We derive closed-form solutions for the linear-quadratic (LQ) optimal control problem subject to integral quadratic constraints. The optimal control is a non-linear function of the current state and the initial state. Furthermore, the optimal control is easily calculated by solving an unconstrained LQ control problem together with an optimal parameter selection problem. Gradient formulae for th...

In this paper we consider a perturbed linear-quadratic control problem on a finite interval. The only difference from the traditional LQ-control problem is that the problem has an extra linear term in the cost function which makes it time-dependent. The major motivation for this extension comes from [4] where we consider applications of very efficient primal-dual interior-point algorithms to th...

This paper introduces certain nonlinear partially observable stochastic optimal control problems which are equivalent to completely observable control problems with finite-dimensional state space. In some cases the optimal control laws are analogous to linear-exponential-quadraticGaussian and linear-quadratic-Gaussian tracking problems. The problems discussed allow nonlinearities to enter the u...

The stability analysis of an adaptive control scheme for robotic manipulators, originally introduced by Horowitz and Tomizuka (1980). is presented in this paper. In the previous stability proof it was assumed that the manipulator parameter variation is negligible compared with the speed of adaptation. I t is shown that this key assumption can be removed by introducing two modifications in the a...

Recently path integral methods have been developed for stochastic optimal control for a wide class of models with non-linear dynamics in continuous space-time. Path integral methods find the control that minimizes the expected cost-to-go. In this paper we show that under the same assumptions, path integral methods generalize directly to risk sensitive stochastic optimal control. Here the method...

We consider a general class of nonlinear optimal policy problems involving forward-looking constraints (such as the Euler equations that are typically present as structural equations in DSGE models), and show that it is possible, under regularity conditions that are straightforward to check, to derive a problem with linear constraints and a quadratic objective that approximates the exact proble...

We investigate turnpike behaviour of discrete time optimal control problems with linear dynamics and linear-quadratic cost functions including state and control constraints. We give necessary and sufficient conditions in terms of spectral criteria and matrix inequalities. As important tools we use the concepts of strict dissipativity and a new property called strict pre-dissipativity of a syste...

This paper presents a numerical method based on quasilinearization and rationalized Haar functions for solving nonlinear optimal control problems including terminal state constraints, state and control inequality constraints. The optimal control problem is converted into a sequence of quadratic programming problems. The rationalized Haar functions with unknown coefficients are used to approxima...