Minimax Programming Research Articles

Robust pole-placement technique for plants with ellipsoidally uncertain parameters

A technique is proposed for synthesizing pole-placement controllers capable of assigning the closed-loop poles of a family of plants inside a specified design region. The design is applicable to plants characterized by uncertain parameters that are known to lie inside an ellipsoid. Ellipsoidal parametric uncertainty descriptions are particularly useful because they arise naturally in the context of parameter estimation, and hence have the advantage of being quantifiable using experimental input-output data. The control-design problem is posed as a minimax program that is shown to be convex, and that can be solved using numerical techniques with global convergence guarantees. Two reliable techniques for relating regions of stable poles to regions of allowed variability for the coefficients of the characteristic polynomial are discussed. The robust pole-placement design technique is illustrated with an example.

Duality in fractional minimax programming

AbstractCertain omissions in the recently introduced dual for fractional minimax programming problem ‘minimize max y ∈ Y f(x, y) / h(x, y), subject to g(x) ≤ 0’, are indicated and two modified duals for this problem are presented. Various fractional programming and generalized fractional programming duals are shown to be special cases of this study.

Non-differentiable pseudo-convex functions and duality for minimax programming problems

Optimality results are derived for a general minimax programming problem under non-differentiable pseudo-convexity assumptions. A dual in terms of Dini derivatives is introduced and duality results are established. Finally, two duals again in terms of Dini derivatives are introduced for a generalized fractional minimax programming problem and corresponding results are studied.

An optimization approach to robust nonlinear control design

Abstract A new procedure of robust control design is presented for nonlinear systems with parametric uncertainty and disturbance. This nonlinear optimization-based approach can design robust nonlinear controllers of widely different structures and arbitrary complexity. By taking the worst-case design approach, a minimax optimization problem is formulated. A number of state-of-the-art optimization procedures are explored as possible candidates for minimaximization. It is determined that the tools of non-smooth analysis and optimization are the most useful for the efficient solution of practical size worst-case design problems. Included in the paper are the significant details of a special two-tier structured minimax programming algorithm implemented in this work. The overall algorithm is used in solving two robust nonlinear control design problems. The controller designs produced by the minimax optimization algorithm are discussed and the performance of the controllers is studied by simulations.

Composite convex programs

A duality theory using conjugate functions is established for mathematical programs that involve the composition of two convex functions. This generalizes our earlier work in quadratic and composite geometric programs. A specific application to minimax programs is given.

Duality for fractional minimax programming problems

AbstractDuality theory is discussed for fractional minimax programming problems. Two dual problems are proposed for the minimax fractional problem: minimize maxy∈Υf(x, y)/h(x, y), subject to g(x) ≤ 0. For each dual problem a duality theorm is established. Mainly these are generalisations of the results of Tanimoto [14] for minimax fractional programming problems. It is noteworthy here that these problems are intimately related to a class of nondifferentiable fractional programming problems.

A multiobjective minimax programming method and its application of optimal design.

A practical approach to nonlinear multiobjective programming problems using penalty functions and the complex search (a derivative free method) was recently proposed by some of the authors. Here, this approach is applied to solving multiobjective minimax programming problems which are modified to multiobjective programming ones by the finite points approximation procedure. Then, a cam design problem is formulated and solved.

Minimax program control of the identification process in nonlinear multistage systems

Minimax program control of the identification process in nonlinear multistage systems

Non-linear programming using least pth optimization with extrapolation†

We present a general approach for solving minimax and non-linear programming problems through a sequence of least pth approximations with extrapolation. Several numerical examples illustrate the effectiveness of the present approach. A comparison with the woll-known SUMT method of Fiaeco and McCormick is made under the same conditions and employing Fletcher's quasi.Newton programme.