Inverse Problems in Multiobjective Dynamic Optimization

Abstract

One of the “practical” problems of control theory motivated primarily by environmental studies consists, loosely speaking, in the following.

$$ \mathop x\limits^. = f(t,x,\omega ),\tau \leqslant t \leqslant \theta $$

((1.1))

with “input variables” x (τ) = x ⁰; ω(•) = ω(θ + σ), τ - θ ≤ σ ≤ 0. These are restricted by inequalities

$$ {h_j}({x^0}) \leqslant {\mu _{j,}}j = 1,...,p $$

((1.2))

$$ {g_s}(\omega ( \bullet )) \leqslant {\beta _s},s = 1,...,q $$

((1.3))

. Also given are the constraints on system trajectories — the “outputs” x(•) = x(θ + σ), τ - θ ≤ σ ≤ 0, i.e.

$$ {\varphi _i}(x( \bullet )) \leqslant {\upsilon _i},i = 1,...,k $$

((1.4))

.