Abstract
SummaryThis paper exposes a methodology to solve state and input constrained optimal control problems for nonlinear systems. In the presented ‘interior penalty’ approach, constraints are penalized in a way that guarantees the strict interiority of the approaching solutions. This property allows one to invoke simple (without constraints) stationarity conditions to characterize the unknowns. A constructive choice for the penalty functions is exhibited. The property of interiority is established, and practical guidelines for implementation are given. A numerical benchmark example is given for illustration. © 2014 The Authors. Optimal Control Applications and Methods published by John Wiley & Sons, Ltd.
Highlights
This paper exposes a methodology allowing one to solve constrained optimal control problems (COCP) for general multi-input multi-output system with nonlinear dynamics. This methodology belongs to the class of interior point methods (IPMs), commonly considered in finite-dimensional optimization, which consists in approaching the optimum by a path strictly lying inside the constraints
We have constructively exhibited three classes of penalized optimal control problems whose optimal costs converge to the optimal control of a given optimal control problem with state and control constraints
A notable feature of all of these penalized problems is that the state penalty is sufficient to guarantee that the state constraints are strictly satisfied; they do not need to be specified in the penalized problem
Summary
This paper exposes a methodology allowing one to solve constrained optimal control problems (COCP) for general multi-input multi-output system with nonlinear dynamics This methodology belongs to the class of interior point methods (IPMs), commonly considered in finite-dimensional optimization, which consists in approaching the optimum by a path strictly lying inside the constraints. It is constructed as the sum of the original cost function and so-called penalty functions that have some diverging asymptotic behavior when the constraints are approached by any tentative solution. Two kinds of penalty methods exist: exterior penalty and interior penalty (a.k.a. barrier methods) In both approaches, minimization of the augmented performance index favors satisfaction of the constraints, depending on the weight of the penalty. Before defining a new penalized problem, let us give some useful properties of the penalty function
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