinite-dimensional systems with unbounded control and observation operators. We assume that the system is stable (in a sense to be defined) and that the associated Popov function is bounded from below. We study the properties of the optimally controlled system, of the optimal cost oper...

We consider the robust optimal control of a law of large numbers approximation of a stochastic network. The robust control problem is formulated as a di®erential game, with one player choosing the policies that determine service and routing assignments, and the other choosing quantities such as the arrival and service rates, subject to constraints. The cost to be minimized by the ̄rst player an...

In this paper we propose an iterative learning algorithm based on observer and linear quadratic performance function. We calculate the initial control value for the iteractive learning algorithm based on the estimation of the states, which guarantees the efficient asymptotic tracking of any desired trajectories. Furthermore, with Linear quadratic optimal control theory, we obtain the optimized ...

The position/force tracking control of Lagrangian mechanical systems with classical nonholonomic constraints is addressed in this paper. The main feature of this paper is that 1) control strategy is developed at the dynamic level and can deal with model uncertainties in the mechanical systems; 2) the proposed control law ensures the desired trajectory tracking of the configuration state of the ...

This paper presents the basic principle, design and simulation of a LQG optimal controller for a mobile cart. The optimal control is a significant branch of control theory, which combines the statistical process theory with the optimal control theory to solve many control problems in uncertain systems like astronavigation, satellite attitude and orbit, civil purpose and industrial processes. In...

A new torque control strategy for brushless motors with minimum torque ripple and minimum copper losses while maintaining the phase currents under magnetic (or current) saturation is presented. The optimal control { a nonlinear map from desired torque and position to the motor's phase currents { is the closed form solution to a quadratic programming problem. Experimental results demonstrate vir...

In this paper a class of semilinear elliptic optimal control problem with pointwise state and control constraints is studied. We show that sufficient second order optimality conditions for regularized problems with small regularization parameter can be obtained from a second order sufficient condition assumed for the unregularized problem. Moreover, error estimates with respect to the regulariz...

We present a new stabilizing control scheme for linear discrete-time systems with input and state constraints. Essentially, we seek a controller that is able to steer all initial states within a controlled invariant set towards the origin without violating the constraints. The control law builds on a predictive control scheme. We show that a prediction horizon of n steps, where n denotes the di...