A penalty/least-squares method for optimal control problems for ®rst-order elliptic systems is considered wherein the constraint equations are enforced via penalization. The convergence, as the penalty parameter tends to zero, of the solution to the penalized optimal control problem to that of the unpenalized one is demonstrated as is the convergence of a gradient method for determining solutio...

In this paper we consider the problem of optimal control of a boundary obstacle problem of the 1-D wave equation. We establish the existence and uniqueness of an optimal obstacle, give the characterization of the obstacle and obtain a Hamilton-Jacobi equation.

We consider a set of continuous algebraic Riccati equations with indefinite quadratic parts that arise in H∞ control problems. It is well known that the approach for solving such type of equations is proposed in the literature. Two matrix sequences are constructed. Three effective methods are described for computing the matrices of the second sequence, where each matrix is the stabilizing solut...

We consider the solution of a stochastic integral control problem, and we study its regularity. In particular, we characterize the optimal cost as the maximum solution of /v V, A(v)u <=f(v) in ’(), u 0 on 0, u where A(v) is a uniformly elliptic second order operator and V is the set of the values of the control.

A direct and non-iterative method for the computation of the in mum for a class of discrete-time H∞ optimal control problem is considered in this paper. The problem formulation is fairly general and does not place any restrictions on any direct feedthrough terms of the given systems. The method is applicable to systems where (i) the transfer function from the disturbance input to the measuremen...

The optimal manoeuvering of a vehicle during a collision avoidance manoeuvre is investigated. A simple model where the vehicle is modelled as point mass and the mathematical formulation of the optimal manoeuvre are presented. The resulting two-point boundary problem is solved by an adaptive finite element method and the theory behind this method is described.

Within a general abstract framework, we show that any optimal control problem in standard form can be translated into a stochastic target problem as defined in [17], whenever the underlying filtered probability space admits a suitable martingale representation property. This provides a unified way of treating these two classes of stochastic control problems. As an illustration, we show, within ...

*Correspondence: [email protected] 1School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, 404000, P.R. China 2College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan, 411105, P.R. China Full list of author information is available at the end of the article Abstract In this paper, we study the mixed finite element methods for general convex optima...

Model Predictive Control is a controller design method which synthesizes a sampled data feedback controller from the iterative solution of open loop optimal control problems. We describe the basic functionality of MPC controllers, their properties regarding feasibility, stability and performance and the assumptions needed in order to rigorously ensure these properties in a nominal setting.