K. H. Wong

Optimal control computation for nonlinear time-lag systems

In this paper, a computational scheme using the technique of control parameterization is developed for solving a class of optimal control problems involving nonlinear hereditary systems with linear control constraints. Several examples have been solved to test the efficiency of the technique.

Optimal control computation for parabolic systems with boundary conditions involving time delays

In this paper, we consider a class of optimal control problems involving a second-order, linear parabolic partial differential equation with Neumann boundary conditions. The time-delayed arguments are assumed to appear in the boundary conditions. A necessary and sufficient condition for optimality is derived, and an iterative method for solving this optimal control problem is proposed. The convergence property of this iterative method is also investigated.On the basis of a finite-element Galerkins scheme, we convert the original distributed optimal control problem into a sequence of approximate problems involving only lumped-parameter systems. A computational algorithm is then developed for each of these approximate problems. For illustration, a one-dimensional example is solved.

Nonlinearly constrained time-delayed optimal control problems

A computational algorithm for solving a class of optimal control problems involving terminal and continuous state constraints of inequality type was developed in Ref. 1. In this paper, we extend the results of Ref. 1 to a more general class of constrained time-delayed optimal control problems, which involves terminal state equality constraints as well as terminal state inequality constraints and continuous state constraints. Two examples have been solved to illustrate the efficiency of the method.

A feasible directions algorithm for time-lag optimal control problems with control and terminal inequality constraints

A computational algorithm for a class of time-lag optimal control problems involving control and terminal inequality constraints is presented. The convergence properties of the algorithm is also investigated. To test the algorithm, an example is solved.

Gradient-flow approach for computing a nonlinear-quadratic optimal-output feedback gain matrix

In this paper, an approach is proposed for solving a nonlinear-quadratic optimal regulator problem with linear static state feedback and infinite planning horizon. For such a problem, approximate problems are introduced and considered, which are obtained by combining a finite-horizon problem with an infinite-horizon linear problem in a certain way. A gradient-flow based algorithm is derived for these approximate problems. It is shown that an optimal solution to the original problem can be found as the limit of a sequence of solutions to the approximate problems. Several important properties are obtained. For illustration, two numerical examples are presented.

Convergence of a feasible directions algorithm for relaxed controls in time-lag systems

In this paper, we consider a class of time-lag optimal control problems involving control and terminal inequality constraints. A feasible direction algorithm has been obtained by Teo, Wong, and Clements for solving this class of optimal control problems. It was shown that anyL∞ accumulation points of the sequence of controls generated by the algorithm satisfy a necessary condition for optimality. However, suchL∞ accumulation points need not exist. The aim of this paper is to prove a convergence result, which ensures that the sequence of controls generated by the algorithm always has accumulation points in the sense of control measure, and these accumulation points satisfy a necessary condition for optimality for the corresponding relaxed problem.

A CLASS OF NONSMOOTH DISCRETE-TIME CONSTRAINED OPTIMAL CONTROL PROBLEMS WITH APPLICATION TO HYDROTHERMAL POWER SYSTEMS

We consider a class of discrete-time constrained optimal control problems in which the cost function is nonsmooth. By using a smoothing technique, the cost function is approximated by a smooth function. Furthermore, the all-time-step inequality constraints on the state variables are transcribed and appended to the cost function. This gives rise to a sequence of discrete-time optimal control problems. Each of these is solvable by existing software packages such as DMISER3. Important convergence properties are established. For illustration, an example involving the long-term planning of hydrothermal power systems is solved using the proposed technique.

Optimal maintenance of stochastically deteriorating systems

A machine maintenance problem were the deterioration of the machine is subject to additive random noise is considered. The objective is then to maximize the discounted net return of the machine. Furthermore, it is also required that the machine maintains a sufficiently good quality state with certain degrees of confidence in part or whole of the machine life span. This problem can be formulated as a constrained stochastic optimal control problem. It is then shown that the stochastic optimal control problem can be converted into an equivalent deterministic optimal control problem and subsequently solved by the technique of control parametrization. Numerical examples are presented to illustrate some of the interesting features of the model.

Convergence analysis of a computational method for time-lag optimal control problems

Abstract We consider a class of non-linear time-lag optimal control problems. The class of admissible controls are taken to be the class of piecewise smooth functions. A control parameterization technique is used to approximate the optimal control problem by a sequence of optimal parameter selection problems. The solution of each of these approximate problems gives rise to a sub-optimal solution to the true optimal control problem in an obvious way. The error bound is derived for the sub-optimal costs and the true optimal cost.